I was doing my trigonometry homework when he told me.
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Yes, I just call it "trig" because I always misspell trigonometry.
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Symbolab can understand and solve algebra, trigonometry, calculus and matrix problems.
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Dr. Wildberger, down the hall from Dr. Mansfield, had a decade earlier proposed teaching trigonometry in terms of ratios rather than angles, and the two wondered that Babylonians took a similar angle-less approach to trigonometry.
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They can help with a lot more than college admissions and trigonometry.
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An art student isn't going to use Biology and Trigonometry in life.
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"This is a whole different way of looking at trigonometry," Mansfield told Science.
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The drudgery of reviewing a year's worth of earth sciences and trigonometry notes.
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Periodic functions are repeating patterns like the undulations of a sine wave in trigonometry.
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In a typical public school curriculum, children are taught geometry, trigonometry, fractions, decimals and algebra.
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The app supports everything from basic arithmetic to more advanced levels of math like trigonometry.
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Half of the relic is missing — the half researchers speculate has the solutions to the trigonometry problems and would help determine if this tablet isn't just a list of Pythagorean triangles, but an actual tool that uses a novel kind of trigonometry to calculate them.
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Of course, if you're a trigonometry nerd, any time of year is good for finding tangents.
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Does she sit at school conferences and talk to their math teacher about trigonometry, or bondage?
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Stacy said her trigonometry textbook this year was so dilapidated, the entire first chapter was gone.
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I may not be able to help with trigonometry, but I can show her these things.
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At 24, having mastered neither algebra nor trigonometry, she begged to throw herself into differential calculus.
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Although she declined interviews, she wrote on Twitter that the trigonometry interpretation ignores the historical context.
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With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own.
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Sara survived the shooting hiding in a closet, "face to face" with students in her trigonometry class.
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To see why this is the case, first consider the Greek trigonometry we are familiar with today.
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While her classmates were studying trigonometry, she knocked on doors of local recording studios and created demos.
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Trigonometry is explained in the context of a sniper working out the range to his human target.
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Back in high school, I was a whiz at geometry, but then stumbled badly in chemistry and trigonometry.
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With two years left on his contract, Hornacek ought to look ahead and leave trigonometry in the past.
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He was sitting in trigonometry class and had an overwhelming feeling that what he was learning wasn't serving him.
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How it works: Modern trigonometry is based on approximations, in part because our mathematics is a base-10 system.
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That gives the relative distances of the satellites, from which your position can be found using old-fashioned trigonometry.
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HBO Max will also get a number of newer shows, like Ghosts, Home, Pure, Stath Lets Flats, and Trigonometry.
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And it rekindles a crazy sense of wonder at, among other things, what one can do practically with trigonometry.
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Why it matters: The tablet, which predates Greek trigonometry by about 103 years, shows a radically different approach to math.
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It is absurd that high school students are taught trigonometry but not statistics, and physical science but not social science.
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When trigonometry sucks, the soccer season looks bleak, or first dates are hell, bath bombs act as a makeshift spa day.
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You could call this statement an axiom: For many young people, algebra, geometry and trigonometry do not add up to laughs.
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I've also always had an interest in math and that's really come in handy with these recent experiments in waves and trigonometry.
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This discovery shows that the ancient Babylonians—and not the Greeks—were the first to study trigonometry, the mathematical study of triangles.
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They include a count from one to five, mathematical operations like addition and multiplication, simple trigonometry and a description of electromagnetic waves.
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It features a super-cute, blue, g-shaped teacher explaining trigonometry, the planets, the water cycle, and more to her rapt students.
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Those who are "working the angles" could either be scammers (try abbreviating that) or they could be people who are studying TRIGonometry.
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And as noted, it's also rewriting history; Greek astronomer Hipparchus, who lived around 120 BC, is normally considered the founding father of trigonometry.
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But these pre-Greek societies lacked the concept of an angle measure, so they were unable to study trigonometry proper until Hipparchus' breakthrough.
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A little over 2,000 years ago, the Greek mathematician Hipparchus of Nicaea created a table that formalized a branch of mathematics called trigonometry.
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Once she had mastered English, Sultana says, she tackled algebra, then geometry and trigonometry, and finally calculus BC. She rises about 5 a.m.
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I'm one of the many who harbor some math doubts, and whether it is trigonometry or number theory, I'll feel a touch of fear.
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Click here to view original GIFHave you ever felt like you deserved the Nobel Prize in trigonometry after successfully parallel parking your compact car?
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Additionally, the drawing's top-down view exposes a rigorous symmetrical trigonometry that can sometimes get lost in the three-dimension volumes of his work.
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Indeed, the director, Jack Fessenden, had to juggle "trigonometry homework or my 'Canterbury Tales' reading" with his moviemaking responsibilities, he says in his production notes.
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Nicole Baltzer, 18, said she was in trigonometry class about 10 minutes before the end of the school day when the fire alarm went off.
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This suggests that Plimpton 322 describes the shapes of right-angle triangles using a novel form of trigonometry based on ratios, rather than angles or circles.
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The perimeter of these 21846n-gons can be obtained from regular polygon trigonometry and we can then use small angle approximation to find the limit, 23π.
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Just for reference, when I was 17, I was busy crying over the complexities of trigonometry and was not being published in The New York Times.
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In 21 Regiomontanus (Johannes Müller), systematizer of trigonometry, published more complete tables as part of his launch of what was essentially the first-ever scientific publishing company.
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After seven years in prison, during which he studied algebra, trigonometry, geometry, and calculus, he wrote to Su asking for advice on how to continue his work.
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How is it possible that a student who can ace his trigonometry tests and get an A+ in English can't apply those same skills to the SAT?
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They competed to see who was best at using a slide rule, the wood and plastic device that helped with multiplication, division, trigonometry and other mathematical calculations.
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You might have to learn trigonometry against your will, but you can at least eat cheese sandwiches and terrible chicken nuggets to your heart's content while doing so.
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When Richardson wouldn't give him her number, she says Moore called her high school, where the principal pulled her out of trigonometry class to answer his phone call.
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Two Australian mathematicians assert that an ancient clay tablet was a tool for working out trigonometry problems, possibly adding to the many techniques that Babylonian mathematicians had mastered.
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If Apple products are so self explanatory your grandparents can use them, this Google product is so counterintuitive that figuring out the nuances feels like solving a trigonometry problem.
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It was very hard for me to understand because it was geometry and trigonometry and angles and all that stuff, and the way I was taught was very different.
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CreditCreditMary Inhea Kang for The New York Times Mention the word "math" and visions of high school arithmetic, thorny trigonometry and those prickly calculus derivatives often come to mind.
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But school was a different story, and Parker says he was "not an enthusiastic student" -- at least until high school, when he was introduced to algebra, Euclidean geometry and trigonometry.
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Anytime I struggled to understand something in algebra or trigonometry, or anytime I had to work through a tough concept in physics, I figured it was an innate lack of ability.
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But according to new research from the University of New South Wales, the Babylonians appear to have formalized the study of angles in trigonometry a full 1,000 years before the Greeks.
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Early astronomy is quite amazing — Hipparchus is possibly best known as "the father of trigonometry," but he also kept a star chart and was the first to document a new star.
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Over the years, researchers have theorized that the tablet was evidence of the use of trigonometry, while others have suggested that the tablet might have been mathematical exercises used by a teacher.
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Let's start off with the graphing calculator your child will likely need for geometry, trigonometry and advanced placement calculus: The TI-84 Plus is running at about $120, according to the index.
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Using trigonometry and shipping containers to estimate oil supply, prognosticating on financial returns by analyzing the number of cars in big box mart parking lots, and even surveying demolished houses after storms.
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But when you arrange it in such a way so that you can use any known ratio of a triangle to find the other sides of a triangle, then it becomes trigonometry.
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She's currently a sophomore there, and taking chemistry, global history, computer science, trigonometry, European literature, and Japanese, where she's written a 12-page picture book in Japanese and is learning how to make sukiyaki.
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As the discipline devoted to studying the relationships between a triangle's angles and sides, trigonometry had been used for hundreds of years by the Egyptians and Babylonians to design pyramids and do rudimentary astronomy.
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Along with these two series, HBO Max will host hundreds of episodes of other BBC series including Top Gear, Luther, The Honorable Woman, and newer series like Pure, Trigonometry, Stath Lets Flats, Home, and Ghosts.
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Wordplay WEDNESDAY PUZZLE — I can honestly say that I got as far in today's theme by Peter A. Collins as I did in my actual high school trigonometry class: Precisely halfway, and then I got confused.
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Adults tend to think of the new year as a fresh start, but for adolescents, it often means a return to certain struggles, whether it's dealing with trigonometry or figuring out how to talk to a crush.
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McLemore is a polymath of extraordinary mathematical and artisanal ability; he has not only constructed this remarkable maze, but also teaches trigonometry to the hired hands on his land, and heals antique clocks that nobody else can repair.
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That did not stop Moore, Richardson explained to the Post: A few days later, she says, she was in trigonometry class at Gadsden High when she was summoned to the principal's office over the intercom in her classroom.
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One of the stronger theories was that it was a teaching aid for checking quadratic problems, but new research conducted by UNSW scientists Daniel Mansfield and Norman Wildberger now confirms the markings on the tablet as a trigonometry table.
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A new interpretation into the nature of an ancient clay tablet known as Plimpton 322 claims that ancient Babylonians might have developed an advanced form of trigonometry — long before Greek mathematicians are commonly believed to have invented the concept.
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Mr. Collins, who is a math teacher by trade (you saw that coming, didn't you?), offers us a set of theme entries that contain the abbreviations for trigonometry functions, like SINe, COSine and TANgent in the shaded/circled squares.
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From when we're just children in pre-school first learning the ropes on hand-eye coordination, to high school students figuring out trigonometry, to masters and doctoral programs honing a chosen craft, teachers are there to guide our way.
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The title translates as "School," and we are indeed in a classroom of sorts, but one in which the subjects are not grammar and trigonometry but how to shoot a handgun and how to construct and detonate a bomb properly.
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On Mansfield's new interpretation, the Plimpton tablet explored trigonometry through the ratios of the sides of a right triangle using the Babylonian base 21 form of mathematics, rather than using angles and the base 260 system we are familiar with today.
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Once the bull's-eye location has been found using the motion tracking system, a connected computer can apply some trigonometry to figure out where the bull's-eye needs to be, and will then send instructions to the motor to move the board there.
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A team of mathematicians studying a famous Babylonian tablet have come to a startling conclusion: the ancient people who created the tablet had an in-depth knowledge of trigonometry, and used a method that is in some ways more accurate than our own.
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Type: Trigonometry Signature move: Law of quadratic reciprocity Pikawack is known to hide in the shadows, seeing by the light of its own generated electricity and waiting to strike unsuspecting victims by rubbing its tiny feet on the carpet and tapping them on the forearm.
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I am sure there's a financial adviser somewhere who could use trigonometry to explain how to whittle a three-car garage out of $20,000 a year, but since I can't afford his services, I'll just be over here in the bottomless-mimosa brunch line.
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You can access a ton of advanced features, like trigonometry calculations, right from your wrist, but the interface never feels cluttered—and it makes good use of the digital crown and voice control if you don't want to stab at the watch screen with your fingers.
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But what made this particular dab on September 2 so special and interesting was that the young woman behind it, Anicca Harriot, a 20-year-old senior majoring in biophysical sciences at Regent University in Virginia Beach, thought it would be fun to calculate and post the precise angle of her dab using trigonometry.
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For all the talk about how Medicare for All is a "pie in the sky" idea, what's left unsaid is that as soon as the wonk trigonometry that undergirds these plans makes contact with the mischiefs of ideology (and the depredations of industry lobbyists), these public option pastries are also launched into the cloud layer.
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Resembling a flash drive, Juul conveys a sense of industry — you're Juuling into your MacBook Air while you are cramming for your test on Theodore Dreiser and thinking about trigonometry — and it is so easy to conceal that, as one mother explained to me, she failed to notice that her daughter was vaping in the back seat of the car as she was driving.
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" One of the things he wanted, it turned out, was to make some of the best club records he's made in years—running the gamut from the claustrophobic techno of "Gameovr," through the the chugging bass and moody vocals of "Out Of Time" and the piercing synths of "Do The Maff," all the way to the anthemic come-to-Jesus breakdowns of "Trigonometry" and the blissful Destiny's Child sample that runs through "Track 10.
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Rational trigonometry is a proposed reformulation of metrical planar and solid geometries (which includes trigonometry) by Canadian mathematician Norman J. Wildberger, currently a professor of mathematics at the University of New South Wales. His ideas are set out in his 2005 book Divine Proportions: Rational Trigonometry to Universal Geometry. According to New Scientist, part of his motivation for an alternative to traditional trigonometry was to avoid some problems that he claims occur when infinite series are used in mathematics. Rational trigonometry avoids direct use of transcendental functions like sine and cosine by substituting their squared equivalents.
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Using trigonometry and the Pythagorean Theorem to construct a regular pentagon.
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Al-Jayyani's The book of unknown arcs of a sphere (a treatise on spherical trigonometry) had a "strong influence on European mathematics". Regiomantus' On Triangles (c. 1463) certainly took his material on spherical trigonometry (without acknowledgment) from Arab sources.
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Scientific fields that make use of trigonometry include: :acoustics, architecture, astronomy, cartography, civil engineering, geophysics, crystallography, electrical engineering, electronics, land surveying and geodesy, many physical sciences, mechanical engineering, machining, medical imaging, number theory, oceanography, optics, pharmacology, probability theory, seismology, statistics, and visual perception That these fields involve trigonometry does not mean knowledge of trigonometry is needed in order to learn anything about them. It does mean that some things in these fields cannot be understood without trigonometry. For example, a professor of music may perhaps know nothing of mathematics, but would probably know that Pythagoras was the earliest known contributor to the mathematical theory of music. In some of the fields of endeavor listed above it is easy to imagine how trigonometry could be used.
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Spherical trigonometry is the branch of spherical geometry that deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam. The subject came to fruition in Early Modern times with important developments by John Napier, Delambre and others, and attained an essentially complete form by the end of the nineteenth century with the publication of Todhunter's textbook Spherical trigonometry for the use of colleges and Schools.
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Figure 1 – A triangle. The angles α, β, and γ are respectively opposite the sides a, b, and c. In trigonometry, Mollweide's formula, sometimes referred to in older texts as Mollweide's equations,Ernest Julius Wilczynski, Plane Trigonometry and Applications, Allyn and Bacon, 1914, page 102 named after Karl Mollweide, is a set of two relationships between sides and angles in a triangle.Michael Sullivan, Trigonometry, Dellen Publishing Company, 1988, page 243.
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His second book, Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, concerns spherical trigonometry.Funk, Martin (2013), Review of Heavenly Mathematics, . He teaches courses on the history of mathematics and trigonometry at MathPath, specifically Heavenly Mathematics and Spherical Trigonometry. He is also well known for the glensheep (as well as to a lesser extent the glenelephant, and to even lesser extent the glenturtle), a two- dimensional animal he coined at MathPath.
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Nevertheless, the hyperbolic angle plays a role when the theorem of Saint-Vincent is advanced with squeeze mapping. Circular trigonometry was extended to the hyperbola by Augustus De Morgan in his textbook Trigonometry and Double Algebra.Augustus De Morgan (1849) Trigonometry and Double Algebra, Chapter VI: "On the connection of common and hyperbolic trigonometry" In 1878 W.K. Clifford used the hyperbolic angle to parametrize a unit hyperbola, describing it as "quasi-harmonic motion". In 1894 Alexander Macfarlane circulated his essay "The Imaginary of Algebra", which used hyperbolic angles to generate hyperbolic versors, in his book Papers on Space Analysis.
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Applying trigonometry (angular diameter), this is equivalent to an apparent 4.96° angle in the sky.
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Sextants are used to measure the angle of the sun or stars with respect to the horizon. Using trigonometry and a marine chronometer, the position of the ship can be determined from such measurements. Historically, trigonometry has been used for locating latitudes and longitudes of sailing vessels, plotting courses, and calculating distances during navigation. Trigonometry is still used in navigation through such means as the Global Positioning System and artificial intelligence for autonomous vehicles.
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The optional modules are Geometry and Trigonometry, Graphs and Relations, Networks and Decision Mathematics, or Matrices.
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If the curvature of the Earth must be allowed for, then spherical trigonometry must be used.
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Abu Nasri Mansur ibn Ali ibn Iraq (; c. 960 – 1036) was a Persian Muslim mathematician and astronomer. He is well known for his work with the spherical sine law.Also the 'sine law' (of geometry and trigonometry, applicable to spherical trigonometry) is attributed, among others, to Alkhujandi.
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178 (Addison Wesley, 2002).Beckenbach, Edwin et al. Modern college algebra and trigonometry, p. 81 (Wadsworth Pub.
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1 . Harwood Publishing, 2007, 131 pages. Menelaus of Alexandria (c. 100 AD) pioneered spherical trigonometry through Menelaus' theorem.
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In Euclidean geometry, angles are used to study polygons and triangles, as well as forming an object of study in their own right. The study of the angles of a triangle or of angles in a unit circle forms the basis of trigonometry.Gelʹfand, Izrailʹ Moiseevič, and Mark Saul. "Trigonometry." 'Trigonometry'.
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Despite the achievements of Shen and Guo's work in trigonometry, another substantial work in Chinese trigonometry would not be published again until 1607, with the dual publication of Euclid's Elements by Chinese official and astronomer Xu Guangqi (1562–1633) and the Italian Jesuit Matteo Ricci (1552–1610).Needham, Volume 3, 110.
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The first trigonometric table was apparently compiled by Hipparchus, who is consequently now known as "the father of trigonometry".
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The problems cover logic, algebra, metaphysics, geometry, trigonometry, geodesy, stereometry, geometry of curves, ballistics, and general and special physics.
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We use these values to estimate the maximum downthrow of the Skinos fault as 1.12 km from basic trigonometry.
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He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. With his solar and lunar theories and his trigonometry, he may have been the first to develop a reliable method to predict solar eclipses. His other reputed achievements include the discovery and measurement of Earth's precession, the compilation of the first comprehensive star catalog of the western world, and possibly the invention of the astrolabe, also of the armillary sphere, which he used during the creation of much of the star catalogue.
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Levi Leonard Conant (March 3, 1857, Littleton, Massachusetts – October 11, 1916, Worcester, Massachusetts) was an American mathematician specializing in trigonometry.
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The trigonometry of a tetrahedron explains the relationships between the lengths and various types of angles of a general tetrahedron.
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In the late 11th century, Omar Khayyám (1048-1131) solved cubic equations using approximate numerical solutions found by interpolation in trigonometric tables. In the 13th century, Nasīr al-Dīn al- Tūsī was the first to treat trigonometry as a mathematical discipline independent from astronomy, and he developed spherical trigonometry into its present form. He listed the six distinct cases of a right-angled triangle in spherical trigonometry, and in his On the Sector Figure, he stated the law of sines for plane and spherical triangles, discovered the law of tangents for spherical triangles, and provided proofs for both these laws. Nasir al-Din al- Tusi has been described as the creator of trigonometry as a mathematical discipline in its own right.
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During the Middle Ages, the study of trigonometry continued in Islamic mathematics, by mathematicians such as Al-Khwarizmi and Abu al-Wafa. It became an independent discipline in the Islamic world, where all six trigonometric functions were known. Translations of Arabic and Greek texts led to trigonometry being adopted as a subject in the Latin West beginning in the Renaissance with Regiomontanus. The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics (Isaac Newton and James Stirling) and reaching its modern form with Leonhard Euler (1748).
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Whereas the Mathematics 1 test covers Algebra II and basic trigonometry, a pre-calculus class is good preparation for Mathematics 2.
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In trigonometry, it is common to use mnemonics to help remember trigonometric identities and the relationships between the various trigonometric functions.
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Global History 1, English 9, 10, 11; Earth Science; Biology; Chemistry; Physics; Integrated Algebra; Geometry; Algebra 2/Trigonometry; and Pre-Calculus.
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His calendar would be used for the next 363 years, the longest period during which a calendar would be used in Chinese history.Asiapac Editorial (2004), 132 He also used mathematical functions in his work relating to spherical trigonometry,Needham, Volume 3, 109.Ho, 105. building upon the knowledge of Shen Kuo's (1031–1095) earlier work in trigonometry.
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Needham, Volume 3, 110. It is debated amongst scholars whether or not his work in trigonometry was based entirely on the work of Shen, or whether it was partially influenced by Islamic mathematics which was largely accepted at Kublai's court. Sal Restivo asserts that Guo Shoujing's work in trigonometry was directly influenced by Shen's work.Restivo, 32.
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Muhyi al-Din is most known for his works in trigonometry, Book on the theorem of Menelaus, Treatise on the calculation of sines. He is also known for his commentaries on classic Greek mathematical works, in particular, his commentary on Book XV of Elements about measurements of the regular polyhedra. His writings on trigonometry "contain certain original elements".
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In mathematics education, precalculus is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework.Cangelosi, J. S. . Teaching mathematics in secondary and middle school, an interactive approach.
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Nevertheless, in the centuries that followed significant advances were made in applied mathematics, most notably trigonometry, largely to address the needs of astronomers. Hipparchus of Nicaea (c. 190–120 BC) is considered the founder of trigonometry for compiling the first known trigonometric table, and to him is also due the systematic use of the 360 degree circle.
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Math Department The Hallahan math department provides 3 different levels of coursework. This includes College Prep., Honors and A.P. The Course Offerings are as follows: College Prep: Algebra I, Geometry and Algebra II, students who opt to take math in their Senior year will have the option of Pre- Calculus/Trigonometry or Algebra III/ Trigonometry Honors: Honors Algebra I, Honors Geometry, Honors Algebra II, students who opt to take math in their senior year will have the option of Pre-Calculus/ Trigonometry or Algebra III/ Trigonometry Advanced Placement: A.P. Calculus, in order to be registered for this course you must have successfully passed the Pre-Calc course and have your Math teachers recommendation. Science Department Hallahan has earned a lot of credit for its well developed Science program.
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The Siddhānta Shiromani (written in 1150) demonstrates Bhaskara's knowledge of trigonometry, including the sine table and relationships between different trigonometric functions. He also developed spherical trigonometry, along with other interesting trigonometrical results. In particular Bhaskara seemed more interested in trigonometry for its own sake than his predecessors who saw it only as a tool for calculation. Among the many interesting results given by Bhaskara, results found in his works include computation of sines of angles of 18 and 36 degrees, and the now well known formulae for \sin\left(a + b\right) and \sin\left(a - b\right) .
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Roy's use of scientific advancements and accurate mathematical formulas paved the way for modern geodesic surveying. His tenure and his work are the dividing line between older, approximate mappings and newer, highly accurate ones in Britain. He is cited repeatedly in early nineteenth century mathematics textbooks for his use of spherical trigonometry in surveying. A Course of Mathematics, Spherical Trigonometry, for example.
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It became very popular and was republished 14 times (last edition in 1938). In 1919–1921, he published other textbooks on plane trigonometry, history of math, algebra, logarithm. He also wrote a textbook on physics (1922) and two textbooks on learning to write (1907 and 1921). The textbook on plane trigonometry was reworked and republished by his son in 1938.
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From Byzantium to Italy. Greek Studies in the Italian Renaissance, London. Trigonometry was still so little known in 16th- century northern Europe that Nicolaus Copernicus devoted two chapters of De revolutionibus orbium coelestium to explain its basic concepts. Driven by the demands of navigation and the growing need for accurate maps of large geographic areas, trigonometry grew into a major branch of mathematics.
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Gyrotrigonometry is the use of gyroconcepts to study hyperbolic triangles. Hyperbolic trigonometry as usually studied uses the hyperbolic functions cosh, sinh etc., and this contrasts with spherical trigonometry which uses the Euclidean trigonometric functions cos, sin, but with spherical triangle identities instead of ordinary plane triangle identities. Gyrotrigonometry takes the approach of using the ordinary trigonometric functions but in conjunction with gyrotriangle identities.
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Sal Restivo writes that Shen's work in the lengths of arcs of circles provided the basis for spherical trigonometry developed in the 13th century by the mathematician and astronomer Guo Shoujing (1231-1316).Restivo, 32. As the historians L. Gauchet and Joseph Needham state, Guo Shoujing used spherical trigonometry in his calculations to improve the calendar system and Chinese astronomy.Gauchet, 151.
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The dual enrollment courses currently offered are: Chemistry 101, English 101, English 102, American History 201, Spanish 101, College Algebra 1021, and Trigonometry 1022.
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Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are performed in a two-dimensional space, or, in other words, in the plane.
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If the angles are given as slopes, then no trigonometry or square roots are necessary: simply check that y/x is between the desired slopes.
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Other translations Clark was involved with include "First Lessons in Astronomy", text-books on geometry, trigonometry, and surveying, and the children's book The Little Philosopher.
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All of the mathematical learning of the Islamic world during the medieval period was available and advanced by Timbuktu scholars: arithmetic, algebra, geometry, and trigonometry.
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Nasīr al-Dīn al- Tūsī was the first to treat trigonometry as a mathematical discipline independent from astronomy, and he developed spherical trigonometry into its present form. He listed the six distinct cases of a right-angled triangle in spherical trigonometry, and in his On the Sector Figure, he stated the law of sines for plane and spherical triangles, discovered the law of tangents for spherical triangles, and provided proofs for both these laws. Knowledge of trigonometric functions and methods reached Western Europe via Latin translations of Ptolemy's Greek Almagest as well as the works of Persian and Arab astronomers such as Al Battani and Nasir al-Din al-Tusi.
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The presence of a right angle in a triangle is the defining factor for right triangles,Wentworth p. 40 making the right angle basic to trigonometry.
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The school taught German language, Hebrew language, Hebrew Bible, Talmud, algebra, geometry, trigonometry, physics, astronomy, world history, Russian history, Russian language, geography, and handwriting and drawing.
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The College Board's recommended preparation is a one-year college preparatory course in physics, a one-year course in algebra and trigonometry, and experience in the laboratory.
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Tupikova et al. (2014), following “the application of spherical trigonometry for the recalculation of Ptolemy’s coordinates”, concluded that it “can with great probability be identified as Tashkurgan”.
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The intermediate curriculum included courses in geography, history, geology, and algebra. The collegiate curriculum included courses in geometry, trigonometry, botany, chemistry, and classical studies, namely Latin and Greek.
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Soon they find out that Teach is after Daniel alone; however, with the application of trigonometry, the ship is able to escape the bay and the pirate band.
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Under the name Linda Gilbert, she became the author of "more than 37 mathematics textbooks" including Elements of Modern Algebra, College Algebra, College Trigonometry, Precalculus, and Matrix Theory.
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For example, in navigation and land surveying, the occasions for the use of trigonometry are in at least some cases simple enough that they can be described in a beginning trigonometry textbook. In the case of music theory, the application of trigonometry is related to work begun by Pythagoras, who observed that the sounds made by plucking two strings of different lengths are consonant if both lengths are small integer multiples of a common length. The resemblance between the shape of a vibrating string and the graph of the sine function is no mere coincidence. In oceanography, the resemblance between the shapes of some waves and the graph of the sine function is also not coincidental.
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Trigonometry is known for its many identities, which are equations used for rewriting trigonometrical expressions to solve equations, to find a more useful expression, or to discover new relationships.
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A software calculator allows the user to perform simple mathematical operations, like addition, multiplication, exponentiation and trigonometry. Data input is typically manual, and the output is a text label.
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A map generated using the Craig retroazimuthal projection centered on Mecca. Unlike most map projections, it preserves the direction from any other point on the map to the center. Spherical trigonometry provides the shortest path from any point on earth to the Kaaba, even though the indicated direction might seem counterintuitive when imagined on a flat world map. For example, the qibla from Alaska obtained through spherical trigonometry is almost due north.
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The College Board suggests as preparation for the test four years of mathematics, including two years of algebra, one year of geometry, and one year of either precalculus or trigonometry. While the precalculus or trigonometry course may be good preparation for this test, students may need to buy extra resource materials if they want to score beyond a 700. The exam covers several years of mathematics, and students are expected to work quickly and efficiently.
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This is the third and last course of the new three-year curriculum. It replaced the elements of "Math B" not covered in geometry. This course covers concepts of advanced algebra, and as well prepares students for pre-calculus and calculus. In 2016, the Board of Regents removed some of the trigonometry concepts and lessons from the course, and the Regents exam has been renamed from "Algebra 2/Trigonometry" to "Algebra II".
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Trigonometry is the second album by Saafir, under the alias Mr. No No. It was released on January 20, 1998, on Wrap Records and featured production from Saafir and Shock G.
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Trigonometry is useful in many physical sciences, including acoustics, and optics. In these areas, they are used to describe sound and light waves, and to solve boundary- and transmission-related problems.
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June 2008 was the last administration of this exam. For the second half of the year, students would begin Math B. They covered logic, geometric figures, and an introduction to trigonometry.
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The Junior Section consists of 5 multiple-choice questions, each with five options, and 20 open-ended questions, geared towards Lower Secondary students. Topics tested include number theory, pattern recognition, geometry, simple combinatorics and algebra. Noticeably, trigonometry is not included as a test subject, because trigonometry is not included in the Lower Secondary mathematical curriculum. Beginning in 2006, a second round was added, based on the Senior Invitational Round, and consists of a 5-question, 3hour long essay/proof.
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Glen Robert Van Brummelen (born 1965) is a Canadian historian of mathematics specializing in historical applications of mathematics to astronomy. In his words, he is the “best trigonometry historian, and the worst trigonometry historian” (as he is the only one). He is president of the Canadian Society for History and Philosophy of Mathematics,CSHPM Council, retrieved 2013-12-26. and was a co-editor of Mathematics and the Historian's Craft: The Kenneth O. May Lectures (Springer, 2005).
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An 8K version added string variables and trigonometry functions. Both the 4K and 8K versions were sold by SWTPC. In January, 1978, Uiterwyk sold the rights of the source code to Motorola.
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Since , an analog to de Moivre's formula also applies to the hyperbolic trigonometry. For all , :(\cosh x + \sinh x)^n = \cosh nx + \sinh nx. Also, if , then one value of will be .
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More than 11,000 of the posts were erected across Britain to enable surveyors to create maps accurate to within metres by measuring angles and using trigonometry to calculate distances between the pillars.
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The embryonic state of trigonometry in China slowly began to change and advance during the Song Dynasty (960–1279), where Chinese mathematicians began to express greater emphasis for the need of spherical trigonometry in calendarical science and astronomical calculations. The polymath Chinese scientist, mathematician and official Shen Kuo (1031–1095) used trigonometric functions to solve mathematical problems of chords and arcs. Victor J. Katz writes that in Shen's formula "technique of intersecting circles", he created an approximation of the arc of a circle s by s = c + 2v2/d, where d is the diameter, v is the versine, c is the length of the chord c subtending the arc.Katz, 308. Sal Restivo writes that Shen's work in the lengths of arcs of circles provided the basis for spherical trigonometry developed in the 13th century by the mathematician and astronomer Guo Shoujing (1231–1316).. As the historians L. Gauchet and Joseph Needham state, Guo Shoujing used spherical trigonometry in his calculations to improve the calendar system and Chinese astronomy.
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An important work in trigonometry in China would not be printed again until the collaborative efforts of Xu Guangqi and his Italian Jesuit associate Matteo Ricci in 1607, during the late Ming Dynasty.
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The Britannica Guide to Algebra and Trigonometry by William L. Hosch p. 105 The Rashtrakuta rulers also patronised men of letters, who wrote in a variety of languages from Sanskrit to the Apabhraṃśas.
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The cosine rule is the fundamental identity of spherical trigonometry: all other identities, including the sine rule, may be derived from the cosine rule: :\cos a= \cos b \cos c + \sin b \sin c \cos A, \\! :\cos b= \cos c \cos a + \sin c \sin a \cos B, \\! :\cos c= \cos a \cos b + \sin a \sin b \cos C, \\! These identities approximate the cosine rule of plane trigonometry if the sides are much smaller than the radius of the sphere.
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He remained in correspondence with Lichtenberg throughout his career. Klügel made an exceptional contribution to trigonometry, unifying formulae and introducing the concept of trigonometric function, (including coining the term) in his Analytische Trigonometrie 1770.
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Boiling Point Apparatus or Hypsometer. Image from "Maps and survey" (1913) by Hinks, Arthur R. A hypsometer is an instrument for measuring height or elevation. Two different principles may be used: trigonometry and atmospheric pressure.
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The earliest mathematical work of antiquity to come down to our time is On the rotating sphere (Περὶ κινουμένης σφαίρας, Peri kinoumenes sphairas) by Autolycus of Pitane, who lived at the end of the fourth century BC. Spherical trigonometry was studied by early Greek mathematicians such as Theodosius of Bithynia, a Greek astronomer and mathematician who wrote the Sphaerics, a book on the geometry of the sphere, and Menelaus of Alexandria, who wrote a book on spherical trigonometry called Sphaerica and developed Menelaus' theorem.
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This is also referred to as the "order of symmetry." Angles are commonly measured in degrees, radians, gons (gradians) and turns, sometimes also in angular mils and binary radians. They are central to polar coordinates and trigonometry.
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Principios Mathematicos José Anastácio da Cunha (1744 – January 1, 1787) was a Portuguese mathematician. He is best known for his work on the theory of equations, algebraic analysis, plain and spherical trigonometry, analytical geometry, and differential calculus.
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Khojandi stated a special case of Fermat's last theorem for n = 3, but his attempted proof of the theorem was incorrect. The spherical law of sines may have also been discovered by Khujandi, but it is uncertain whether he discovered it first, or whether Abu Nasr Mansur, Abul Wafa or Nasir al-Din al-Tusi discovered it first.Also the 'sine law' (of geometry and trigonometry, applicable to spherical trigonometry) is attributed, among others, to Alkhujandi. (The three others are Abul Wafa Bozjani, Nasiruddin Tusi and Abu Nasr Mansur).
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Ordinary trigonometry studies triangles in the Euclidean plane R2. There are a number of ways of defining the ordinary Euclidean geometric trigonometric functions on real numbers: right-angled triangle definitions, unit-circle definitions, series definitions, definitions via differential equations, definitions using functional equations. Generalizations of trigonometric functions are often developed by starting with one of the above methods and adapting it to a situation other than the real numbers of Euclidean geometry. Generally, trigonometry can be the study of triples of points in any kind of geometry or space.
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In 1807 he was invited to join the University of Kazan by the founder Stepan Jakowlewitsch Rumowski (1734–1812), and went there in 1808 where he was appointed to the chair of Mathematics. During his twelve years tenure he lectured on the History of Mathematics, Higher Arithmetic, Differential and Integral Calculus, Analytical Geometry and Trigonometry, Spherical Trigonometry, Analytical Mechanics and Astronomy. During this time he taught Nikolai Ivanovich Lobachevsky. In 1821 he moved to the University of Dorpat, now Tartu, Estonia, where he founded the Centre for Differential geometry.
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Rational trigonometry makes nearly all problems solvable with only addition, subtraction, multiplication or division, as trigonometric functions (of angle) are purposefully avoided in favour of trigonometric ratios in quadratic form. At most, therefore, results required as distance (or angle) can be approximated from an exact-valued rational equivalent of quadrance (or spread) after these simpler operations have been carried out. To make use of this advantage however, each problem must either be given, or set up, in terms of prior quadrances and spreads, which entails additional work.Olga Kosheleva (2008), "Rational trigonometry: computational viewpoint", Geombinatorics, Vol.
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Hipparchus, credited with compiling the first trigonometric table, has been described as "the father of trigonometry". Sumerian astronomers studied angle measure, using a division of circles into 360 degrees.Aaboe, Asger (2001). Episodes from the Early History of Astronomy.
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Johann Anton Edler von Braunmühl (22 December 1853 Tiflis – 7 March 1908 München) was a German historian of mathematics and mathematician who worked on synthetic geometry and trigonometry. In 1879 he married Franziska Stölzl; they had two daughters.
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Approximately 10-14% of questions focus on Numbers and Operations, 38-42% focus on Algebra and functions, 38-42% focus on Geometry (including Euclidean, coordinate, three-dimensional, and trigonometry), and 6-10% focus on Data analysis, Statistics, and probability.
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For centuries, spherical trigonometry has been used for locating solar, lunar, and stellar positions, predicting eclipses, and describing the orbits of the planets.Neugebauer, Otto. "Mathematical methods in ancient astronomy." Bulletin of the American Mathematical Society 54.11 (1948): 1013-1041.
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Mathematics courses include Economics; Functions, Statistics and Trigonometry; Statistics; and Calculus. Science classes include Integrated Science, Biology, Chemistry, Physics, and Environmental Applications as well as basic and AP computer programming. Social studies classes include World History, Psychology, and Sociology.
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Scholars agree that the retreat house at Poplar Forest is an excellent example of octagonal symmetry; Jefferson's design for the building reflects a consistent geometric approach likely made possible by his well-known proficiency in algebra, geometry, trigonometry and Newtonian calculus.
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Fazlıoğlu characterised his works by their "high level of geometry, trigonometry (especially spherical trigonometry), and numerical analysis", and their style of writing that is easy to understand and apply. Among his earliest works was a book of mathematical geography titled I'lam al-'ibad fi a'lam al-bilad ("Notices on the Distances of Cities of the World"), written in Ottoman Turkish. It includes a list of 100 major cities from Morocco to China, and the coordinates, distance from Istanbul, the qibla (direction that indicates Mecca) of each city. It was written in 1525 and was dedicated to Suleiman the Magnificent.
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Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.R. Nagel (ed.), Encyclopedia of Science, 2nd Ed., The Gale Group (2002) The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation.
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He was among the founders Recreații Științifice, the country's first scientific periodical addressed to young people and to a generalist audience. Briefly involved in politics, he was vice president of the Romanian Senate during the fourth conservative government of Lascăr Catargiu (1892–1896). Tereza Culianu-Petrescu, "O biografie", Observator Cultural, nr. 87, October 2001 Culianu's textbooks include an 1870 one on differential and integral calculus, the first published Romanian- language course on mathematical analysis; and ones on elementary algebra (1872), applied geometry (1874), plane and spherical trigonometry (1875), cosmography (1893), plane trigonometry (1894) and high-school cosmography (1895).
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His discoveries opened the doors to what has today come to be known as mathematical analysis. Mādhavan made contributions to the study of infinite series, calculus, trigonometry, geometry, and algebra in his works Mahajyānayana prakāra ("Methods for the great sines") and Venuaroham.
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Among his works on astronomy, only the first seven treatises of his Almagest (Kitāb al-Majisṭī) are now extant. The work covers numerous topics in the fields of plane and spherical trigonometry, planetary theory, and solutions to determine the direction of Qibla.
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In September 1885, Lt. Paddock earned a spot at the prestigious Cavalry and Infantry School at Fort Leavenworth, Kansas, later renamed the Army Command and General Staff College. For almost two years, Paddock studied subjects such as trigonometry, surveying, military law and topography.
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A right angle is equal to 90 degrees. A line segment (AB) drawn so that it forms right angles with a line (CD). In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn.Wentworth p.
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Domain Decomposition, Operator Trigonometry, Robin Condition, Contemporary Mathematics, 218. 432-437. He is known especially for the Robin boundary condition. The French Academy of Sciences awarded him the Prix Francœur for 1893 and again for 1897 and the Prix Poncelet for 1895.
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Berlin: Springer-Verlag. He further produced a set of astronomical tables and wrote about calendaric works, as well as the astrolabe and the sundial. He also made important contributions to trigonometry, producing accurate sine and cosine tables, and the first table of tangents.
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Fundamentum Astronomiae is a historic manuscript presented by Jost Bürgi to Emperor Rudolf II in 1592. It describes Bürgi's trigonometry based algorithms called Kunstweg which can be used to calculate sines at arbitrary precision.Staudacher, S., 2014. Jost Bürgi, Kepler und der Kaiser.
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Linear algebra, analytic geometry, plane and spherical trigonometry, and statistics in research are taken during sophomore. Differential and integral calculus and Differential equations, and Advanced Statistics are learned by juniors. Seniors tackle advanced topics in mathematics. Students takes a four-year English course.
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Spherical triangle In spherical trigonometry, the half side formula relates the angles and lengths of the sides of spherical triangles, which are triangles drawn on the surface of a sphere and so have curved sides and do not obey the formulas for plane triangles.
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Courses offered include: AP Literature and Composition, AP Language and Composition, AP US Government, and AP Government and Politics. Honors classes offered include Honors Algebra 1, Honors Geometry, Honors Advanced Algebra II and Trigonometry, Honors Pre-Calculus, Honors American Literatures, Honors World Literatures, Honors Biology.
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The volume and surface area of a cylinder, cone sphere and torus are calculated using pi. Pi is also used in calculating planetary orbit times, gaussian curves and alternating current. In calculus, there are infinite series that involve pi and pi is used in trigonometry.
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The problems posed are divided into five events - Individual events A, B, C, and D, and the team event. Events A, B, C, and D usually consist of algebra, geometry, trigonometry, and precalculus topics, respectively. The team event is a mix of all four.
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Reservoirs in the form of Hafirs were developed in Kush to store water and boost irrigation.Fritz Hintze, Kush XI; pp.222-224.Bloomeries and blast furnaces were developed during the seventh century BC in Meroe. Kushite sundials applied mathematics in the form of advanced trigonometry.
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This work was printed in Basel by Oswald Schreckenfuchs, including a Latin translation. See Allgemeine Enzyklopädie der Wissenschaften und der Künste, Part 1, Vol. 1, p. 157.Poggendorff’s Handwörterbuch, Volume I, A-L, 1863 Leipzig Other works included papers on astrology, trigonometry, and music.
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Al-Khwārizmī's Zīj al-Sindhind also contained tables for the trigonometric functions of sines and cosine. A related treatise on spherical trigonometry is also attributed to him. Al-Khwārizmī produced accurate sine and cosine tables, and the first table of tangents.Jacques Sesiano, "Islamic mathematics", p.
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The opening pages contain a diagram of Pascal's triangle. The summation of a finite arithmetic series is also covered in the book. Guo Shoujing applied mathematics to the construction of calendars. He was one of the first mathematicians in China to work on spherical trigonometry.
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The spreads of the angles at those points are , and , are the quadrances of the triangle sides opposite , respectively. As in classical trigonometry, if we know three of the six elements , , and these three are not the three , then we can compute the other three.
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Muslim mathematicians introduced Euclidean Geometry, Spherical trigonometry and Arabic numerals in China. Kublai brought siege engineers Ismail and Al al- Din to China, and together they invented the "Muslim trebuchet" (or Huihui Pao), which was utilized by Kublai Khan during the Battle of Xiangyang.
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He was also the first to find the general geometric solution to cubic equations. He was also very influential in calendar reform. In the 13th century, Nasir al-Din Tusi (Nasireddin) made advances in spherical trigonometry. He also wrote influential work on Euclid's parallel postulate.
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In spherical trigonometry and hyperbolic trigonometry, the area of a triangle is proportional to the amount by which its interior angles fail to add up to 180°, or equivalently by the (inverse) amount by which its exterior angles fail to add up to 360°. The area of a spherical triangle is proportional to its excess, by Girard's theorem – the amount by which its interior angles add up to more than 180°, which is equal to the amount by which its exterior angles add up to less than 360°. The area of a hyperbolic triangle, conversely is proportional to its defect, as established by Johann Heinrich Lambert.
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The Book of Unknown Arcs of a Sphere written by the Islamic mathematician Al-Jayyani is considered to be the first treatise on spherical trigonometry. The book contains formulae for right-handed triangles, the general law of sines, and the solution of a spherical triangle by means of the polar triangle.School of Mathematical and Computational Sciences University of St Andrews The book On Triangles by Regiomontanus, written around 1463, is the first pure trigonometrical work in Europe. However, Gerolamo Cardano noted a century later that much of its material on spherical trigonometry was taken from the twelfth-century work of the Andalusi scholar Jabir ibn Aflah.
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Thus, in spherical geometry, angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects; for example, the sum of the interior angles of a triangle exceeds 180 degrees. Spherical geometry is not elliptic geometry, but is rather a subset of elliptic geometry. For example, it shares with that geometry the property that a line has no parallels through a given point. Contrast this with Euclidean geometry, in which a line has one parallel through a given point, and hyperbolic geometry, in which a line has two parallels and an infinite number of ultraparallels through a given point.
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Sutton was born in Hertford, North Carolina. Her parents were Annie McNair Nixon and John Calhoun Nixon, and she had three brothers: John Stuart Nixon, Norris Lee Nixon, and Thomas Rufus Nixon. She gained a B.S. from the North Carolina Agricultural and Technical State University in 1946, and an MA from New York University in 1951. She was awarded the first PhD in mathematics education to an African American at New York University in 1962, for a dissertation titled Concept learning in trigonometry and analytic geometry at the college level: a comparative study of two methods of teaching trigonometry and analytic geometry at the college level.
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Heron reports in his Metrica (about 60 CE) that Archimedes continued the computation in a now lost book, but then attributes an incorrect value to him. Archimedes uses no trigonometry in this computation and the difficulty in applying the method lies in obtaining good approximations for the square roots that are involved. Trigonometry, in the form of a table of chord lengths in a circle, was probably used by Claudius Ptolemy of Alexandria to obtain the value of given in the Almagest (circa 150 CE). Advances in the approximation of (when the methods are known) were made by increasing the number of sides of the polygons used in the computation.
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The older one, at the harbour entrance, dates to the 1880s and is made of boiler plate, the newer one, constructed in 1937, stands atop the hill and is still in use today, though using an automated system rather than a manned operation system. The point has a lookout and picnic area, a grassy area extends mostly over it and a cliff walk is available along the fence built to stop suicides and other dangers. A trigonometry station, though broken, stands at the eastern tip of the point. The point is shaped roughly like a B and has an inwards facing area to the right of the trigonometry station.
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Schilling: Über die geometrische Bedeutung der Formeln der sphärischen Trigonometrie im Falle complexer Argumente (On the geometric meaning of the formulas of spherical trigonometry in the case of complex arguments), Math. Annalen, vol. 39, 1891, p. 598 (same as the article in Nachrichten Göttinger Akad. Wiss.
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Maxime Bôcher (August 28, 1867 – September 12, 1918) was an American mathematician who published about 100 papers on differential equations, series, and algebra. He also wrote elementary texts such as Trigonometry and Analytic Geometry. Bôcher's theorem, Bôcher's equation, and the Bôcher Memorial Prize are named after him.
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Ephraim Chambers Cyclopædia (1728). Table of Trigonometry, 1728 Cyclopædia. Cyclopædia: or, An Universal Dictionary of Arts and Sciences is an encyclopedia prepared by Ephraim Chambers and first published in 1728; Two volumes in folio. six more editions appeared between 1728 and 1751 with a Supplement in 1753.
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Students taking the SAT Subject Test in Physics are prohibited from using any resources during the test, including textbooks, notes, or formula sheets. Although there are mathematics questions including trigonometry, the use of a calculator is not allowed. All scratch work must be done directly in the test booklet.
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Other fields that use trigonometry or trigonometric functions include music theory, geodesy, audio synthesis, architecture, electronics, biology, medical imaging (CT scans and ultrasound), chemistry, number theory (and hence cryptology), seismology, meteorology, oceanography, image compression, phonetics, economics, electrical engineering, mechanical engineering, civil engineering, computer graphics, cartography, crystallography and game development.
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Trigonometry tells you roughly where the mobile transmitter is located. In wireless telephone systems, the phones transmit continually when off-hook, making continual tracking and the collection of many location samples possible. This is one type of location system required by Federal Communications Commission Rules for wireless Enhanced 911.
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"Innis (Empire), p.88. Innis contends that the flexibility of the oral tradition encouraged the introduction of a new medium, mathematics. Thales of Miletus may have discovered trigonometry. He also studied geometry and astronomy, using mathematics as "a means of discarding allegory and myth and advancing universal generalizations.
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Jan Jansz de Jonge Stampioen (1610, Rotterdam - 1653, The Hague) was a Dutch mathematician famous for his published work on spherical trigonometry. In 1638 he moved to The Hague to become tutor of William II, Prince of Orange. In 1644 he was employed to tutor Christiaan Huygens in mathematics.
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Because is closely related to the circle, it is found in many formulae from the fields of geometry and trigonometry, particularly those concerning circles, spheres, or ellipses. Other branches of science, such as statistics, physics, Fourier analysis, and number theory, also include in some of their important formulae.
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In trigonometry, the trigonometric functions, such as \sin, \cos, and \tan, are unary operations. This is because it is possible to provide only one term as input for these functions and retrieve a result. By contrast, binary operations, such as addition, require two different terms to compute a result.
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He received an education for the Royal Navy: including mathematics of trigonometry and geometry, practical navigation including using of nautical instruments, finding latitudes and longitudes and making navigational calculations from observing the sun, moon and tides and the drawing of maps and charts, taking land measurements and sketching landscapes.
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An Investigation of Secondary School Algebra Teachers' Mathematical Knowledge for Teaching Algebraic Equation Solving, p. 56 (ProQuest, 2007): "The quadratic formula is the most general method for solving quadratic equations and is derived from another general method: completing the square."Rockswold, Gary. College algebra and trigonometry and precalculus, p.
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Improvements that were made were generally suggested by others. Outside of Connecticut he was known principally through his textbooks. Rockwood. In 1814, Day published An Introduction to Algebra, which went through many editions. This was followed by works on trigonometry, geometry, and the mathematical principles of navigation and surveying.
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In 1970 Flanders published the first of several useful textbooks for topics commonly taught at college level: with Justin Jesse Price and Robert R. Korfhage a text on Calculus was distributed by Academic Press. With J. J. Price, Flanders also wrote Elementary Functions and Analytic Geometry (1973) and Introductory College Mathematics: with Linear Algebra and Finite Mathematics (1974). With both J.J. Price and R.R. Korfhage, Flanders wrote First Course in Calculus with Analytic Geometry (1974) and Second Course in Calculus (1974). To support the recruitment of students with capacity to follow these courses, some works on precalculus mathematics were written with J.J. Price: Algebra (1975), Trigonometry (1975), Algebra and Trigonometry (1981), Precalculus Mathematics (1981), and College Algebra (1982).
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In order to give students high school credit and Regents credit, Francis Lewis offers numerous classes such as integrated algebra, geometry, trigonometry/algebra II, pre-trigonometry, English, living environment/biology, chemistry, physics, earth science, global history and geography, U.S. History and geography, U.S. government and economics, health, forensic science, sports medicine, literature, music appreciation, art, and graphic design. As physical education classes, Francis Lewis High School offers frisbee, racket sports, soccer, basketball, yoga and dance, walking, weight training and conditioning, and volleyball. The school offers music electives including chorus, concert choir, honors concert band, jazz ensemble, guitar, keyboard, marching band, and string orchestra. Students may take music electives for as long as their high school tenure.
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The mathematics of trigonometry and exponentials are related but not exactly the same; exponential notation emphasizes the whole, whereas and notations emphasize the parts. This can be rhetorically useful to mathematicians and engineers when discussing this function, and further serve as a mnemonic (for ). The notation is convenient for math students whose knowledge of trigonometry and complex numbers permit this notation, but whose conceptual understanding does not yet permit the notation . As students learn concepts that build on prior knowledge, it is important not to force them into levels of math for which they are not yet prepared: the usual proof that requires calculus, which the student may not have studied before encountering the expression .
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In 1809 Woodhouse published a textbook covering planar trigonometry and spherical trigonometry and the next year a historical treatise on the calculus of variations and isoperimetrical problems. He next produced an astronomy; of which the first book (usually bound in two volumes), on practical and descriptive astronomy, was issued in 1812, and the second book, containing an account of the treatment of physical astronomy by Pierre-Simon Laplace and other continental writers, was issued in 1818. He became the Lucasian Professor of Mathematics in 1820, and subsequently the Plumian professor in the university. As Plumian Professor he was responsible for installing and adjusting the transit instruments and clocks at the Cambridge Observatory.
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In 1777, he was made Hofprediger at Königsberg castle church. Schultz’s appointment as professor of mathematics to the government on 11 August 1786 was recommended by the Königsberg senate, at the same time that Kant was serving as rector at Königsberg. As a Professor of mathematics, he had a duty to provide lectures, which he did in arithmetic and geometry in the summer, and trigonometry and astronomy in the winter. Apart from a lecture series in metaphysics during the first half of his second year, and pedagogy that each professor took turns offering, Schultz offered mathematics lectures, focusing on pure and applied mathematics: Arithmetic, Geometry, Trigonometry, Algebra, finite and infinite analysis, Astronomy, Mechanics and Optics.
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Page from The Compendious Book on Calculation by Completion and Balancing by Muhammad ibn Mūsā al-Khwārizmī (c. AD 820) Previous works were later translated and expanded in the medieval Islamic world by Muslim mathematicians of mostly Persian and Arab descent, who enunciated a large number of theorems which freed the subject of trigonometry from dependence upon the complete quadrilateral, as was the case in Hellenistic mathematics due to the application of Menelaus' theorem. According to E. S. Kennedy, it was after this development in Islamic mathematics that "the first real trigonometry emerged, in the sense that only then did the object of study become the spherical or plane triangle, its sides and angles." (cf.
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They are significant in that they contain the first instance of trigonometric relations based on the half-chord, as is the case in modern trigonometry, rather than the full chord, as was the case in Ptolemaic trigonometry. Through a series of translation errors, the words "sine" and "cosine" derive from the Sanskrit "jiya" and "kojiya". sine rule in Yuktibhāṣā Around 500 AD, Aryabhata wrote the Aryabhatiya, a slim volume, written in verse, intended to supplement the rules of calculation used in astronomy and mathematical mensuration, though with no feeling for logic or deductive methodology. Though about half of the entries are wrong, it is in the Aryabhatiya that the decimal place-value system first appears.
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Little is known of his life over the next several years. In 1830 he suffered from smallpox. The following year he attended military college to study arithmetic, algebra, speculative geometry and plane trigonometry. After completing his studies, in October 1831 he was ordered to accompany students to Acapulco for shipboard duty.
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The subject of astronomy came up in their talks and the part the stars play in the determining of correct time. The professors loaned books on mathematics and astronomy to Johnson. He mastered algebra, geometry, trigonometry, and basic astronomy. In 1887 he met a Professor Harrington of Ann Arbor, Michigan.
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If the information in regards to solar positions and site geometry are known, the solar envelope can be directly calculated using trigonometry. The current computer software can be the easiest and fastest way for calculating the solar envelope using the same principle that is being used in the heliodon method.
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In linear algebra, geometry, and trigonometry, the Cayley–Menger determinant is a formula for the content, i.e. the higher-dimensional volume, of a n-dimensional simplex in terms of the squares of all of the distances between pairs of its vertices. The determinant is named after Arthur Cayley and Karl Menger.
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The High School University (HSU) magnet offers a traditional college preparatory curriculum with electives. The Math/Science/Technology (MST) magnet specifically prepares students for college programs in engineering, science and math. Minimal requirements for MST students include courses in algebra, trigonometry, calculus (including mandatory AP Calculus), biology, chemistry and computer programming.
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Dewar is the co-author with Dennis G. Zill of a series of mathematics textbooks on algebra, trigonometry, precalculus, and calculus. With C. Bennett and M. Fisher, she is also the author of The scholarship of teaching and learning: A guide for scientists, engineers, and mathematicians (Oxford University Press, 2018).
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In 1922 he was appointed as a mathematics teacher at the Kashi Vidyapeeth. He worked at the Kashi Vidyapeeth until 1930. After that, he wrote a few books in Sanskrit for high school students on Trigonometry and Algebra. He also edited books on Ellipse and Calculus written by Sudhakar Dwivedi.
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Since squaring is a monotonic function of non-negative values, minimizing squared distance is equivalent to minimizing the Euclidean distance, so the optimization problem is equivalent in terms of either, but easier to solve using squared distance. In the terminology of rational trigonometry, squared Euclidean distance is also called quadrance.
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He was one of those who initiated mathematics in the Philippines. He contributed extensively to the progression of mathematics and the mathematics learning in the country. He has made fundamental studies such as on stratifiable congruences and geometric inequalities. Dr. Favila has also co- authored textbooks in algebra and trigonometry.
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The main offerings of the mathematics department are those required by New York for graduation. Courses in introductory geometry, trigonometry, and precalculus are offered, in addition to courses on problem solving, SAT preparation, and life math. For the students interested in advanced mathematics, course offerings include honors precalculus, AP Calculus, and AP Statistics.
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A theodolite is used to measure the angle between indicators on the two ends of the subtense bar. The distance from the telescope to the subtense bar is the height of an isosceles triangle formed with the theodolite at the upper vertex and the subtense bar length at its base, determined by trigonometry.
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Abu Ali al-Hassan al-Marrakushi (fl. 1281/2) was a Moroccan astronomer and mathematician. He was especially important in the field of trigonometry. He described more than 240 stars. He is the author of a very large compendium on spherical astronomy and astronomical instruments (sundials, astrolabes) entitled ami’ al-mabadi' wa'l-ghayat.
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In August, 1884, her father was ruined by a fire, in which he lost US$100,000. Wilson decided to support herself and became a teacher at Cynthiana high school. She divided the teaching of the four-year course with the principal. She taught French, German, Latin, arithmetic, algebra, geometry, trigonometry, English and history.
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That year Ramanujan entered Town Higher Secondary School, where he encountered formal mathematics for the first time. A child prodigy by age 11, he had exhausted the mathematical knowledge of two college students who were lodgers at his home. He was later lent a book written by S. L. Loney on advanced trigonometry.
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He also delivered some lectures on geometry to future techers in the university of Zürich. From 1903 he had a teaching post in the technical school of Burgdorf. He was the author of several text books for secondary level very valued and reedited several times. The matters included stereometry, trigonometry, algebra and arithmetic.
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Fragments of texts during this period indicate that Arabs adopted the sine function (inherited from India) in place of the chords of arc used in Greek trigonometry. According to David King, after the rise of Islam, the religious obligation to determine the qibla and prayer times inspired more progress in astronomy for centuries.
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Cyclometricus, 1621 In addition to the Eratosthenes Batavus, he published (1621), and Tiphys Batavus (1624). He also edited Coeli et siderum in eo errantium observationes Hassiacae (1618), containing the astronomical observations of Landgrave William IV of Hesse. A work on trigonometry (Doctrina triangulorum) authored by Snellius was published a year after his death.
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King Edward I Richard of Wallingford, the mathematician and astronomer, became Abbott of St Albans in 1326.Chambers Biographical Dictionary, "Robert of Wallingford", p. 1127. He is regarded as the father of modern trigonometry. Hertford Castle was used as a gaol for a series of important captives during the Hundred Years' War.
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Wildberger states that there are five basic laws in rational trigonometry. He also states that these laws can be verified using high-school level mathematics. Some are equivalent to standard trigonometrical formulae with the variables expressed as quadrance and spread. In the following five formulae, we have a triangle made of three points .
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Pipers Creek rises about northwest of the Ballengarra trigonometry station, within the Ballengarra State Forest. The river flows generally east by south and then south before reaching its confluence with the Maria River north northeast of Telegraph Point. The river descends over its course. The Pacific Highway transverses the river near Kundabung.
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Vogt 1974, p. 3. Some graduates were not enthusiastic about the first year of their training. For example, Paul von Hindenburg thought that the history of ancient battles should be minimized to give more time to modern, and that trigonometry was only useful to those who would be surveyors. The final two years satisfied him.
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The tests focused on the state's academic standards for reading, writing, mathematics and science. The science exam included content in science, technology, ecology and the environmental studies. The mathematics exam included algebra I, algebra II, geometry and trigonometry. The standards were first published in 1998 and are mandated by the Pennsylvania State Board of Education.
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If the grade is known, then the rate of ascent can be calculated using trigonometry. Suppose that the car is ascending at . Standard models for the Earth's atmosphere imply that the temperature drops about per kilometer ascended (called the lapse rate). To find the temperature drop per hour, we can apply the chain rule.
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Among Napier's early followers were the instrument makers Edmund Gunter and John Speidell. The development of logarithms is given credit as the largest single factor in the general adoption of decimal arithmetic. The Trissotetras (1645) of Thomas Urquhart builds on Napier's work, in trigonometry. Henry Briggs (mathematician) was an early adopter of the Napierian logarithm.
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Suffering from occasional poor health as a boy, he was educated at home by the Reverend Edward Wilson. An intelligent child, Pitt quickly became proficient in Latin and Greek. He was admitted to Pembroke College, Cambridge, on 26 April 1773, a month before turning fourteen. He studied political philosophy, classics, mathematics, trigonometry, chemistry and history.
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Methodios Anthrakites' signature. Anthrakites was born in the village of Kaminia (Καμινιά) or Kamnia (Καμνιά), in the Zagori region (Epirus). He studied in the Gioumeios (later Balaneios) School in Ioannina under Georgios Sougdouris. After becoming a priest, he left for Venice in 1697, where he studied Philosophy and Mathematics (geometry, trigonometry, astronomy and physics).
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Their main hiding place was a dugout 170 cm long, 150 cm wide and 120 cm tall. Felix Zandman shared this hideaway with three other Jewish refugees. One of them, his uncle Sender Freydowicz, taught him trigonometry and advanced mathematics in the long hours of darkness.Mordecai Paldiel, Saving the Jews Chapter: Sheltering and Hiding.
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In days gone by, mathematics and proof was often intertwined with practical questions – with populations like the Egyptians and the Greeks showing an interest in surveying land.Krantz, Steven G. The History and Concept of Mathematical Proof. February 5, 2007. This led to a natural curiosity with regards to geometry and trigonometry – particularly triangles and rectangles.
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He returned to Ballarat in April 1855, and towards the end of the year he began to study surveying. He was appointed as an amateur to John Hamlet Taylor, the Acting District Surveyor of the Ballarat Survey Office on Sturt Street. William spent several months learning trigonometry, Euclidian geometry and in 1856 studied field surveying.
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The lines (of quadrance ) and (of quadrance ) are perpendicular (their spread is 1) if and only if: : Q_1 + Q_2 = Q_3. where is the quadrance between and . This is equivalent to the Pythagorean theorem (and its converse). There are many classical proofs of Pythagoras's theorem; this one is framed in the terms of rational trigonometry.
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However, as noted earlier, it is possible to define sine, cosine, and in a way that is totally independent of trigonometry, in which case the proof is valid by the change of variables formula and Fubini's theorem, assuming the basic properties of sine and cosine (which can also be proved without assuming anything about their relation to circles).
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Not down the mines or up chimneys, mind, but working with computers or something relevant. Everything I learned after 11 was a waste of time. Trigonometry, Boyle's law: it's never been of any use to me. They should have been teaching me the life skills I was going to need, such as building relationships, parenting and managing money.
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Fuss was born in Basel, Switzerland. He moved to Saint Petersburg to serve as a mathematical assistant to Leonhard Euler from 1773-1783, and remained there until his death. He contributed to spherical trigonometry, differential equations, the optics of microscopes and telescopes, differential geometry, and actuarial science. He also contributed to Euclidean geometry, including the problem of Apollonius.
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Triangle with sides a,b,c and respectively opposite angles A,B,C Trigonometry has been noted for its many identities, that is, equations that are true for all possible inputs. Identities involving only angles are known as trigonometric identities. Other equations, known as triangle identities, relate both the sides and angles of a given triangle.
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Helping Nature: from Galileo's Mechanics to everyday life is an interactive exhibit showing how Galileo used mathematics to reveal the working of simple machines. Weapons of mass education features mathematically based games and puzzles. Other historical sections include A short history of calculus, A short history of trigonometry, Ancient mathematics through stamps, and Pink Numbers – Women and Mathematics.
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U.S. Military Academy commandant William Worth (1820–28) between 1845 and 1849 Thayer met with George Bomford (New York) and Robert E. Lee (Virginia). Bomford was questioned about his parental correspondence by Thayer while Lee questioned Thayer about trigonometry problems for artillery gunnery.Agnew. pp. 12–19. Classes and barracks inspections continued as usual that day.Agnew. pp. 20–30.
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The half-chords were called ardha-jyās or jyā-ardhas. These terms were again shortened to jyā by omitting the qualifier ardha which meant "half of". The Sanskrit word koṭi has the meaning of "point, cusp", and specifically "the curved end of a bow". In trigonometry, it came to denote "the complement of an arc to 90°".
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Author of around 170 scientific articles and books, Steinhaus has left his legacy and contribution in many branches of mathematics, such as functional analysis, geometry, mathematical logic, and trigonometry. Notably he is regarded as one of the early founders of game theory and probability theory which led to later development of more comprehensive approaches by other scholars.
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Using simple trigonometry, a rough estimate of the altitude of the aircraft could then be determined. These measurements could only take place during the fleeting moments when the antenna passed by a particular target, over a longer time the signal was continually jumping about as the radar crossed different targets, requiring considerable experience to properly interpret the display.
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During this era, while timekeeping technology stagnated or was forgotten in Europe, in the Islamic world it advanced, both because of the Islamic Golden Age and because timekeeping was important for determining when to pray.Encyclopedia Britannica: Sundial Their improvements included using algebra and trigonometry (the former being invented by Persian mathematician al-Khwarizmi) to increase accuracy.
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The George Washington University Statement of Personal Data. During the time that Taylor taught at the George Washington University from 1929-1958 the mathematics department was relatively basic. He taught classes in advanced analytics, geometry, and tensor analysis. In 1950-1951 the department expanded a little, offering 34 classes ranging from college algebra to analytic geometry to plane trigonometry.
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In the third year, they studied geography, planar trigonometry, algebra, surveying and military history. In the fourth year, they studied cross-sections of cones, differentiation, integration, mechanics, ballistics, astronomy, fortifications and shooting practice. The fourth year curriculum required knowledge of advanced mathematics. Mining as a part of the military (lağımcılık), map drawing and artillery were among other areas studied.
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Various approaches to geometry have based exercises on relations of angles, segments, and triangles. The topic of trigonometry gains many of its exercises from the trigonometric identities. In college mathematics exercises often depend on functions of a real variable or application of theorems. The standard exercises of calculus involve finding derivatives and integrals of specified functions.
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A megagon or 1 000 000-gon is a polygon with 1 million sides (mega-, from the Greek μέγας megas, meaning "great").Dugopolski, Mark, College AbrakaDABbra and Trigonometry, 2nd ed, Addison-Wesley, 1999. Page 505. . Even if drawn at the size of the Earth, a regular megagon would be very difficult to distinguish from a circle.
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After the war's end in 1763 he switched to the artillery branch with the rank of lieutenant. The Minister of War Étienne François, duc de Choiseul, noting Lespinasse's intelligence, assigned him to write a treatise on practical trigonometry and leveling. This paper was published in 1768. Lespinasse had been promoted to captain on 24 March 1767.
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In the final section, the "Gola" or "The Sphere," Aryabhata goes into great detail describing the celestial relationship between the Earth and the cosmos. This section is noted for describing the rotation of the Earth on its axis. It further uses the armillary sphere and details rules relating to problems of trigonometry and the computation of eclipses.
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Active methods use unilateral transmission and passive reflection. Active rangefinding methods include laser, lidar, radar, sonar and ultrasonic rangefinding. Other devices measure distance using trigonometry are stadiametric, coincidence and stereoscopic rangefinders. Older methodologies that use a set of known information (usually distance or target sizes) to make the measurement, have been in regular use since the 18th century.
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The slope of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter m. Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged during the 3rd century BC from applications of geometry to astronomical studies.
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Many sailing instructions only specify the length of the windward leg and the total course length, but see below on the use of the law of sines, trigonometry table and spreadsheets to calculate the angles and other leg lengths. The angles of the triangle may not always be perfectly sharp, either, since it is a course.
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A large portion of the math section is problem-solving, in which students are required to both analyze and draw conclusions from numerical data (like graphs and charts) or compute answers to a problem using previous mathematical knowledge. The other portion of the exam requires knowledge in advanced topics like calculus, algebra, trigonometry, probability, and conic sections.
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At the time, classes were held two hours a night, six nights a week. When the mines were closed, students met for six hours a day. They studied spelling, reading, writing, grammar, composition, algebra, bookkeeping, geometry, trigonometry, mechanical drawing, physics, chemistry, mineralogy, drafting, mining, and other courses. The curriculum was designed to produce intelligent foremen, not engineers.
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Notre Dame holds a variety of classes. Foreign language choices are limited to French or Spanish, which are begun in seventh grade and required. A standard selection of mathematics is available, including pre- algebra, algebra, geometry, trigonometry, pre-calculus, calculus, and statistics. The sciences offered include living environment, physical sciences, earth science, biology, chemistry, and physics.
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Sound rangers are military specialists who locate enemy artillery using sound. They use equipment such as super-sensitive microphones to pick up the sounds of firing. By using a combination of surveying techniques and trigonometry they then calculate the locations of enemy batteries. These results are then transmitted by radio to their own artillery, who used it for targeting.
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In 1904, Curtiss taught at Yale University for one year. He then served as a professor at Northwestern University from 1905 to 1943, including 20 years as Chair of the Mathematics Department. Curtiss authored textbooks on trigonometry and analytic geometry with Elton James Moulton. He also published the second Carus Mathematical Monograph, Analytic Functions of a Complex Variable.
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He wrote his only novel Karan Ghelo which he started in 1863 and completed in 1866. The novel depicts Karan Vaghela, the last Rajput ruler of Gujarat (c.1296 - 1304) who was defeated by the Turkish forces of Alauddin Khilji in 1298. He translated R. G. Bhandarkar’s Sanskrit Margopadeshika and an English textbook on trigonometry into Gujarati.
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Eventually, Bean gives up and cries out "Oh, Mummy!" before placing his head on the desk and sleeping for the remainder of the exam. Two minutes before the end, the invigilator gives instructions on what to do with the papers once the exam is over. From this, Bean realises that there were two papers in the envelope – a green calculus paper and a white trigonometry paper, with each student given a choice as to which to do (although the invigilator logically should have stated this at the beginning). Bean takes out the trigonometry paper and frantically tries to complete it hurriedly, but his pen has run out of ink and won't write anything, so he steals the other student's pen (forgetting about the many spares he came prepared with).
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Pitiscus supported Frederick's subsequent measures against the Roman Catholic Church. Pitiscus achieved fame with his influential work written in Latin, called Trigonometria: sive de solutione triangulorum tractatus brevis et perspicuus (1595, first edition printed in Heidelberg), which introducedGroundbreaking Scientific Experiments, Inventions, and Discoveries the word trigonometry to the English and French languages, translations into which had appeared in 1614 and 1619, respectively. It consists of five books on plane and spherical trigonometry. Pitiscus is sometimes credited with inventing the decimal point, the symbol separating integers from decimal fractions, which appears in his trigonometrical tables and was subsequently accepted by John Napier in his logarithmic papers (1614 and 1619). Pitiscus edited Thesaurus mathematicus (1613) in which he improved the trigonometric tables of Georg Joachim Rheticus and also corrected Rheticus’s Magnus Canon doctrinæ triangulorum.
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Rational trigonometry follows an approach built on the methods of linear algebra to the topics of elementary (high school level) geometry. Distance is replaced with its squared value (quadrance) and 'angle' is replaced with the squared value of the usual sine ratio (spread) associated to either angle between two lines. (The complement of Spread, known as cross, also corresponds to a scaled form of the inner product between line segments taken as vectors). The three main laws in trigonometry – Pythagoras's theorem, the sine law and the cosine law – are given in rational (square-equivalent) form, and are augmented by two further laws – the triple quad formula (relating the quadrances of three collinear points) and the triple spread formula (relating the spreads of three concurrent lines) –, giving the five main laws of the subject.
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The exsecant (exsec, exs) and excosecant (excosec, excsc, exc) are trigonometric functions defined in terms of the secant and cosecant functions. They used to be important in fields such as surveying, railway engineering, civil engineering, astronomy, and spherical trigonometry and could help improve accuracy, but are rarely used today except to simplify some calculations. A unit circle with trigonometric functions.
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John Samuel Forrest was born at Hamilton, South Lanarkshire, Scotland, on 20 August 1907, one of the three children of Samuel Norris Forrest and his wife Elizabeth. Samuel Norris Forrest was a teacher of mathematics at Hamilton Academy and author of text-books on mathematics, trigonometry and calculus.Mathematics for Engineering Students: Two Year General Course. Authors Joseph Sanger and Samuel Norris Forrest.
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Murdoch was a longtime friend to both Millar and Andrew Mitchell. Murdoch was author of Mercator's Sailing, applied to the true Figure of the Earth ; with an Introduction, &c.;, 4to, London, 1741. To the Philosophical Transactions he communicated eight papers, two of which Trigonometry abridged, 1758, and On Geographical Maps, 1758, exist in the original manuscript among the Additional MSS.
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In 1592 Magini published Tabula tetragonica, and in 1606 devised extremely accurate trigonometric tables. He also worked on the geometry of the sphere and applications of trigonometry, for which he invented calculating devices. He also worked on the problem of mirrors and published on the theory of concave spherical mirrors. He also published a commentary on Ptolemy’s Geographia (Cologne, 1596).
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Triangulation point signed by iron rod In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to it from known points. Specifically in surveying, triangulation involves only angle measurements, rather than measuring distances to the point directly as in trilateration; the use of both angles and distance measurements is referred to as triangulateration.
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The PSSAs test the students on their proficiency of the state's Academic Standards for reading, writing, mathematics, and science. For example, the Science exam included content in science, technology, ecology and the environmental studies and the mathematics exam included algebra I, algebra II, geometry and trigonometry. These standards were first published in 1998 and are mandated by the Pennsylvania State Board of Education.
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On the utility of the nautical mile. Each circle shown is a great circle—the analogue of a line in spherical trigonometry—and hence the shortest path connecting two points on the globular surface. Meridians are great circles that pass through the poles. The nautical mile was originally defined as one minute of arc along a meridian of the Earth.
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One author describes the gamma function as "Arguably, the most common special function, or the least 'special' of them. The other transcendental functions […] are called 'special' because you could conceivably avoid some of them by staying away from many specialized mathematical topics. On the other hand, the gamma function is most difficult to avoid."Michon, G. P. "Trigonometry and Basic Functions ". Numericana.
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The Science exam included content in science, technology, ecology and the environmental studies. The mathematics exam included: algebra I, algebra II, geometry, and trigonometry. The standards were first published in 1998 and are mandated by the Pennsylvania State Board of Education. In 2013, the Commonwealth of Pennsylvania changed its high school assessments to the Keystone Exams in Algebra 1, Reading/literature and Biology1.
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The Science exam included content in science, technology, ecology and the environmental studies. The mathematics exam included: algebra I, algebra II, geometry and trigonometry. The standards were first published in 1998 and are mandated by the Pennsylvania State Board of Education. In 2013, the Commonwealth of Pennsylvania changed its high school assessments to the Keystone Exams in Algebra 1, Reading/literature and Biology1.
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The Science exam included content in science, technology, ecology and the environmental studies. The mathematics exam included: algebra I, algebra II, geometry and trigonometry. The standards were first published in 1998 and are mandated by the Pennsylvania State Board of Education. In 2013, the Commonwealth of Pennsylvania changed its high school assessments to the Keystone Exams in Algebra 1, Reading/literature and Biology1.
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His publications covered topics on mathematics and astronomy, including sundials, spherical trigonometry, and celestial maps and globes. One of his works also included useful biographical information on several hundred mathematicians and instrument makers of Nuremberg. Greenwich, Copenhagen, Cassel, and Berlin. Doppelmayr developed a close relationship with the Dominican friar and cartographer Johann Batist Homann, the founder of a famous cartographic publishing firm.
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Fox Creek High School partners with nearby Piedmont Technical College to offer a selection of advanced dual-enrollment courses. Students take college level American and world history, college level English, college level biology, and college level trigonometry and calculus. All dual- enrollment courses are taken on Fox Creek's campus through accredited teachers. In addition, the school offers multiple Advanced Placement courses.
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No matter what the weather might be, school buses almost always ran. The school had very few "snow days". The curriculum at Buckingham High School was collegiate in nature. Course offerings were limited – mathematics (algebra, geometry & trigonometry), English, French, science (physics & chemistry), as well as history and geography. Latin was offered in the 1950s but this course was dropped due to insufficient enrolment.
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It has been "revised to eliminate the sections for numerical calculations, conversions, geometry, and trigonometry. Items have been added in the following areas: data analysis, interpretation, and sufficiency; quantitative comparison; and probability and statistics." During 2014 and 2015, examinees may have seen some questions that reflect such changes, however, they weren't scored. Actual changes to the sections didn't take place sooner than 2015.
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The Project Mathematics! series of videos is a teaching aid for teachers to help students understand the basics of geometry and trigonometry. The series was developed by Tom M. Apostol and James F. Blinn, both from the California Institute of Technology. Apostol led the production of the series, while Blinn provided the computer animation used to depict the ideas beings discussed.
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After the war Rawlings remained in the Air Force, transferring to a commission as Flight Lieutenant, Technical Branch, in 1948. Rawlings wrote several books; a training manual 'Electricity for Air Training' published in 1941. and mathematics books covering Trigonometry, the Slide rule and Calculus. Prior to joining the school he was Director of Studies at the naval training establishment HMS Worcester.
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The radial components measured by the tilted beams are the vector sum of the horizontal motion of the air toward or away from the radar and any vertical motion present in the beam. Using appropriate trigonometry, the three-dimensional meteorological velocity components (u,v,w) and wind speed and wind direction are calculated from the radial velocities with corrections for vertical motions.
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The Science exam included content in science, technology, ecology and the environmental studies. The mathematics exam included: algebra I, algebra II, geometry and trigonometry. The standards were first published in 1998 and are mandated by the Pennsylvania State Board of Education. In 2013, the Commonwealth of Pennsylvania changed its high school assessments to the Keystone Exams in Algebra 1, Reading/literature and Biology1.
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This describes the basics of astronomy, the movements of heavenly bodies, the working of the telescope, and sunspots, although the existence of these had been known in China for some time. Schall likewise revised and published two works by Schreck on trigonometry, Da ce () (The Great Measurement) and Ge-yuan ba-xian biao () (A Table of Eight Lines), the latter together with Rho.
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Eli Maor (born 1937), an Israel-born historian of mathematics, is the author of several books about the history of mathematics. Eli Maor received his PhD at the Technion – Israel Institute of Technology. He teaches the history of mathematics at Loyola University Chicago.Eli Maor biography at Princeton University Press Maor was the editor of the article on trigonometry for the Encyclopædia Britannica.
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Associate degree programs emphasize the practical field knowledge that is needed to maintain or troubleshoot existing electrical/electronic systems or to build and test new design prototypes. Discipline-specific program outcomes include the application of circuit analysis and design, analog and digital electronics, computer programming, associated software, and relevant engineering standards Coursework must be at a minimum algebra and trigonometry based.
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The Science exam included content in science, technology, ecology and the environmental studies. The mathematics exam included: algebra I, algebra II, geometry and trigonometry. The standards were first published in 1998 and are mandated by the Pennsylvania State Board of Education. In 2013, the Commonwealth of Pennsylvania changed its high school assessments to the Keystone Exams in Algebra 1, Reading/literature and Biology1.
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Union College offered primary, secondary and tertiary education. College subjects included Greek and Latin, Trigonometry and Geometry, Chemistry and Physics, Logic and Moral Science. Besides the classical academic education, emphasis was placed on character development, a vocational programme, laws of health, physical training and culture. The College was open to all races and no distinction was made with regard to religious affiliation.
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By convention, letters at the beginning of the alphabet (e.g. a, b, c) are typically used to represent constants, and those toward the end of the alphabet (e.g. x, y and ) are used to represent variables.William L. Hosch (editor), The Britannica Guide to Algebra and Trigonometry, Britannica Educational Publishing, The Rosen Publishing Group, 2010, , 9781615302192, page 71 They are usually written in italics.
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Besides being intensely trained in workshops, students studied algebra, descriptive geometry, trigonometry, technical drawing, industrial mechanics, physics and chemistry, besides Spanish, history and geography. This was a four-year education that later, in 1858, extended to five years. Graduates were called 'apprentices'. In 1886 the EAO moved to a bigger building, located at Quinta Normal, where it would stay up until now.
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Dymchurch played a significant rôle in the Anglo-French Survey (1784–1790), which linked the Royal Greenwich Observatory with the Paris Observatory using trigonometry. There were two base-lines for the English part of the survey, on Hounslow Heath and on Romney Marsh. The Romney Marsh base-line extended from Ruckinge to High Nook, on the sea-wall near Dymchurch.
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Edgar (1999), p. 19. A natural leader, he became a prefect and rose to the rank of colour sergeant in the school's Cadet unit. In 1913, Potts sat and passed the University of Adelaide's entrance exam for English, geometry and trigonometry. In early 1914 he left Guilford and moved to Pinjarra where he attended Fairbridge Farm School, working as a farmhand.
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He was bored with this and had enrolled at Lincolns Inn when he was recruited to use his trigonometry to help conduct a survey in the Highlands. This new work was done in the summer with the more difficult months being passed in London. Drummond took this opportunity to improve his knowledge of mathematics and science. He attended lectures by Sir Michael Faraday.
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The Rush Creek (officially designated as a river) rises about south-east of the Parr Spur Ridge Trigonometry Station, near Mile Ridge and east of the Putty Road. The river flows generally north-east by east before reaching its confluence with Webbs Creek in remote country within the Parr State Conservation Area, south-west of . The river descends over its course.
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Mathematician and mathematical historian Carl Benjamin Boyer writes, "Bradwardine developed the Boethian theory of double or triple or, more generally, what we would call 'n-tuple' proportion". Boyer also writes that "the works of Bradwardine had contained some fundamentals of trigonometry". Yet "Bradwardine and his Oxford colleagues did not quite make the breakthrough to modern science." The most essential missing tool was algebra.
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In Kresa's era the Trigonometric functions were derived using geometry. Kresa was the first to introduce algebraic number to trigonometry. Kresa's death was followed by a decline in mathematics and science in the Czech Crown lands due to the dogmatic application of Catholic Church doctrines. With Slavíček having gone to China, scientific work largely disappeared from the Czech lands for two decades.
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Link Crew is made up of about 20 juniors and seniors who are leaders in the school. These student leaders host events all year with the freshmen to improve school spirit. Math League is a fun competition where students go to other schools to compete with math questions. The math topics are algebra, geometry, trigonometry, algebra 2, and pre-calc.
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The Science exam included content in science, technology, ecology and the environmental studies. The mathematics exam included: algebra I, algebra II, geometry and trigonometry. The standards were first published in 1998 and are mandated by the Pennsylvania State Board of Education. In 2013, the Commonwealth of Pennsylvania changed its high school assessments to the Keystone Exams in Algebra 1, Reading/literature and Biology1.
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By 1938, the United States Navy had developed an electromechanical analog computer small enough to use aboard a submarine. This was the Torpedo Data Computer, which used trigonometry to solve the problem of firing a torpedo at a moving target. During World War II similar devices were developed in other countries as well. Zuse's Z3, the first fully automatic, digital (electromechanical) computer.
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Math B was required to receive a High School Regents Diploma with Advanced Designation. The course replaces the former "Course 3" curriculum, which focused almost solely on trigonometry. Math B focused on a whole range of topics. It was taken after the student has completed and passed Math A. A Regents exam was taken at the end of the -year course.
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Dow's around 1917 included Physiology, Botany, Chemistry, General Science, and Domestic Science. The latter class involved different curricula each term: dietaries, cookery, household administration and care, food chemistry, and (advanced) cookery. Mrs. Dow's held psychology, history of philosophy, political economy, social science, and ethics and logic classes. Mathematics classes around that time included Algebra, Plane Geometry, Solid Geometry, Trigonometry, and Arithmetic and Accounts.
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Toelken went to several schools in his home town and then spent 1794-1802 at the Pädagogium, graduating with honours. Toelken continued his education privately, studying French, English and Italian under several teachers. He taught himself ancient Greek and studied spherical trigonometry under Gottfried Reinhold Treviranus. On 25 April 1804, Toelken matriculated in the theological faculty of Georgia Augusta at Göttingen.
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'Indian Numerals', MacTutor History of Mathematics Archive, School of Mathematics and Statistics, University of St. Andrews, Scotland. During the 14th–16th centuries, the Kerala school of astronomy and mathematics made significant advances in astronomy and especially mathematics, including fields such as trigonometry and analysis. In particular, Madhava of Sangamagrama is considered the "founder of mathematical analysis".George G. Joseph (1991).
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The most characteristic product of Greek mathematics may be the theory of conic sections, which was largely developed in the Hellenistic period. The methods used made no explicit use of algebra, nor trigonometry. Eudoxus of Cnidus developed a theory of real numbers strikingly similar to the modern theory of the Dedekind cut, developed by Richard Dedekind, who acknowledged Eudoxus as inspiration.
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The Taichu calendar established a framework for traditional calendars, with later calendars adding to the basic formula. The Dàmíng Calendar (), created in the Liang dynasty by Zu Chongzhi, introduced the equinoxes. The use of a syzygy to determine the lunar month was first described in the Tang dynasty Wùyín Yuán Calendar (). The Yuan dynasty Shòushí calendar () used spherical trigonometry to find the length of the tropical year.
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His Quadripartitum was the first text on spherical trigonometry to be published in Western Europe. The rectangulus was a form of skeleton torquetum. This was a series of nested angular scales, so that measurements in azimuth and elevation could be made directly in polar coordinates, relative to the ecliptic. Conversion from these coordinates though was difficult, involving what was the leading mathematics of the day.
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In the sciences, the scholars learn Biology, Chemistry and Physics as separate subjects starting the second year. Computer Science is also offered in all year levels. The mathematics department offers subjects in Elementary Algebra, Advanced Algebra, Plane Geometry, Trigonometry, Selected Topics in Number Theory, Statistics and Elementary Analysis among others. Four years of studies in English, Filipino, and the Social Science are part of the Humanities curriculum.
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When she arrived in the Ottoman Empire, she was thirty-one years old. She eventually became the principal of the girls' high school in Sivas, where she taught algebra and geometry. As a supervisor of schools in the neighboring villages, she was also a teacher of Bible studies and trigonometry at the Sivas Teachers College. She became fluent in Armenian and was conversational in Turkish and French.
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The school works with local landowners to manage their forested and open lands for future generations. Students immerse themselves in all aspects of land stewardship, including walking the land with owners, figuring the trigonometry of easement boundaries, rebuilding animal habitat for local fauna while inventorying forest species, working with local conservation agencies to draft management plans, and helping land owners to implement those plans.
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There is a significant speed-up (known since 2001) of the winding number algorithm. It uses signed crossings, based on whether each crossing is left-to-right or right-to-left. Details and C++ code are given at the link in the following annotation .. Angles are not used, and no trigonometry is involved. The code is as fast as the simple boundary crossing algorithm.
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During Dr. Weyl's time here, he and Dr. Taylor worked together in the GW math department. During 1946 the department is noted as having taught advanced analytics, geometry, and tensor analysis. Some time shortly after 1946 however the department developed thirty-four additional courses in everything from collegiate algebra to analytic geometry and plane trigonometry. Today the university awards a "grand math prize" in Taylor's honor.
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Bardwell graduated from Mount Holyoke College in 1866 and remained to teach there for 33 years. She taught algebra, trigonometry, physics, and astronomy. She was also the director of the John Payson Williston Observatory at the college from its opening in 1881 until 1896, during which time she oversaw its growth. Improvements in telescopes allowed her and her students to observe sunspots, lunar occultations, and variable stars.
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Unit circle: the radius has length 1. The variable t measures the angle referred to as θ in the text. In trigonometry, a unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system. Let a line through the origin, making an angle of θ with the positive half of the x-axis, intersect the unit circle.
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His mathematical works were in the areas of spherical trigonometry, as well as conic sections. He published an original work on conic sections in 1522 and is one of several mathematicians sometimes credited with the invention of prosthaphaeresis, which simplifies tedious computations by the use of trigonometric formulas, sometimes called Werner's formulas.Howard Eves, An Introduction to the History of Mathematics, Sixth Edition, p. 309, Thompson, 1990, .
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During this first decade the school term runs for five months and the four teachers on the staff are paid a salary of $20.00 per month. Subjects offered during this period include advanced studies such as trigonometry, astronomy, and calculus. Classes during the early years of the school’s existence were housed in the Tazewell County Courthouse. Professor W. A. Evans was named the second principal at THS.
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Pre-calculus usually combines advanced algebra (or "Algebra III") and geometry with trigonometry. Depending on school district, several courses may be compacted and combined within one school year, either studied sequentially or simultaneously. Without such acceleration it may be not possible to take more advanced classes like calculus in high school. College algebra is offered at many community colleges and generally has a prerequisite of intermediate algebra.
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In particular, the "simplified instrument" (jianyi) and the large gnomon at the Gaocheng Astronomical Observatory show traces of Islamic influence. While formulating the Shoushili calendar in 1281, Shoujing's work in spherical trigonometry may have also been partially influenced by Islamic mathematics, which was largely accepted at Kublai's court.Ho, Peng Yoke. (2000). Li, Qi, and Shu: An Introduction to Science and Civilization in China, p. 105.
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A second arm suspended from the main sight tube was pushed up and down as the horizontal portion slid. This arm was measured against a short vertical bar marked with altitude corrections. The system indicated only corrections, not the actual altitude. Two or more posts had to work in concert to use the system, using two measured angles and simple trigonometry to solve the altitude.
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Microsoft Windows NT Calculator Version 3.1 A simple arithmetic calculator was first included with Windows 1.0.Windows 1.01 - Graphical User Interface Gallery In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
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In 1847 his health broke down and he returned to Sheffield working as a chaplain and teacher. Earnshaw published several mathematical and physical articles and books. His most famous contribution, "Earnshaw's theorem", shows the impossibility of stable levitating permanent magnets: other topics included optics, waves, dynamics and acoustics in physics, calculus, trigonometry and partial differential equations in mathematics. As a clergyman, he published several sermons and treatises.
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By convention, letters at the beginning of the alphabet (e.g. a, b, c) are typically used to represent constants, and those toward the end of the alphabet (e.g. x, y and z) are used to represent variables.William L. Hosch (editor), The Britannica Guide to Algebra and Trigonometry, Britannica Educational Publishing, The Rosen Publishing Group, 2010, , 9781615302192, page 71 They are usually written in italics.
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He had become interested in wireless communications after learning about the wireless operators aboard the Titanic when it sank. While he was with the navy, he made himself an expert on radio technology: "I just got hold of a lot of textbooks and taught myself while I was standing watch at night." He also subsequently taught himself trigonometry, calculus, chemistry, physics, and metallurgy, among other subjects.
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In addition, trigonometry, having evolved in the Hellenistic world and having been introduced into ancient India through the translation of Greek works, was further advanced in India, and, in particular, the modern definitions of sine and cosine were developed there. These mathematical concepts were transmitted to the Middle East, China, and Europe and led to further developments that now form the foundations of many areas of mathematics.
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He worked in algebra, trigonometry and geometry; and on the decimal expansion of π. His publication of 1595, Parvum theatrum urbium, contained Latin verse on the cities of Italy (possibly written by Thomas Edwards).Matthew Steggle, 'Edwards, Thomas (fl. 1587–1595)’, Oxford Dictionary of National Biography, Oxford University Press, 2004 He solved the Problem of Apollonius using a new method that involved intersecting hyperbolas.
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He had used the term as early as 1871, while in 1869, Thomas Muir, then of the University of St Andrews, vacillated between the terms rad, radial, and radian. In 1874, after a consultation with James Thomson, Muir adopted radian. The name radian was not universally adopted for some time after this. Longmans' School Trigonometry still called the radian circular measure when published in 1890.
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Following the death of spanish king Charles II in 1700 Kresa went back to Prague. He obtained a doctorate in theology at Charles University and also started to teach theology there. At the same time he was privately teaching mathematics and was acquiring mathematical apparatus for the Department of Mathematics. He was engaged in arithmetic, fractions and logarithms, trigonometry, astronomy, algebra, as well as military architecture.
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The ALU is capable of performing two classes of operations: arithmetic and logic. The set of arithmetic operations that a particular ALU supports may be limited to addition and subtraction, or might include multiplication, division, trigonometry functions such as sine, cosine, etc., and square roots. Some can only operate on whole numbers (integers) while others use floating point to represent real numbers, albeit with limited precision.
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He taught Algebra, Euclidean Geometry, Trigonometry and Analytic Geometry. After ten years of teaching, Wenninger felt he was becoming a bit stale. At the suggestion of his headmaster, Wenninger attended the Columbia Teachers College in summer sessions over a four-year period in the late fifties. It was here that his interest in the "New Math" was formed and his studies of the polyhedra began.
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On the album, despite the frightening the name "Triggernometry" (a mixture of the words "trigger" and "trigonometry"), it became noticeably less street negligence and noticeably more "musical". If you do not listen to the lyrics - the album is quite funny, with a fervent presentation of the lyrics, good rhythm and various pleasant finds in the accompaniment. If you listen - the album is even more funny. Well done.
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Her most recent TV work includes the film direction of the BBC Two TV series, Trigonometry. The TV series premiered at the “Berlinale Series” section of Berlinale in 2020. Film producer In 2005, Tsangari founded Haos Film, a production and post-production studio based in Athens. Her producing credits include three films directed by Yorgos Lanthimos: Kinetta (2005), Dogtooth (2009), as an associate producer, and Alps (2011).
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Elias ben Ḥayyim Cohen Höchheimer (or Hechim) was an eighteenth century Jewish astronomer and mathematician. Born in Hochheim, Höchheimer lived a long time in Hildburghausen and died in Amsterdam. He was the author of Shebile di- Reḳi'a (Prague, 1784), on trigonometry and astronomy, Sefer Yalde ha-Zeman (Prague, 1786), a commentary on Jedaiah Bedersi's Beḥinat ha-'Olam, and two German-language textbooks on arithmetic.
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Hemming wrote An Elementary Treatise on the Differential and Integral Calculus (Cambridge, 1848; 2nd edit. 1852); First Book on Plane Trigonometry (1851); and Billiards Mathematically Treated (1899; 2nd edit. 1904). He published Reports of Cases adjudged in the High Court of Chancery, before Sir William Page Wood for 1859–62 (2 vols. 1861–3, with Henry Robert Vaughan Johnson); and for 1862–65 (2 vols.
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He left manuscripts and scientific instruments to a number of Oxford colleges, perhaps including the bequest of the Oriel astrolabe (c. 1340), which is now in the Museum of the History of Science. He was one of the earliest European mathematicians to work on trigonometry. Authorship of the treatise The equatorie of the planetis has been attributed to Bredon, though also to Geoffrey Chaucer or another contemporary.
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Along with a later 17th-century Chinese illustration of Guo's mathematical proofs, Needham states that: > Guo used a quadrangular spherical pyramid, the basal quadrilateral of which > consisted of one equatorial and one ecliptic arc, together with two meridian > arcs, one of which passed through the summer solstice point...By such > methods he was able to obtain the du lü (degrees of equator corresponding to > degrees of ecliptic), the ji cha (values of chords for given ecliptic arcs), > and the cha lü (difference between chords of arcs differing by 1 > degree).Needham, Volume 3, 109–110. Despite the achievements of Shen and Guo's work in trigonometry, another substantial work in Chinese trigonometry would not be published again until 1607, with the dual publication of Euclid's Elements by Chinese official and astronomer Xu Guangqi (1562-1633) and the Italian Jesuit Matteo Ricci (1552-1610).Needham, Volume 3, 110.
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On leaving the RAF, he joined BOAC in 1953 as a navigator and pilot, while initially continuing to fly in the Royal Auxiliary Air Force with 604 (County of Middlesex) Squadron at North Weald in Essex.Norman Tebbit, Upwardly Mobile. Of his airline navigation training, he later said: "In those days it was a considerable academic syllabus. You had to be up to speed on spherical trigonometry to get through it".
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Atanasije Nikolić (Serbian: ; Bački Brestovac, Bačka, 18 January 1803 — Belgrade, 28 July 1882) was a Serbian educator, the first mathematics professor and rector at the Lyceum in Kragujevac. He wrote the first undergraduate textbooks in mathematics, algebra, geometry, trigonometry in the Serbian language.He was also employed by the Serbian Ministry of Construction and Public Works as an architect in the then capital city of Kragujevac and later Belgrade.
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With František Wolf, Beckenbach founded in 1951 the Pacific Journal of Mathematics, of which he was the first editor. In 1983, he received the Distinguished Service Award from the Mathematical Association of America. Beckenbach was famous for his work on inequalities and for this subject organized three Oberwolfach seminars (in 1976, 1978, and 1981). He was a co-author of several college textbooks in mathematics, including algebra, trigonometry, and analytic geometry.
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He was a student of Abu'l-Wafa and a teacher of and also an important colleague of the mathematician, Al-Biruni. Together, they were responsible for great discoveries in mathematics and dedicated many works to one another. Most of Abu Nasri's work focused on math, but some of his writings were on astronomy. In mathematics, he had many important writings on trigonometry, which were developed from the writings of Ptolemy.
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There are few large lecture classes. In sharp contrast to all public universities and many private universities in the United States, no classes, labs or other courses are taught by graduate students. Grinnell College expects all students to possess significant academic achievements. For example, the math department does not offer any basic-level classes such as college algebra, trigonometry, or pre-calculus, and remedial classes are not offered in any subject.
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The second section is a 60-minute, 60-question math test with the usual distribution of questions being approximately 14 covering pre-algebra, 10 elementary algebra, 9 intermediate algebra, 14 plane geometry, 9 coordinate geometry, and 4 elementary trigonometry questions. However, the distribution of question topics varies from test to test. The difficulty of questions usually increases as you get to higher question numbers. Calculators are permitted in this section only.
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Hipparchus of Nicaea (; , Hipparkhos; ) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry but is most famous for his incidental discovery of precession of the equinoxes.G J Toomer's chapter "Ptolemy and his Greek Predecessors" in "Astronomy before the Telescope", British Museum Press, 1996, p. 81. Hipparchus was born in Nicaea, Bithynia (now İznik, Turkey), and probably died on the island of Rhodes, Greece.
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Bartholomaeus Pitiscus was the first to use the word, publishing his Trigonometria in 1595. Gemma Frisius described for the first time the method of triangulation still used today in surveying. It was Leonhard Euler who fully incorporated complex numbers into trigonometry. The works of the Scottish mathematicians James Gregory in the 17th century and Colin Maclaurin in the 18th century were influential in the development of trigonometric series.
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Stanford, CA: Stanford University Press He taught astronomy and mathematics in Orange and later lived in Tarascon, both towns in the Holy Roman Empire that are now part of modern-day France. Bonfils studied the works of Gersonides (Levi ben Gershom), the father of modern trigonometry, and Al-Battani and even taught at the academy founded by Gersonides in Orange.Dimont, Max I. (2004). Jews, God, and History. Signet ClassicsShatzmiller, Joseph (2013).
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Sun assisted his mentor Paul Xu with the editing of his trigonometry textbook Principles of Right Triangles Gōugǔ Yì). Like Xu, Sun also wrote his own treatises on military science and geometry, incorporating the European knowledge being introduced by their Jesuit instructors. The mathematical works included the Miscellanea on Western Learning (Xixue Zazhu), How to Do Geometry Jǐhé Yòngfǎ), and Western Calculation Tàixī Suànyāo). One military work was his Jingwu Quanbian.
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In 1709, he became Savilian Professor of Astronomy, and also served as vice-principal of Hart Hall, Oxford. He was acquainted with the Scottish mathematician Robert Simson and provided a supporting testimonial when Simson was under consideration for appointment as Professor of Mathematics at the University of Glasgow. Caswell's publications included a book on trigonometry in 1685. He died on 28 April 1712, and is buried in Holywell Cemetery in Oxford.
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Some students will take Earth Science or Physics during freshman year depending on how their science grades were from middle school. Then, students will take Chemistry or Physics during their sophomore, junior or senior year. Other students will also have the option to take AP Biology or AP Environmental Science. The Mathematics department offers a sequence of math: Algebra, Geometry, and Trigonometry that help students to prepare for Regents exams.
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The solar zenith angle is the angle between the sun’s rays and the vertical. It is closely related to the solar altitude angle, which is the angle between the sun’s rays and a horizontal plane. Since these two angles are complementary, the cosine of either one of them equals the sine of the other. They can both be calculated with the same formula, using results from spherical trigonometry.
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When test screenings to humanities students revealed that their greatest difficulty learning calculus was a weak background in trigonometry, Apostol wrote a primer on the subject to be distributed with the telecourse. After advising the production of The Mechanical Universe, Apostol decided that a similar series, geared to high- school mathematics, would be beneficial. This became the later Caltech series Project Mathematics!, which also featured computer animation by Blinn.
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By that time she had studied plane and spherical trigonometry, conic sections and James Ferguson's Astronomy. Now she first read Isaac Newton's Principia, which she continued to study. Her inheritance from Greig gave her the freedom to pursue intellectual interests. John Playfair, professor of natural philosophy at University of Edinburgh, encouraged her studies, and through him she began a correspondence with William Wallace, with whom she discussed mathematical problems.
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The schools have teams for the content areas of English, Mathematics, Science, Social Studies. The English team has an approved reading list each season focusing on selected plays, novels, short stories, nonfiction, and poetry as well as specific terminology. The Math team focuses on studies from Algebra I, Algebra II, Geometry, and Trigonometry. The science team focuses on the studies of physical science, earth science, biology, and chemistry.
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The classical equations, derived from spherical trigonometry, for the longitudinal coordinate are presented to the right of a bracket; simply dividing the first equation by the second gives the convenient tangent equation seen on the left. , sec. 2A The rotation matrix equivalent is given beneath each case. , section 11.43 This division is ambiguous because tan has a period of 180° () whereas cos and sin have periods of 360° (2).
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Theodosius appears to have written Sphaerics as a supplement to Euclid's Elements, allowing its application in astronomy. Elements had lacked spherical geometry. Sphaerics had its own shortcomings, for example Hipparchus had already introduced trigonometry, but Theodosius makes no use of it, perhaps because he was basing it on an earlier work by Eudoxus. Theodosius' primary function in this, and other, works is to gather together existing information into one place.
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Computer engineering is referred to as computer science and engineering at some universities. Most entry-level computer engineering jobs require at least a bachelor's degree in computer engineering (or computer science and engineering). Typically one must learn an array of mathematics such as calculus, algebra and trigonometry and some computer science classes. Sometimes a degree in electronic engineering is accepted, due to the similarity of the two fields.
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The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System. One parsec is approximately equal to , or , and equates to about . A parsec is obtained by the use of parallax and trigonometry, and is defined as the distance at which one astronomical unit subtends an angle of one arcsecond ( of a degree). This corresponds to approximately astronomical units, i.e.
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He assisted with the Anglo-French Survey (1784–1790) to calculate the precise distance between the Paris Observatory and the Royal Greenwich Observatory by means of trigonometry. To this end in 1787 he visited Dover and London together with Dominique, comte de Cassini and Pierre Méchain. The three also visited William Herschel, the discoverer of the planet Uranus. Legendre lost his private fortune in 1793 during the French Revolution.
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In the form of sin2(θ) the haversine of the double-angle Δ describes the relation between spreads and angles in rational trigonometry, a proposed reformulation of metrical planar and solid geometries by Norman John Wildberger since 2005. As sagitta and cosagitta, double-angle Δ variants of the haversine and havercosine have also found new uses in describing the correlation and anti-correlation of correlated photons in quantum mechanics.
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The symbol √ is called the radical sign or radix. For example, the principal square root of 9 is 3, which is denoted by = 3, because and 3 is nonnegative. However raising x to the power of 0.5 using the key works if the number is entered as a real number with a complex part equal to zero. Inverse and hyperbolic trigonometry functions cannot be used with complex numbers.
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Eduard Study, more properly Christian Hugo Eduard Study (March 23, 1862 – January 6, 1930), was a German mathematician known for work on invariant theory of ternary forms (1889) and for the study of spherical trigonometry. He is also known for contributions to space geometry, hypercomplex numbers, and criticism of early physical chemistry. Study was born in Coburg in the Duchy of Saxe-Coburg-Gotha. His family was of Jewish descent.
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Ida Minerva Tarbell, 1890Tarbell left school wanting to contribute to society but unsure of how to do it, she became a teacher. Tarbell began her career as headmistress at Poland Union Seminary in Poland, Ohio in August 1880. The school was both a high school and provided continuing education courses for local teachers. Tarbell taught classes in geology, botany, geometry, and trigonometry as well as languages: Greek, Latin, French, and German.
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Mathematician and mathematical historian Carl Benjamin Boyer writes, "Bradwardine developed the Boethian theory of double or triple or, more generally, what we would call 'n-tuple' proportion". Boyer also writes that "the works of Bradwardine had contained some fundamentals of trigonometry gleaned from Muslim sources". Yet "Bradwardine and his Oxford colleagues did not quite make the breakthrough to modern science" (Cantor 2001, p. 122). The most essential missing tool was calculus.
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Courses such as physical and Life Science serve as introductory alternatives to those classes. Other science studies include Geology, Anatomy, Astronomy, Health science, Environmental Science, and Forensic Science. High school mathematics courses typically include Pre- algebra, algebra I, geometry, Algebra II w/ trigonometry classes. Advanced study options can include precalculus, calculus, statistics, and discrete math generally with an opportunity to earn Advanced Placement (AP) or International Baccalaureate (IB) accreditation.
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In undamaged pipes, the signals picked up by the receiver probe are from two waves: one that travels along the surface and one that reflects off the far wall. When a crack is present, there is a diffraction of the ultrasonic wave from the tip(s) of the crack. Using the measured time of flight of the pulse, the depth of a crack tips can be calculated automatically by simple trigonometry.
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Baruch Solomon Löwenstein (born in mid-nineteenth century, Włodarka, Russia) was a Jewish mathematician. He wrote Bikkure ha-Limmudiyyot, explanations of mathematical passages in the works of Abraham ibn Ezra, Moses Maimonides, and Joseph Delmedigo. He also annotated and published in 1863 a second edition of Shebile di-Reḳia, by Elias ben Ḥayyim Kohen Höchheimer, on the rules of the calendar, with the elements of geometry, trigonometry, and astronomy.
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By January 1701 a government decree had established the Mathematics and Navigation School. By June the school moved to the Sukharev Tower, a repurposed city gate and a Moscow landmark until its demolition in the 1930s. The school taught arithmetic, trigonometry, navigation, astronomy and surveying. Within a few years there were 500 pupils at the school, and by 1715 1200 specialists are thought to have graduated from the school.
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Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics (Rhind Mathematical Papyrus) and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy. In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata (sixth century CE), who discovered the sine function.
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The book Divine Proportions shows the application of calculus using rational trigonometric functions, including three-dimensional volume calculations. It also deals with rational trigonometry's application to situations involving irrationals, such as the proof that Platonic Solids all have rational 'spreads' between their faces.See Divine Proportions for numerous examples of calculus done with rational trigonometric functions, as well as problems involving the application of rational trigonometry to situations containing irrationals.
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The school also offers dual credit courses through Elizabethtown Community and Technical College, Western Kentucky University, Morehead State University, Somerset Community College, and Maysville Community College. These classes include European History 104, European History 105, English 101, English 102, Astronomy 101, Speech 145, College Algebra, Trigonometry, Calculus, and Contemporary Math. These classes serve as an opportunity for students to receive college credit while taking classes from Grayson County High School teachers.
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Although Shen Kuo (1031–1095) and Guo Shoujing (1231–1316) had laid the basis for trigonometry in China, another important work in Chinese trigonometry would not be published again until 1607 with the efforts of Xu Guangqi and Matteo Ricci. Ironically, some inventions which had their origins in ancient China were reintroduced to China from Europe during the late Ming; for example, the field mill. The Chinese calendar was in need of reform since it inadequately measured the solar year at 365 ¼ days, giving an error of 10 min and 14 sec a year or roughly a full day every 128 years. Although the Ming had adopted Guo Shoujing's Shoushi calendar of 1281, which was just as accurate as the Gregorian Calendar, the Ming Directorate of Astronomy failed to periodically readjust it; this was perhaps due to their lack of expertise since their offices had become hereditary in the Ming and the Statutes of the Ming prohibited private involvement in astronomy.
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Kushite sundials applied mathematics in the form of advanced trigonometry. The earliest practical water-powered machines, the water wheel and watermill, first appeared in the Persian Empire, in what are now Iraq and Iran, by the early 4th century BC. In ancient Greece, the works of Archimedes (287–212 BC) influenced mechanics in the Western tradition. In Roman Egypt, Heron of Alexandria (c. 10–70 AD) created the first steam-powered device (Aeolipile).
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Bees in a natural hive, located at Coromandel Valley, South Australia. Beelining (also known as bee lining, bee hunting, and coursing bees) is an ancient art used to locate feral bee colonies. It is performed by capturing and marking foraging worker bees, then releasing them from various points to establish (by elementary trigonometry) the direction and distance of the colony's home. Beeliners generally have homemade capture boxes which aid them in their quest.
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As well as trigonometry and algebra and other subjects which seem not to have interested him particularly, he continued cycling and learned to sing. "This," said Hensley, was "for the promotion of the Temperance cause, to which he devoted himself by assisting in the entertainments and addresses of a Temperance Brigade of young men." Keith- Falconer went up to Trinity College, Cambridge, in September 1874. He lived at 21 Market Hill until he married.
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Pages 77-81 cover the essentials of spherical trigonometry, a topic of considerable interest at the time because of its use in celestial navigation. The third chapter introduces the vector calculus notation based on the del operator. The Helmholtz decomposition of a vector field is given on page 237. The final eight pages develop bivectors as these were integral to the course on the electromagnetic theory of light that Professor Gibbs taught at Yale.
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Exact solutions, based on three-dimensional geometry and spherical trigonometry, began to appear in the mid-9th century. Habash al-Hasib wrote an early example, using an orthographic projection. Another group of solutions uses trigonometric formulas, for example Al-Nayrizi's four-step application of Menelaus's theorem. Subsequent scholars, including Ibn Yunus, Abu al-Wafa, Ibn al-Haitham and Al-Biruni, proposed other methods which are confirmed to be accurate from the viewpoint of modern astronomy.
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Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe. The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics.
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Baldwin published in 1895 a pamphlet, Hints on teaching Arithmetic. He was author of a text-book on Elementary Solid Geometry (1890) and The Algebra of Coplanar Vectors and Trigonometry (1899). In pure mathematics he published papers in the Transactions of the Cambridge Philosophical Society and the Quarterly Journal of Mathematics. He was elected Fellow of the Royal Society on 1 June 1876, in recognition of his work on the method of moving axes.
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In 1280, Guo completed the calendar, calculating a year to be 365.2425 days, just 26 seconds off the year's current measurement. In 1283, Guo was promoted to director of the Observatory in Beijing and, in 1292, he became the head of the Water Works Bureau. Throughout his life he also did extensive work with spherical trigonometry. After Kublai Khan's death, Guo continued to be an advisor to Kublai's successors, working on hydraulics and astronomy.
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From 1899 he was an adjunct professor at the University of Göttingen, where he taught descriptive geometry and oversaw the collection of mathematical equipment. In 1904 he became a professor at the TH Danzig, where he was rector from 1917 to 1919. He retired in 1936. In his dissertation, he developed a new interpretation of the formulas of spherical trigonometry as a relationship between the invariants of three quadratic forms and their functional determinants.
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Millennial Harbinger, Vol. V, No. XI, p. 712. The early years of operation had four grades. They were compared to an intensive high school education which included all courses: Ray's Higher Arithmetic, two years of Algebra, plane geometry, trigonometry, physics, botany, physiology, psychology, astronomy, physical geography, chemistry, geology, mineralogy, zoology, grammar, spelling, diacritical marks, rhetoric, American and English Literature, classics, U.S. History, English History, ancient, medieval, and modern history, Latin, and instrumental and vocal music.
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In Hong Kong, the syllabus of HKCEE additional mathematics covered three main topics, algebra, calculus and analytic geometry. In algebra, the topics covered include mathematical induction, binomial theorem, quadratic equations, trigonometry, inequalities, 2D-vectors and complex number, whereas in calculus, the topics covered include limit, differentiation and integration. In the HKDSE (i.e. the module 2 of mathematics), some new topics are added: matrix and determinant, and an introduction to the Euler's number.
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215 These Greek and Indian works were translated and expanded by medieval Islamic mathematicians. By the 10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated their values, and were applying them to problems in spherical geometry.Gingerich, Owen. "Islamic astronomy." Scientific American 254.4 (1986): 74-83 The Persian polymath Nasir al-Din al-Tusi has been described as the creator of trigonometry as a mathematical discipline in its own right.
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In mathematics, the Robin boundary condition (; properly ), or third type boundary condition, is a type of boundary condition, named after Victor Gustave Robin (1855-1897).Gustafson, K., (1998). Domain Decomposition, Operator Trigonometry, Robin Condition, Contemporary Mathematics, 218. 432-437. When imposed on an ordinary or a partial differential equation, it is a specification of a linear combination of the values of a function and the values of its derivative on the boundary of the domain.
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Maximilian Steven Percival "Twitch" Williams III is mainly seen as the "brains" of the partnership. He is the one who usually solves or puts the pieces together in the rare crimes the detectives encounter. A brilliant mathematician who excelled at trigonometry, he has used his knowledge of angles to become an excellent marksman. A shooting prodigy, Twitch makes up for his small size with his ability to handle twin pistols with extreme accuracy and efficiency.
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Catoni, D. Boccaletti, R. Cannata, V. Catoni, E. Nichelatti, P. Zampetti. (2008) The Mathematics of Minkowski Space- Time, Birkhäuser Verlag, Basel. Chapter 4: Trigonometry in the Minkowski plane. .Fjelstadt, P. (1986) "Extending Special Relativity with Perplex Numbers", American Journal of Physics 54 :416.Louis Kauffman (1985) "Transformations in Special Relativity", International Journal of Theoretical Physics 24:223–36.Sobczyk, G.(1995) Hyperbolic Number Plane, also published in College Mathematics Journal 26:268–80.
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COFFEE's memory management is handled entirely by a garbage collection process; essentially this means that it looks after itself, and the programmer seldom needs to worry about it. However, it is possible to control the process explicitly when necessary. 3D graphics programming makes extensive use of certain mathematical techniques, notably trigonometry and vector arithmetic. COFFEE is well equipped in this area, with a good set of mathematical functions and a built-in vector datatype.
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Tollet was interested in education; in 1685 William Molyneux, a member of the Dublin society wrote to Halley in London mentioning an eleven-year-old girl that he had trained in arithmetic, algebra, geometry and trigonometry. He also ensured the education of his own daughter. In 1718 he purchased a country home at Betley Hall, Staffordshire for his retirement but died there in 1719. He had married Elizabeth Oakes on the Isle of Man.
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The painting shows much of the details of the inscriptions on the disk and half disk, which make up the top of this particular kind of torquetum. A 14th century instrument, the rectangulus, was invented by Richard of Wallingford. This carried out the same task as the torquetum, but was calibrated with linear scales, read by plumb lines. This simplified the spherical trigonometry by resolving the polar measurements directly into their Cartesian components.
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Business functionalities included percentage change, markup, currency exchange and unit conversions. It also had math capabilities such as trigonometry and graphing. Upscale functionality, at the time of release, included the ability to design your own problem solving equations and storing text directly in the calculator using the letter keyboard on the left side. The calculator could also be connected to a printer using a special cable; which allowed you to print out the generated graphs.
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Formal instruction in numeracy begins at age 6/7 with the four primary operations of arithmetic. Fractions are introduced at age 9/10, decimal numbers and proportions at age 10/11, percentages and rates of interest at age 11/12, algebra at age 12/13. At the secondary level, topics include algebra, geometry, conics, trigonometry, probability, combinatorics and calculus. Descriptive geometry and projective geometry are introduced at age 15/16 and 16/17, respectively.
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With the decline of ancient Greece, the development of maths stagnated in Europe. However the progress of mathematics continued in the East. Du Sautoy describes both the Chinese use of maths in engineering projects and their belief in the mystical powers of numbers. He mentions Qin Jiushao. He describes Indian mathematicians’ invention of trigonometry; their introduction of a symbol for the number zero and their contribution to the new concepts of infinity and negative numbers.
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In 2007, Vibal won the first National Book Development Board (NBDB) Quality Seal Award for its Experiencing Mathematics – Advanced Algebra, Trigonometry and Statistics. Two years later, the Vibal achieved the Quality Seal Award for two of its textbooks: Rainbows in English Grade 5 and Excelling in Mathematics Grade 3. In 2010, Language and Literature IV was accorded the same seal. In 2011, Vibal, Procter & Gamble, Samsung, and Robinsons Supermarket introduced the "eStudyante" program.
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The course introduces concepts such as basic trigonometry, angles of elevation and depression, and methods of proving triangle congruence. Algebra II, advanced Algebra or intermediate algebra has a prerequisite of Algebra I. Historically, intermediate algebra has been a high school level course. The Common Core mathematical standards recognize both the sequential as well as the integrated approach to teaching high-school mathematics, which resulted in increased adoption of integrated math programs for high school.
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A sample photograph showing how the Gibraltar model, on display at the Gibraltar Museum, includes every house and roadway. From 1861 to 1865, Warren worked on surveying Gibraltar. During this time he surveyed the Rock of Gibraltar using trigonometry and with the support of Major-General Frome, he created two long scale detailed models of Gibraltar. One of these was kept at Woolwich, but the other, which survives, is on display at Gibraltar Museum.
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If an apprentice was retained ashore, he would either be boarded in the town, or anywhere convenient such as the house in Grape Lane where there was space. Young also described Cook studying in the attic with the aid of candles provided by Mary Prowd, a family servant. Like any ambitious apprentice, Cook would have studied algebra, geometry, trigonometry and navigation, probably with the help of schoolmasters paid for by the ship owners.
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José Javier Escribano Benito, Eduardo Torroja Caballé from Real Sociedad Matematica Española. In 1869, Torroja became a research fellow at the Astronomical Observatory in Madrid, where he contributed to the geodesic triangulation of Spain, initiated by the General Carlos Ibáñez. While working at that Research Institute, he became Assistant Professor at the Faculty of Sciences. In 1873 he became a full professor of Algebra, Geometry, Trigonometry and Analytic Geometry at the University of Valencia.
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Curriculum for the school included the Latin language, Greek and Roman history, medieval and modern history, English, algebra, trigonometry, chemistry, and physics. In 1891, the California state legislature provided for incorporation of union high school districts. The city of Santa Paula agreed with the Congregational Church Association to convert Santa Paula Academy to a public school and renamed it Santa Paula High School. Santa Paula High School expanded rapidly throughout the early 20th century.
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Grade 9: Religion, Physical Education, English, Global Studies/ A.P. World History, Regents Integrated Algebra, Regents Living Environment, Foreign Language, Latin, Fine Arts, Computer Concepts, Latin Honors. Grade 10: Religion, Physical Education, English, Global Studies/ A.P. World History, Regents Geometry, Regent Chemistry or Earth Science, Foreign Language Two, Art, Health. Grade 11: Religion, Physical Education, Regents English, Regents U.S. History, Regents Algebra2 and Trigonometry, Regents Physics or Chemistry, Regents Foreign Language Three, Approved Electives.
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Magnitsky was born into a peasant family. According to some accounts, he graduated from the Slavic Greek Latin Academy in Moscow. From 1701 and until his death, he taught arithmetic, geometry and trigonometry at the Moscow School of Mathematics and Navigation, becoming its director in 1716. In 1703, Magnitsky wrote his famous Arithmetic (Арифметика; 2,400 copies), which was used as the principal textbook on mathematics in Russia until the middle of the 18th century.
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Under the Caliphate of Córdoba, al-Andalus was a beacon of learning, and the city of Córdoba, the largest in Europe, became one of the leading cultural and economic centres throughout the Mediterranean Basin, Europe, and the Islamic world. Achievements that advanced Islamic and Western science came from al-Andalus, including major advances in trigonometry (Geber), astronomy (Arzachel), surgery (Abulcasis Al Zahrawi), pharmacology (Avenzoar), and agronomy (Ibn Bassal and Abū l-Khayr al-Ishbīlī).
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1900 BC), some have even asserted that the ancient Babylonians had a table of secants.Joseph (2000b, pp.383-84). There is, however, much debate as to whether it is a table of Pythagorean triples, a solution of quadratic equations, or a trigonometric table. The Egyptians, on the other hand, used a primitive form of trigonometry for building pyramids in the 2nd millennium BC. The Rhind Mathematical Papyrus, written by the Egyptian scribe Ahmes (c.
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Guo Shoujing (1231-1316) In China, Aryabhata's table of sines were translated into the Chinese mathematical book of the Kaiyuan Zhanjing, compiled in 718 AD during the Tang Dynasty.Needham, Volume 3, 109. Although the Chinese excelled in other fields of mathematics such as solid geometry, binomial theorem, and complex algebraic formulas, early forms of trigonometry were not as widely appreciated as in the earlier Greek, Hellenistic, Indian and Islamic worlds.Needham, Volume 3, 108–109.
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Quadrance and distance (as its square root) both measure separation of points in Euclidean space. Following Pythagoras's theorem, the quadrance of two points and in a plane is therefore defined as the sum of squares of differences in the x and y coordinates: : Q(A_1, A_2) = (x_2 - x_1)^2 + (y_2 - y_1)^2. The triangle inequality d_3 \leq d_1 + d_2 is expressed under rational trigonometry as (Q_3 - Q_1 - Q_2)^2 \leq 4 Q_1 Q_2 .
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He emphasized religious and moral training and required every student to attend chapel. Students at Mary Sharp, unlike those at other female colleges and academies, studied algebra, geometry, and trigonometry; Latin and Greek; English literature, grammar, and composition; ancient, English, and American history; philosophy and rhetoric; geography and geology; and botany, chemistry, astronomy, and physiology. The college awarded its first degrees in 1855. The economic depression of the 1890s led to its closure in 1896.
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DeskCalc is a simple Calculator that can perform different tasks related to mathematics. It has a simple interface and on the front screen it has some functions or buttons which can perform addition, subtraction, multiplication and division but it is not restricted to these only. DeskCalc can also perform tasks related to trigonometry. The type of the calculator can also be changed into scientific, radical or any other type to use it for different purposes.
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There was a big demand for these books, especially as supplies were constrained by wartime paper shortages. In June 1941 The Times reported that "sailors, soldiers and airmen have helped to bring the figures of Teach Yourself Mathematics (by John Davidson, 1938) and Teach Yourself Trigonometry (by Percival Abbott, 1940) to nearly 50,000 apiece".The Times, 28 June 1941, p.2 Barely two months later the number had risen to 80,000 each.
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Driven by the demands of navigation and the growing need for accurate maps of large areas, trigonometry grew to be a major branch of mathematics. Bartholomaeus Pitiscus was the first to use the word, publishing his Trigonometria in 1595. Regiomontanus's table of sines and cosines was published in 1533. During the Renaissance the desire of artists to represent the natural world realistically, together with the rediscovered philosophy of the Greeks, led artists to study mathematics.
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He was also President of the Mathematical Association in 1900. In 1908 he published A Treatise on Spherical Astronomy,R. S. Ball (1908) A Treatise on Spherical Astronomy Google preview which is a textbook on astronomy starting from spherical trigonometry and the celestial sphere, considering atmospheric refraction and aberration of light, and introducing basic use of a generalised instrument. His work The Story of the Heavens is mentioned in the "Ithaca" chapter of Ulysses.
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Woodrow Wilson National Fellowship Foundation Irène studied in this environment for about two years. Irène and her sister Ève were sent to Poland to spend the summer with their Aunt Bronya (Marie's sister) when Irène was thirteen. Irène's education was so rigorous that she still had a German and trigonometry lesson every day of that break. Irène re-entered a more orthodox learning environment by going back to high school at the Collège Sévigné in central Paris until 1914.
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The family moved to Little Hunting Creek in 1735, then to Ferry Farm near Fredericksburg, Virginia, in 1738. When Augustine died in 1743, Washington inherited Ferry Farm and ten slaves; his older half- brother Lawrence inherited Little Hunting Creek and renamed it Mount Vernon. Washington did not have the formal education his elder brothers received at Appleby Grammar School in England, but he did learn mathematics, trigonometry, and land surveying. He was a talented draftsman and map-maker.
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By using trigonometry the user of an Abney level can determine height, volume, and grade.H. A. Calkins and J. B. Yule, The Abney Level Handbook, United States Forest Service, 1927. Abney levels are made with square tubular bodies so that they may also be used to directly measure the slopes of plane surfaces by simply placing the body of the level on the surface, adjusting the level, and then reading the angle off of the scale.
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The RCW catalogue states the Hα image size is 3'×2. RCW 88 is located about 3300 parsecs (10,000 light years) from us, though other estimates place this at a closer 1800±300 pc. or 1800±200 pc. Assuming the former distance and the diameter as 5'-6' across, finds by simple trigonometry the true size subtends a minimum of 5±1 parsecs (16±3 light-years.) This small emission nebula shows a mean radial velocity of −18 km.
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The English Department includes courses in journalism, speech, composition (language), literature, and other concepts of the English language. The Mathematics Department offers courses in geometry, algebra, trigonometry, precalculus AB calculus, BC calculus, advanced calculus, finance, statistics, and computer science. The Social Studies department has courses in American and world history as well as courses which focus on aspects of society such as law and money. The Science Department offers classes in biology, chemistry, physics, environmental science, and biotechnology.
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Today's precalculus text computes e as the limit of (1 + 1/n)n as n approaches infinity. An exposition on compound interest in financial mathematics may motivate this limit. Another difference in the modern text is avoidance of complex numbers, except as they may arise as roots of a quadratic equation with a negative discriminant, or in Euler's formula as application of trigonometry. Euler used not only complex numbers but also infinite series in his precalculus.
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Boyer pp. 237, 274 One of the earliest works on trigonometry by a northern European mathematician is De Triangulis by the 15th century German mathematician Regiomontanus, who was encouraged to write, and provided with a copy of the Almagest, by the Byzantine Greek scholar cardinal Basilios Bessarion with whom he lived for several years. At the same time, another translation of the Almagest from Greek into Latin was completed by the Cretan George of Trebizond.N.G. Wilson (1992).
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A common use of mnemonics is to remember facts and relationships in trigonometry. For example, the sine, cosine, and tangent ratios in a right triangle can be remembered by representing them and their corresponding sides as strings of letters. For instance, a mnemonic is SOH-CAH-TOA: :Sine = Opposite ÷ Hypotenuse :Cosine = Adjacent ÷ Hypotenuse :Tangent = Opposite ÷ Adjacent One way to remember the letters is to sound them out phonetically (i.e., SOH-CAH-TOA, which is pronounced 'so-ka-'toe-uh' ).
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What Stark didn't know was that his prep-school trigonometry professor and football coach, John Crowe, had sent game films of him to Florida State, where Crowe had been an All-America defensive back in 1958. Stark got a call from a Seminole coach in February. "I had barely heard of Florida State", he says, "but I went down and liked what I saw." He enrolled for the spring semester and competed in the high jump for FSU.
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Campbell attended the Blair Academy, a boarding school in rural Warren County, New Jersey, but did not graduate because of lack of credits for French and trigonometry., chapter 1. He also attended, without graduating, the Massachusetts Institute of Technology (MIT), where he was befriended by the mathematician Norbert Wiener (who coined the term cybernetics) – but he failed German and MIT dismissed him. After one year at Duke University, he graduated with a Bachelor of Science in physics in 1932.
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WIMATS is an application software to transcript mathematical and scientific text input into braille script in braille presses. Based on the Nemeth Code, the output can be printed in a variety of braille embossers. This transcription software was jointly developed by Webel Mediatronics Limited (WML) and International Council for Education of People with Visual Impairment (ICEVI), and was officially launched on 17 July 2006. WIMATS support inputs of arithmetic, algebra, geometry, trigonometry, calculus, vector, set notations and Greek alphabets.
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AP Physics B was supposed to be equivalent to an introductory algebra-based college course in physics, with a laboratory component. The course was non-calculus-based, utilizing algebra and basic trigonometry to solve various physics problems. AP Physics B was divided into five different sections: Newtonian mechanics, fluid mechanics and thermal physics, electricity and magnetism, waves and optics, and atomic and nuclear physics. AP Physics B was replaced in 2014 by AP Physics 1 and 2.
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Born in Brescia in 1747, he begun studying architecture and later was awarded a pension by a wealthy patron to continue his studies. In 1774 he had the chair of physics and mathematics. In 1777 he published his Elements of Geometry and Trigonometry. Thanks to the fame of the book, he became a consultant of the Republic of Venice being among the five physicists who took care of the problem of the floodings of the Brenta river.
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Additionally, a brief introduction to art history is included. The Economics Basic Guide reviews fundamental economic concepts in addition to the basics of macroeconomics and microeconomics. The Language and Literature Basic Guide provides students with a basic grounding in the analysis of literature and introduces key terms such as synecdoche, metonymy, assonance, and aphorism. The Math Basic Guide offers a general overview of major topics in high school math, including algebra, geometry, trigonometry, calculus, and statistics.
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The surveyor locates the point on the ground immediately below the branch tip on one end of the measurements and marks that position. He then moves to opposite side of the crown and locates the point under that branch tip. The spread along that line is the horizontal distance between those two positions. On steeply sloping ground (over 15 degrees) the taped distance between the two points can be corrected to a true horizontal by using basic trigonometry.
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At MathPath, students learn about many math topics that are rarely taught in American schools, or taught in much depth, such as non-Euclidean geometry, advanced Euclidean geometry, number theory, combinatorics, induction, spherical trigonometry, mathematical origami, and the mathematics of card shuffling. They also learn some history of math and work on mathematical writing. Topics vary somewhat each year, depending on instructor interest. As well, students have the opportunity to prepare for contests such as MATHCOUNTS, AMC, or AIME.
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Fine Arts: Visual Arts, Chorus, Dramatic Arts, Band – The Fine Arts department is meant to help teach students how to better understand human ideals and aspiration through artistic expression. It includes performing arts, the visual arts and theater arts. Math – The Mathematics department is meant to help students gain better problem solving, communication, reasoning and connection-making skills. The math studied includes numbers and operations, algebra, functions, geometry, trigonometry, statistics, probability, discrete mathematics, analysis and calculus.
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Originally, various traditional methods were used to determine the qibla, and from the eighth century onwards Muslim astronomers developed methods based on mathematical astronomy, especially computations techniques based on spherical trigonometry using a location's latitudes and longitudes. In the fourteenth century, the astronomer Shams al-Din al-Khalili compiled a table containing the qibla for all latitudes and longitudes. Scientific instruments, such as the astrolabe, helped Muslims orient themselves for prayer facing the city of Mecca.
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In pursuing the history in years before Lorentz enunciated his expressions, one looks to the essence of the concept. In mathematical terms, Lorentz transformations are squeeze mappings, the linear transformations that turn a square into a rectangles of the same area. Before Euler, the squeezing was studied as quadrature of the hyperbola and led to the hyperbolic logarithm. In 1748 Euler issued his precalculus textbook where the number e is exploited for trigonometry in the unit circle.
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From the 9th century onward they were using spherical trigonometry and map projection methods to determine these quantities accurately. The calculation is essentially the conversion of the equatorial polar coordinates of Mecca (i.e. its longitude and latitude) to its polar coordinates (i.e. its qibla and distance) relative to a system whose reference meridian is the great circle through the given location and the Earth's poles, and whose polar axis is the line through the location and its antipodal point.
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An average student, however, will end with at least Algebra 2 & Trigonometry in their senior year. Students who pass the Integrated Algebra or Algebra I Regents at the end of the 8th grade are placed in Geometry instead of Algebra in their freshmen year. These students are then invited to take either Pre Calculus or AP Calculus their senior year. Students need not take Pre Calculus in order to take AP Calculus; however, it is recommended.
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Yi Xing, the mathematician and Buddhist monk was credited for calculating the tangent table. Instead, the early Chinese used an empirical substitute known as chong cha, while practical use of plane trigonometry in using the sine, the tangent, and the secant were known. Yi Xing was famed for his genius, and was known to have calculated the number of possible positions on a go board game (though without a symbol for zero he had difficulties expressing the number).
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Li Zhi on the other hand, investigated on a form of algebraic geometry based on tiān yuán shù. His book; Ceyuan haijing revolutionized the idea of inscribing a circle into triangles, by turning this geometry problem by algebra instead of the traditional method of using Pythagorean theorem. Guo Shoujing of this era also worked on spherical trigonometry for precise astronomical calculations. At this point of mathematical history, a lot of modern western mathematics were already discovered by Chinese mathematicians.
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Binocular stereo vision method requires two identical cameras with parallel optical axis to observe one same object, acquiring two images from different points of view. In terms of trigonometry relations, depth information can be calculated from disparity. Binocular stereo vision method is well developed and stably contributes to favorable 3D reconstruction, leading to a better performance when compared to other 3D construction. Unfortunately, it is computationally intensive, besides it performs rather poorly when baseline distance is large.
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Crüger published treatises on many scientific subjects and contributed to the progress of trigonometry, geography and astronomy, and to the development of astronomical instruments. In the years 1627 to 1630, Crüger was the teacher of a teenager of the Hewelke family who would become known later as Johannes Hevelius, the astronomer. After Hevelius had returned to Danzig in 1634, the dying Crüger appealedSelenographia Geschichte der Mondkarten to him to pursue astronomy. Hevelius gratefully mentions Crüger in his Machina coelestis.
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Linear features are measured with very similar methods, where "plunge" is the dip angle and "trend" is analogous to the dip direction value. Apparent dip is the name of any dip measured in a vertical plane that is not perpendicular to the strike line. True dip can be calculated from apparent dip using trigonometry if the strike is known. Geologic cross sections use apparent dip when they are drawn at some angle not perpendicular to strike.
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In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity) states that for any real number and integer it holds that :\big(\cos (x) + i \sin (x)\big)^n = \cos (nx) + i \sin (nx), where is the imaginary unit (). The formula is named after Abraham de Moivre, although he never stated it in his works. The expression is sometimes abbreviated to . The formula is important because it connects complex numbers and trigonometry.
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Its first principal was Edward Mann Butler, one of Kentucky's most prominent educators and a man who later became the state's most trusted historian. The school offered both high school and college level courses in English, geography, French, Latin, geometry, and trigonometry. It had an average of 45 to 50 students, who paid $20 for a six- month term. Despite the school's early success, pressure from newly established public schools would force its closure in 1829.
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Clara Eliza Smith (May 20, 1865 – May 12, 1943) was an American mathematician specializing in complex analysis who became the Helen Day Gould Professor of Mathematics at Wellesley College. Smith was the daughter of Georgiana and Edward Smith, of Northford, Connecticut. She studied at Mount Holyoke College, then a seminary, while also studying art at Yale University. Her studies in the seminary program included geometry and trigonometry, but the college did not offer degrees at that time.
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Alquist graduated with a Bachelor of Arts degree from MacMurray College in 1966 and a Master of Arts degree from Washington University in St. Louis in 1967. Her professional career began as an algebra and trigonometry teacher and a counselor in the public schools. In 1981, she served as PTA president and then beginning in 1983 served eight years as a member and then president of the board of education of the Cupertino Union School District.
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1, No. 1, pp. 18–25. The laws of rational trigonometry, being algebraic, introduce subtleties into the solutions of problems, such as non-additivity of quadrances of collinear points (via the triple quad formula) or spreads of concurrent lines (via the triple spread formula) to give rational-valued outputs. By contrast, in the classical subject linearity is incorporated into distance and angular measurements to simplify these operations, albeit by 'transcendental' techniques employing real numbers entailing approximate valued output.
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In his On the Sector Figure, he stated the law of sines for plane and spherical triangles, and provided proofs for this law. According to Glen Van Brummelen, "The Law of Sines is really Regiomontanus's foundation for his solutions of right-angled triangles in Book IV, and these solutions are in turn the bases for his solutions of general triangles."Glen Van Brummelen (2009). "The mathematics of the heavens and the earth: the early history of trigonometry".
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Right angle triangle A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the hypotenuse (side c in the figure). The sides adjacent to the right angle are called legs (or catheti, singular: cathetus).
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Another theory is that the Babylonians subdivided the circle using the angle of an equilateral triangle as the basic unit, and further subdivided the latter into 60 parts following their sexagesimal numeric system. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle. A chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree.
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He continued to wear, throughout his life, the three medals and Sebastopol clasp which were awarded to him. At the Royal Hospital School he would have been instructed in mathematics as were necessary for the study of navigation and nautical astronomy, including geometry, algebra, and elementary trigonometry; and, in connection with these, the elements of astronomy, with mathematical and physical geography."Greenwich Royal Hospital Schools", The Illustrated London News, February 19th, 1848, accessed 17 October 2013.
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Students must pass complete programs in science and mathematics including biology, chemistry, physics, algebra, geometry, trigonometry, and calculus. Graduates meet or exceed the Minnesota Graduation Standards in all areas. Students may be moved into a different mathematics course level depending on performance. Since its founding, MSA has encouraged its juniors and seniors to take advantage of Minnesota's Post Secondary Enrollment Option, in which high school students can take courses at a college or university in Minnesota, tuition paid by the state of Minnesota.
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During a conversation with Bill Jenkins, Bowman became excited by the possibility of a career that combined his interest in quantitative analysis with public health. He briefly joined the mathematical statistics programme at Duke University before realising that he wanted to focus on biostatistics. He eventually moved to the University of Michigan to specialise in biostatistics, where he completed coursework in epidemiology and earned a master's degree in 1995. Whilst a graduate student Bowman taught trigonometry at the Washtenaw Community College.
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The idea of using hours of equal time length throughout the year was the innovation of Ibn al-Shatir in 1371, based on earlier developments in trigonometry by al-Battānī. Ibn al- Shatir was aware that "using a gnomon that is parallel to the Earth's axis will produce sundials whose hour lines indicate equal hours on any day of the year." His sundial is the oldest polar-axis sundial still in existence. The concept later appeared in Western sundials from at least 1446.
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He completed a MSc degree with Applied Mathematics major. Vaidya's first stint at teaching was at the Dharmendra Singhji College in Rajkot, where he joined as a lecturer in 1940, soon after completing his MSc examinations. Vaidya taught trigonometry and arithmetic to undergraduate students. The college was then managed by the St Xavier's College, Bombay for half the term, after which the royal family of Rajkot under His Highness Pradyumansinhji Lakhajirajsinhji, the 14th Thakore Saheb of Rajkot, took control of the college.
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Cantor's father had been a member of the Saint Petersburg stock exchange; when he became ill, the family moved to Germany in 1856, first to Wiesbaden, then to Frankfurt, seeking milder winters than those of Saint Petersburg. In 1860, Cantor graduated with distinction from the Realschule in Darmstadt; his exceptional skills in mathematics, trigonometry in particular, were noted. In August 1862, he then graduated from the "Höhere Gewerbeschule Darmstadt", now the Technische Universität Darmstadt. In 1862, Cantor entered the Swiss Federal Polytechnic.
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Doug Manchester characterizes the topic of the book as "recreational engineering". It only requires a standard background in mathematics including basic geometry, trigonometry, and a small amount of calculus. Owen Smith calls it "a great book for engineers and mathematicians, as well as the interested lay person", writing that it is particularly good at laying bare the mathematical foundations of seemingly-simple problems. Similarly, Ronald Huston recommends it to "mathematicians, engineers, and physicists", as well as interested members of the general public.
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He became a full professor at the Grande école on 19 November 1869. There he was the head of the Mathematics Department and then became its rector. He retired from the Grande école (Visoka škola) which by then was soon-to-become the newly-formed University of Belgrade after 33 years of dedicated educational work. Josimović wrote university textbooks in Serbia in trigonometry, mathematics, mechanics, geometry, descriptive geometry and perspective, as well as a textbook on civil architecture and road construction.
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Herget taught astronomy at the University of Cincinnati. He was a pioneer in the use of machine methods, and eventually digital computers, in the solving of scientific and specifically astronomical problems (for example, in the calculation of ephemeris tables for minor planets). During World War II he applied these same talents to the war effort, helping to locate U-boats by means of the application of spherical trigonometry. Herget established the Minor Planet Center at the university after the war in 1947.
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Scan angle is the optical angle that a set of scanners normally achieves at a given rate of points per second. The wider the angle, the larger the area the scan covers—but the more difficult it is for the scanner accurately track due to physical limitations of the scanner mechanism. For example, a 20 degree angle provides a 3.5 metre scanned area at a distance of 10 metres from scanner to screen. Scan angles can be calculated using trigonometry.
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Flatness refers to the shape of a liquid's free surface. On planet Earth, the flatness of a liquid is a function of the curvature of the Earth, and from trigonometry, can be found to deviate from true flatness by approximately 19.6 nanometers over an area of 1 square meter, a deviation which is dominated by the effects of surface tension. This calculation using the Earth's mean radius at sea level, however a liquid will be slightly flatter at the poles.
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In 1729, when he was 16, he returned to Spain and applied for entry to the Royal Company of Marine Guards, the Spanish military school for naval officers. He entered the academy in 1730 and studied modern technical and scientific studies subjects such as geometry, trigonometry, astronomy, navigation, hydrography, and cartography. He also completed his education in the humanities with classes in drawing, music, and dancing. He earned the reputation of being an outstanding student and his fellow students called him Euclid.
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He wanted students to be educated in the works of the leading scientists of the ancient world, saying that the professor of geometry should teach Euclid's Elements, Apollonius's Conics, and the works of Archimedes; tuition in trigonometry was to be shared by the two professors. As many students would have had little mathematical knowledge, the professors were also permitted to provide instruction in basic mathematics in English (as opposed to Latin, the language used in education at Oxford at the time).
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Gunter's scale or Gunter's rule, generally called the "Gunter" by seamen, is a large plane scale, usually long by about 1½ inches broad (40 mm), engraved with various scales, or lines. On one side are placed the natural lines (as the line of chords, the line of sines, tangents, rhumbs, etc.), and on the other side the corresponding artificial or logarithmic ones. By means of this instrument questions in navigation, trigonometry, etc., are solved with the aid of a pair of compasses.
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Bretschneider's formula generalizes Brahmagupta's formula for the area of a cyclic quadrilateral, which in turn generalizes Heron's formula for the area of a triangle. The trigonometric adjustment in Bretschneider's formula for non-cyclicality of the quadrilateral can be rewritten non-trigonometrically in terms of the sides and the diagonals and to giveJ. L. Coolidge, "A historically interesting formula for the area of a quadrilateral", American Mathematical Monthly, 46 (1939) 345–347. (JSTOR)E. W. Hobson: A Treatise on Plane Trigonometry.
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The slope of the rake is measured by the number of horizontal units it takes for one vertical unit measured in the direction of the slope, or by the equivalent percentage. A rake of one horizontal unit to one vertical unit (1 in 1) would give an angle of 45° from the horizontal. Rakes of 1 in 18 (5.56%) to 1 in 48 (2.08%) were more common. Converting the rake ratio to an angle requires the application of some basic trigonometry.
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In New York State, middle school and high school students are expected to pass their Regents Exams with a 65 or higher in order to graduate and receive the Regents Diploma. In the English Comprehensive test taken in 2014, 80% of students passed and 85% of students passed the general education exams for the Regents that same year. In Mathematics, 58% of students passed the Integrated Algebra Regents, 52% passed the Geometry Regents, 67% passed the Algebra 2/ Trigonometry Regents.
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Modern gnomonics has its root in the nascent European astronomy of the 16th Century. The first works, in Latin, were published by Sebastian Münster in 1531 and Oronce Fine in 1532, rapidly followed by books in French. At the end of the 17th century, gnomonics developed notably in the application of spherical trigonometry. Several methods, both graphical and analytical, were published in books which allowed the creation of sundials of greater or lesser precision to be placed on buildings and in gardens.
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Bells Creek rises in the western suburbs of Sydney about west by south of the Woodstock trigonometry station in , and flows generally north by east before reaching its confluence with Eastern Creek, east of the suburb of . The course of the creek is approximately . In 2005, the Bells Creek catchment area was rated the fourteenth-highest polluting catchment out of the twenty-two catchments in the Blacktown local government area. Bells Creek catchment can be split into two defined halves.
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Reedy Creek rises in the western suburbs of Sydney about north-west of the Melville trigonometry station in the Memorial Park located in the suburb of . The creek flows generally north-east by north before reaching its confluence with Eastern Creek, in the suburb of , west of Sydney Motorsport Park. The course of the creek is approximately . In 2005, the Reedy Creek catchment area was rated the lowest polluting catchment out of the twenty-two catchments in the Blacktown local government area.
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Diagram illustrating a method proposed and used by Al-Biruni (973–1048) to estimate the radius and circumference of the Earth The Muslim scholars, who held to the spherical Earth theory, used it to calculate the distance and direction from any given point on the earth to Mecca. This determined the Qibla, or Muslim direction of prayer. Muslim mathematicians developed spherical trigonometry which was used in these calculations.David A. King, Astronomy in the Service of Islam, (Aldershot (U.K.): Variorum), 1993.
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Problems arose in the translation of technical jargon, particularly in regards to the new electronics that were built into the Mirage such as three dimensional trigonometry based resolvers, transistors and printed circuit boards. This made it difficult for the technical team to construct accurate English blueprints. Differences in French technical drawings and the use of the metric system, which had not yet been adopted in Australia, also increased the time and cost of the production of designs that were usable by Australian tradesmen.
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The first courses in mathematics were offered in 1760 when undergraduates enrolled in classes such as algebra, trigonometry, geometry, and conic sections. Walter Minto was one of the earliest teachers of mathematics beginning in 1787. By the beginning of the twentieth century, the department became "one of the world's great centers of mathematical teaching and research." President Woodrow Wilson appointed Henry Burchard Fine as dean of the faculty in 1903 and later as the first chairman of the Department of Mathematics in 1905.
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He was also a pioneer in spherical trigonometry. In 830 AD, Habash al-Hasib al-Marwazi produced the first table of cotangents. Muhammad ibn Jābir al-Harrānī al-Battānī (Albatenius) (853-929 AD) discovered the reciprocal functions of secant and cosecant, and produced the first table of cosecants for each degree from 1° to 90°. By the 10th century AD, in the work of Abū al-Wafā' al-Būzjānī, Muslim mathematicians were using all six trigonometric functions.Boyer (1991) p. 238.
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The Kindra Creek (technically a river) rises near Warre Warral trigonometry station southwest of , sourced by runoff from the Great Dividing Range. The creek flows generally southwest and then northwest before reaching its confluence with the Mimosa Creek to form Redbank Creek (itself a tributary of a series of watercourses that combine to form an old anabranch of the Murrumbidgee River now part of an irrigation channel of the Murrumbidgee Irrigation Area), north of the locality of . The creek descends over its course.
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In practice, it was generally simpler to have the aircraft fly in such a way to zero out any sideways motion before the drop, and thereby eliminate this factor. This is normally accomplished using a common flying techniques known as crabbing or sideslip. Bombsights are sighting devices that are pointed in a particular direction, or aimed. Although the solution outlined above returns a point in space, simple trigonometry can be used to convert this point into an angle relative to the ground.
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A geodesic on an oblate ellipsoid The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an oblate ellipsoid, a slightly flattened sphere. A geodesic is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface. The solution of a triangulation network on an ellipsoid is therefore a set of exercises in spheroidal trigonometry .
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After 1820, Day taught mental and moral philosophy, and in 1838 published An Inquiry Respecting the Self-determining Power of the Will and A Course of Mathematics containing The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying; and in 1841 An Examination of President Edwards's _Inquiry on the Freedom of the Will_. He also contributed numerous articles to periodicals, and published a few sermons. Dat was responsible for the publication of "The Yale Report of 1828" defending the classical curriculum.
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In East Prussia the concept Gewerbeschule stems from Christian Peter Wilhelm Beuth opening the Gewerbeinstitut zur Industrieförderung (commercial institute for the advancement of industry) which he call a "Gewerbeschule". It took youngsters in their final three years of secondary education (from 12 to 16). It trained the students in geometry, arithmetic, physics, chemistry, technical- and freehand drawing, trigonometry, statics, mechanics and engineering. On completion, the youngsters could find work in engineering, the textile and chemical industries or move onto further education.
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AP Physics B was an Advanced Placement Physics course equivalent to a year- long introductory college course in basic physics concepts. High school students studied Newtonian mechanics, electromagnetism, fluid mechanics, thermal physics, waves, optics, atomic and nuclear physics in preparation for a cumulative exam given each May. The course was algebra-based and involved algebra and trigonometry to solve various physics problems. This course also helped prepare students for the SAT Subject Test in Physics, also administered by the College Board.
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She wore utilitarian clothes instead of the fashionable garments worn by many women of the day and she was described as "strong willed" at a time when, in contrast, a man might have been described as highly principled. As a mathematics professor, she was described as controversial. She questioned the truth of the Bible in front of students. She had very high standards of education, giving more than half of her students D grades during the first year she taught from her trigonometry book.
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In 1840 Tate became master of the mathematical and scientific department at the Battersea teacher training college; this was a private venture founded in 1839–40 by James Kay-Shuttleworth. Kay-Shuttleworth recruited Tate and two Scots, William Horne and Walter McLeod, to launch what was a new initiative in training, and textbook writing. Tate went on to write educational works on mathematics, mechanics, drawing, and natural science. His Principles of Geometry, Mensuration, Trigonometry, Land Surveying, and Levelling (London, 1848) was translated into Hindustani.
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In mathematics (in particular geometry and trigonometry) and all natural sciences (e.g. astronomy and geophysics), the angular distance (a. k. a. angular separation, apparent distance, or apparent separation) between two point objects, as viewed from a location different from either of these objects, is the angle of length between the two directions originating from the observer and pointing toward these two objects. Angular distance shows up in the classical mechanics of rotating objects alongside angular velocity, angular acceleration, angular momentum, moment of inertia and torque.
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In 1854, when his family returned to Philadelphia, he became a student at that city's Institute for Colored Youth (ICY). Managed by the Society of Friends (Quakers), ICY's curriculum included classical study of Latin, Greek, geometry, and trigonometry. While a student at ICY, Catto presented papers and took part in scholarly discussions at "a young men's instruction society". Led by fellow ICY student Jacob C. White Jr., they met weekly at the ICY (which eventually was renamed as the Banneker Institute, in honor of Benjamin Banneker).
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Following the acceptance of heliocentrism and equal hours, as well as advances in trigonometry, sundials appeared in their present form during the Renaissance, when they were built in large numbers. In 1524, the French astronomer Oronce Finé constructed an ivory sundial, which still exists; later, in 1570, the Italian astronomer Giovanni Padovani published a treatise including instructions for the manufacture and laying out of mural (vertical) and horizontal sundials. Similarly, Giuseppe Biancani's Constructio instrumenti ad horologia solaria (c. 1620) discusses how to construct sundials.
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The Cambridge had been preceded by the Sinclair Executive, Sinclair's first pocket calculator, in September 1972. At the time the Executive was smaller and noticeably thinner than any of its competitors, at , fitting easily into a shirt pocket. A major factor in the Cambridge's success was its low price; the Cambridge was launched in August 1973, selling for ( + VAT) fully assembled or ( + VAT) as a kit. An extensive manual explained how to calculate functions such as trigonometry, n-th root extraction and compound interest on the device.
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The Boydell Press, 1995, p. 83. He began his formal studies at Caen, moving to Paris in 1642. Du Hamel demonstrated an early aptitude for scholarly work, and at the age of eighteen published an explanation of the work of Theodosius of Bithynia called Sphériques de Théodose, to which he added a treatise on trigonometry. He also showed an interest in a religious career, entering the Congregation of the Oratory in 1643, choosing them over other sects due to their focus on service and scholarship.
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Napier was famous for his devices to assist with these issues of computation. He invented a well-known mathematical artifact, the ingenious numbering rods more quaintly known as “Napier's bones,” that offered mechanical means for facilitating computation. In addition, Napier recognized the potential of the recent developments in mathematics, particularly those of prosthaphaeresis, decimal fractions, and symbolic index arithmetic, to tackle the issue of reducing computation. He appreciated that, for the most part, practitioners who had laborious computations generally did them in the context of trigonometry.
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Irene Kirke Leache was born in 1839 on a farm, Wood Park, in Fauquier County, Virginia to Jane Roberts (née Hunton) and Dr. Jesse Willett Leache. Utilizing her father's extensive library, Leache was self-taught in algebra, calculus, geometry and trigonometry, as well as the German language. She left the family home for Westmoreland County when she was hired by the Carter family to teach their children. At the onset of the Civil War, she returned to her home to find their crops ruined.
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The departure of Svetlana called for a radical change in the musical style of the band – instead of replacing the string instruments with another musician, Snipers acquired a keyboardist (first Alexei Samarin, then Airat Sadykov). February 2003 saw the band give their largest yet concert at the famous Moscow sports arena Luzhniki. A new acoustic album Trigonometriya ("Trigonometry") is recorded during a concert at Moscow Art Theatre in May 2003. The band's 10th anniversary is celebrated with a large concert and a party at the B2 club.
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He also examined Indian concepts in trigonometry. His Elements of Geometry first appeared in 1795 and has passed through many editions; his Outlines of Natural Philosophy (2 vols., 1812–1816) consist of the propositions and formulae which were the basis of his class lectures. Playfair's contributions to pure mathematics were not considerable, his papers "On the Arithmetic of Impossible Quantities" and "On the Causes which Affect the Accuracy of Barometrical Measurements", and his Elements of Geometry, all already referred to, being the most important.
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If we are willing to accept a possible error of 0.5%, we can use formulas of spherical trigonometry on the sphere that best approximates the surface of the earth. The shortest distance along the surface of a sphere between two points on the surface is along the great-circle which contains the two points. The great-circle distance article gives the formula for calculating the distance along a great-circle on a sphere about the size of the Earth. That article includes an example of the calculation.
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A sickly child, Gordon Childe was educated at home for several years, before receiving a private-school education in North Sydney. In 1907, he began attending Sydney Church of England Grammar School, gaining his Junior Matriculation in 1909 and Senior Matriculation in 1910. At school he studied ancient history, French, Greek, Latin, geometry, algebra, and trigonometry, achieving good marks in all subjects, but he was bullied because of his physical appearance and unathletic physique. In July 1910 his mother died; his father soon remarried.
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A standard ruler is an astronomical object for which the actual physical size is known. By measuring its angular size in the sky, one can use simple trigonometry to determine its distance from Earth. In simple terms, this is because objects of a fixed size appear smaller the further away they are. Measuring distances is of great importance in cosmology, as the relationship between the distance and redshift of an object can be used to measure the expansion rate and geometry of the Universe.
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For telescopic angles, the approximations of \sin(\alpha) = \tan(\alpha) = \alpha greatly simplify the trigonometry, enabling one to scale objects measured in milliradians through a telescope by a factor of 1000 for distance or height. An object 5 meters high, for example, will cover 1 mrad at 5000 meters, or 5 mrad at 1000 meters, or 25 mrad at 200 meters. Since the radian expresses a ratio, it is independent of the units used; an object 6 feet high covering 1 mrad will be 6000 feet distant.
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In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. In topology, it is often denoted as because it is a one-dimensional unit -sphere. If is a point on the unit circle's circumference, then and are the lengths of the legs of a right triangle whose hypotenuse has length 1.
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Since he never had been to high school, he pursued private studies of languages and mathematics in Ansbach, in 1796. In 1797, he came to Berlin, where he worked under the astronomer Johann Elert Bode as a geometer, and was involved with astronomical and geodetic studies. From 1804 to 1806, he was the leader of a team which worked on the survey of Ansbach. In 1808, he was invited by Joseph von Utzschneider to Munich to work on trigonometry for the newly formed Tax Survey Commission.
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Episode 2- The class think Mr. North has become nice, but it turns out to be his twin brother, Neil, who is as different in temperament from his brother as he could possibly be. He makes learning fun through musical geography and trampolining trigonometry, but it doesn't last long- Mr. North returns, badder than ever. Episode 3- The gang go on an end- of-term trip to a summer camp. They discover that their arch enemy, Basher Baines', school, are on the trip as well.
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Cuno Hoffmeister (2 February 1892 – 2 January 1968) was a German astronomer, observer and discoverer of variable stars, comets and minor planets, and founder of Sonneberg Observatory. Born in Sonneberg in 1892 to Carl and Marie Hoffmeister, Cuno Hoffmeister obtained his first telescope in 1905 and became an avid amateur astronomer. After his father lost most of his money in 1914, Hoffmeister had to leave school in 1916 to start an apprenticeship in his father's company. During this time he continued to study spherical mathematics and trigonometry.
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The Encyclopædia Britannica: A Dictionary of Arts, Sciences, Literature and General Information, Hugh Chisholm The table of sines by the Indian mathematician, Aryabhata, were translated into the Chinese mathematical book of the Kaiyuan Zhanjing, compiled in 718 AD during the Tang Dynasty.Needham, Volume 3, 109. Although the Chinese excelled in other fields of mathematics such as solid geometry, binomial theorem, and complex algebraic formulas,early forms of trigonometry were not as widely appreciated as in the contemporary Indian and Islamic mathematics.Needham, Volume 3, 108-109.
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Departure p and the difference in latitude ΔφAB can be worked out with simple trigonometry. Plane sailing (also, colloquially and historically, spelled plain sailing) is an approximate method of navigation over small ranges of latitude and longitude. With the course and distance known, the difference in latitude ΔφAB between A and B can be found, as well as the departure, the distance made good east or west. The difference in longitude ΔλAB is unknown and has to be calculated using meridional parts as in Mercator sailing.
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The college was founded by Colonel John Le Marchant at the Antelope Inn in 1799 as a facility for training junior officers in the British Army who aspired to staff duties. Training was provided in trigonometry, geometry, French language and siege warfare. The facilities proved too small and the institution moved to a building in West Street in Farnham in 1813 before being redesignated the Senior Division of the Royal Military College, Sandhurst in 1820 and then becoming the Staff College, Camberley in 1858.
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In Macfarlane's paper there is an effort to produce "trigonometry on the surface of the equilateral hyperboloids" through the algebra of hyperbolic quaternions, now re-identified in an associative ring of eight real dimensions. The effort is reinforced by a plate of nine figures on page 181. They illustrate the descriptive power of his "space analysis" method. For example, figure 7 is the common Minkowski diagram used today in special relativity to discuss change of velocity of a frame of reference and relativity of simultaneity.
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He also wrote a treatise, Maqala fi ma'rifat as-samt li-aiy sa'a aradta wa fi aiy maudi aradta ("On the Determination of the Azimuth for an Arbitrary Time and an Arbitrary Place"), his only known surviving work on astronomy. In it, he provided two graphical methods and an arithmetic one of calculating the azimuth—the angular measurement of a heavenly object's location. The arithmetic method corresponds to the cosine rule in spherical trigonometry, and was later used by Al-Battani (c. 858 – 929).
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MWD typically concerns measurement taken of the wellbore (the hole) inclination from vertical, and also magnetic direction from north. Using basic trigonometry, a three-dimensional plot of the path of the well can be produced. Essentially, a MWD operator measures the trajectory of the hole as it is drilled (for example, data updates arrive and are processed every few seconds or faster). This information is then used to drill in a pre-planned direction into the formation which contains the oil, gas, water or condensate.
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Abraham de Moivre (; 26 May 166727 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He moved to England at a young age due to the religious persecution of Huguenots in France beginning in 1685. He was a friend of Isaac Newton, Edmond Halley, and James Stirling. Among his fellow Huguenot exiles in England, he was a colleague of the editor and translator Pierre des Maizeaux.
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Holmboe also taught mathematics at a military college, from 1826 until his death, and was promoted to professor at the Royal Frederick University in 1834. His later publications include Stereometrie (Stereometry) (1833), Plan- og sfærisk Trigonometrie (Plan and Spherical Trigonometry) (1834), and Lærebog i den høiere Mathematik (Textbook of Advanced Mathematics) (1849). Holmboe was an influence on other mathematicians as well as Abel, including Ole Jacob Broch (born 1818). At the university, Holmboe again met Christopher Hansteen, who had become a professor there in 1816.
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Fig. 1 – A triangle. The angles (or ), (or ), and (or ) are respectively opposite the sides , , and . In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles. Using notation as in Fig. 1, the law of cosines states :c^2 = a^2 + b^2 - 2ab\cos\gamma, where denotes the angle contained between sides of lengths and and opposite the side of length .
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At the conclusion of the one-year course, students take the New York State Regents exam for Algebra II. This is the last Regents exam in mathematics students could take. Like the former "Math B" Regents, it is considered one of the hardest High School Regents examinations, along with the Physical Setting/Chemistry regents and the Physical Setting/Physics regents. The Algebra 2/Trigonometry exam was given from June 2010 through January 2017 and the new Algebra II Exam has been given since June 2016.
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Cabri Geometry is a commercial interactive geometry software produced by the French company Cabrilog for teaching and learning geometry and trigonometry... It was designed with ease-of-use in mind. The program allows the user to animate geometric figures, proving a significant advantage over those drawn on a blackboard. Relationships between points on a geometric object may easily be demonstrated, which can be useful in the learning process. There are also graphing and display functions which allow exploration of the connections between geometry and algebra.
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In trigonometry and geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly (trilateration). The point can then be fixed as the third point of a triangle with one known side and two known angles. For acoustic localization this means that if the source direction is measured at two or more locations in space, it is possible to triangulate its location.
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Deer and wallabies are a not uncommon sight, with occasional snakes and feral goats seen. The Mount Kembla Summit Track goes along the same small stretch of dry bush that begins the Ring Track but then branches to the left after a map/information stand. It climbs gradually up the summit ridge and on to the two summit plateaus, one by one, before going along the second to the trigonometry station. The plateaus are both thin and go in an east–west direction along the ridge.
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Euclid showed in Book XIII, Proposition 10 of his Elements that the area of the square on the side of a regular pentagon inscribed in a circle is equal to the sum of the areas of the squares on the sides of the regular hexagon and the regular decagon inscribed in the same circle. In the language of modern trigonometry, this says: :\sin^2 18^\circ +\sin^2 30^\circ =\sin^2 36^\circ . Ptolemy used this proposition to compute some angles in his table of chords.
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As the laws of rational trigonometry give algebraic (and not transcendental) relations, they apply in generality to algebraic number fields beyond the rational numbers. Specifically, any finite field which does not have characteristic 2 reproduces a form of these laws, and thus a finite field geometry., page 1. Another version of this article is at Le Anh Vinh, Dang Phuong Dung (2008), "Explicit tough Ramsey Graphs ", Proceedings of International Conference on Relations, Orders and Graphs: Interaction with Computer Science 2008, Nouha Editions, 139–146.
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Their house is now the Captain Cook Memorial Museum. Cook was taken on as a merchant navy apprentice in their small fleet of vessels, plying coal along the English coast. His first assignment was aboard the collier Freelove, and he spent several years on this and various other coasters, sailing between the Tyne and London. As part of his apprenticeship, Cook applied himself to the study of algebra, geometry, trigonometry, navigation and astronomy—all skills he would need one day to command his own ship.
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Later, he co-authored his Calculus with Trigonometry and Analytic Geometry textbook with Frank Wang, then a graduate student in mathematics at MIT. As Saxon published books that he authored or co-authored, he found other authors to write books all the way down to kindergarten level. Stephen Hake of El Monte, California authored books for 5th, 6th, 7th and 8th grades titled Math 54, Math 65, Math 76 and Math 87. Nancy Larson of West Haven, Connecticut authored programs titled Math K, Math 1, Math 2 and Math 3.
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The greatest mathematician of antiquity is often held to be Archimedes (c. 287–212 BC) of Syracuse. He developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus. Other notable achievements of Greek mathematics are conic sections (Apollonius of Perga, 3rd century BC), trigonometry Hipparchus of Nicaea (2nd century BC), and the beginnings of algebra (Diophantus, 3rd century AD).
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The idea of using hours of equal length throughout the year was the innovation of Abu'l-Hasan Ibn al-Shatir in 1371, based on earlier developments in trigonometry by Muhammad ibn Jābir al- Harrānī al-Battānī (Albategni). Ibn al-Shatir was aware that "using a gnomon that is parallel to the Earth's axis will produce sundials whose hour lines indicate equal hours on any day of the year". His sundial is the oldest polar- axis sundial still in existence. The concept appeared in Western sundials starting in 1446.
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Another work, Kifayat al-qanu' fi al-'amal bi'r-rub' al-maqtu was written in Arabic and was a commentary on the works of an earlier muwaqqit Sibt al-Maridini. His other works, Kifayat al-waqt, also known as Risala fi al-muqantarat (1529), was written in Turkish and describes an instrument called the astrolabic quadrant, as well as other themes in geometry, trigonometry, and astronomy. Today 120 copies of this work are extant in various libraries. His Tashil al-miqat (1529) discusses the science of timekeeping and the sine quadrant (al-rub' al- mujayyab).
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He published a series of textbooks on algebra, geometry and trigonometry, analytical geometry, and calculus. He wrote treatises on natural science for the use of his pupils; some of these were lithographed and others were privately printed at Woodstock: Theoretical Mechanics in 1873; Animal Physics in 1874; and Principles of Cosmography in 1878. At Georgetown Observatory, in 1850, Sestini made a series of sunspot drawings, which were engraved and published (44 plates) as "Appendix A" of the Naval Observatory volume for 1847, printed in 1853. The work was republished in 1898.
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Among his more famous pupils were Lord Kelvin, James Clerk Maxwell and Isaac Todhunter. Francis Galton praised his teaching style: He also coached Edward Routh who went on to be Senior Wrangler and himself a prodigious "wrangler maker".. In 1833, Hopkins published Elements of Trigonometry and became distinguished for his mathematical knowledge. There was a famous story that the theory of George Green (1793–1841) was almost forgotten. In 1845, Lord Kelvin (William Thomson, a young man in 1845) got some copies of Green's 1828 short book from William Hopkins.
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In 1831, the Surveyor General of India George Everest was searching for a brilliant young mathematician with a particular proficiency in spherical trigonometry, the math teacher of Indian "Hindu" College John Tytler recommended his pupil Sikdar, then only 19. Sikdar joined the Great Trigonometric Survey in December 1831 as a "computer" at a salary of thirty rupees per month. Soon he was sent to Sironj (near Dehradun) where he excelled in geodetic survey. Apart from mastering the usual geodetic processes, he invented quite a few of his own.
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Najm al‐Dīn al‐Miṣrī () was a 13th-century Egyptian astronomer mostly known for writing a large astronomical table that had nearly 415,000 entries. The table is considered to be the largest of its kind ever produced by one person during the Middle Ages. Although the main purpose of the work was astronomical timekeeping, it can also be used to solve all problems of spherical trigonometry by changing the arguments of the table. Najm al‐Din also wrote an important illustrated treatise that describes more than 100 different astronomical instruments, including ones he invented himself.
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Human computers were used to compile 18th and 19th century Western European mathematical tables, for example those for trigonometry and logarithms. Although these tables were most often known by the names of the principal mathematician involved in the project, such tables were often in fact the work of an army of unknown and unsung computers. Ever more accurate tables to a high degree of precision were needed for navigation and engineering. Approaches differed, but one was to break up the project into a form of long distance work from home piece work.
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To convert this to the real range on the ground, the plotter used basic trigonometry on a right angle triangle; the slant range was the hypotenuse and the open angle was the measurement from the radiogoniometer. The base and opposite sides could then be calculated, revealing the distance and altitude. An important correction was the curvature of the Earth, which became significant at the ranges CH worked at. Once calculated, this allowed the range to be properly plotted, revealing the grid square for the target, which was then reported up the chain.
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When asked to describe the album, Zammuto said "You're getting verrry sleepy." On April 5, 2010, the duo announced that The Way Out would be released through Temporary Residence Limited in July. On April 27 Pitchfork Media began streaming the track "Beautiful People", which Zammuto described as "a three part christian harmony mixed with a sort of euro-disco-trash beat, an orchestra’s worth of sampled brass and lyrics about the twelfth root of two (my favorite irrational number), trigonometry and tangrams". The album was released on July 20.
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In his earlier years Wallace was an occasional contributor to Leybourne's Mathematical Repository and the Gentleman's Mathematical Companion. Between 1801 and 1810 he contributed articles on "Algebra", "Conic Sections", "Trigonometry", and several others in mathematical and physical science to the fourth edition of the Encyclopædia Britannica, and some of these were retained in subsequent editions from the fifth to the eighth inclusive. He was also the author of the principal mathematical articles in the Edinburgh Encyclopædia, edited by David Brewster. He also contributed many important papers to the Transactions of the Royal Society of Edinburgh.
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Students focusing on Pre-Health can often major in any subject; however, they will also take a broad range of science courses including general chemistry and organic chemistry, often earning a minor in chemistry, mathematics, often up to basic calculus, general biology with overviews of genetics and taxonomy, and calculus or trigonometry-based physics. The requirements beyond the sciences are often light, many schools require a human sciences or psychology course. No schools actually require anatomy or diagnostic courses as these are universally regarded as first year medical courses.
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Photo of a sector The other side of the same sector The sector, also known as a proportional compass or military compass, was a major calculating instrument in use from the end of the sixteenth century until the nineteenth century. It is an instrument consisting of two rulers of equal length joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various mathematical calculations. It was used for solving problems in proportion, trigonometry, multiplication and division, and for various functions, such as squares and cube roots.
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At the time, Antonelli was unable to speak any English, only Irish; she would remember prayers in Irish for the rest of her life. She attended parochial grade school in Chestnut Hill and J. W. Hallahan Catholic Girls High School in Philadelphia. In high school, she had taken a year of algebra, a year of plane geometry, a second year of algebra, and a year of trigonometry and solid geometry.Autumn Stanley: Mothers and Daughters of Invention: Notes for a Revised History of Technology, The Scarecrow Press, 1993, pp.
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442–443, After graduating high school, she enrolled in Chestnut Hill College for Women. During her studies, she took every mathematics course offered, including spherical trigonometry, differential calculus, projective geometry, partial differential equations, and statistics. She graduated with a degree in mathematics in June 1942, one of only a few mathematics majors out of a class of 92 women. During her third year of college, Antonelli was looking for relevant jobs, knowing that she wanted to work in mathematics but did not want to be a school teacher.
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Trigonometry tells us that the sine of a 30° angle is 1/2, whereas the sine of a 90° angle is 1. Therefore, the sunbeam hitting the ground at a 30° angle spreads the same amount of light over twice as much area (if we imagine the Sun shining from the south at noon, the north- south width doubles; the east-west width does not). Consequently, the amount of light falling on each square mile is only half as much. Figure 3 This is a diagram of the seasons.
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1811 which Otley identifies as (in their modern names) Scafell Pike and Scafell, something which can be confirmed from the 1811 account, a modern map and some elementary trigonometry. . Once Scafell Pike (which has its own convoluted name history) had been identified as England's highest mountain, that fact and the greater interest in climbing and fell-walking necessitated the Scafell Range being broken down into a number of individually named elements. This process was completed before the death of Jonathan Otley in 1856, as Otley commented on this change.
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Diagram illustrating a method proposed and used by Al-Biruni to estimate the radius and circumference of the Earth in the 11th century. Abu Rayhan al-Biruni (973–1048) devised a novel method of determining the earth's radius by means of the observation of the height of a mountain. He carried it out at Nandana in Pind Dadan Khan (present-day Pakistan). He used trigonometry to calculate the radius of the Earth using measurements of the height of a hill and measurement of the dip in the horizon from the top of that hill.
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In various applications of trigonometry, it is useful to rewrite the trigonometric functions (such as sine and cosine) in terms of rational functions of a new variable . These identities are known collectively as the tangent half-angle formulae because of the definition of . These identities can be useful in calculus for converting rational functions in sine and cosine to functions of in order to find their antiderivatives. Technically, the existence of the tangent half-angle formulae stems from the fact that the circle is an algebraic curve of genus 0.
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The Lénárt sphere was invented by István Lénárt in Hungary in the early 1990s and its use is described in his 2003 book comparing planar and spherical geometry. Spherical trigonometry used to be an important mathematics topic from antiquity through the end of World War II, and has been replaced in modern education and (in navigation) with more algorithmic methods as well as GPS, including the Haversine formula, linear algebraic matrix multiplication, and Napier's pentagon. The Lénárt sphere is still widely used throughout Europe in non-Euclidean geometry as well as GIS courses.
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All students take four years of mathematics to include the studies of geometry, algebra II, trigonometry, pre-calculus, calculus, and differential equations. In recent years, students have been divided into an “Accelerated” or “Level” track. The course of study is largely the same, but the “Accelerated” track includes a more in-depth analysis of theoretical topics whereas the “Level” track takes a more applied approach. The culmination of the “Accelerated” track is usually AP Calculus or differential equations whereas “Level” students can choose between calculus, statistics, and finite math.
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The Jyotisha text Brahma-siddhanta, probably composed in the 5th century CE, discusses how to use the movement of planets, sun and moon to keep time and calendar. This text also lists trigonometry and mathematical formulae to support its theory of orbits, predict planetary positions and calculate relative mean positions of celestial nodes and apsides. The text is notable for presenting very large integers, such as 4.32 billion years as the lifetime of the current universe. The ancient Hindu texts on Jyotisha only discuss time keeping, and never mention astrology or prophecy.
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The oldest undergraduate engineering program in the Ivy League, Brown's first course specifically in engineering was offered in 1847. It was a professional engineering program called, "English and Scientific Course", and was a one or two-year program and included courses in mechanics, geometry, surveying, navigation, mensuration of heights and distances, chemistry and trigonometry. In 1850, the civil engineering curriculum was inaugurated as a focused one and a half year program. During the late 19th century, engineering instructional laboratories were held in University Hall, Sayles Hall and Wilson Hall.
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Polygonometry was a significant part of Lexell's work. He used the trigonometric approach using the advance in trigonometry made mainly by Euler and presented a general method of solving simple polygons in two articles "On solving rectilinear polygons". Lexell discussed two separate groups of problems: the first had the polygon defined by its sides and angles, the second with its diagonals and angles between diagonals and sides. For the problems of the first group Lexell derived two general formulas giving n equations allowing to solve a polygon with n sides.
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Alexander Bogomolny (January 4, 1948 July 7, 2018) was a Soviet-born Israeli American mathematician. He was Professor Emeritus of Mathematics at the University of Iowa, and formerly research fellow at the Moscow Institute of Electronics and Mathematics, senior instructor at Hebrew University and software consultant at Ben Gurion University. He wrote extensively about arithmetic, probability, algebra, geometry, trigonometry and mathematical games. He was known for his contribution to heuristics and mathematics education, creating and maintaining the mathematically themed educational website Cut-the-Knot for the Mathematical Association of America (MAA) Online.
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Red (A), Green (B), Blue (C) 16-bit lookup table file sample. (Lines 14 to 65524 not shown) In data analysis applications, such as image processing, a lookup table (LUT) is used to transform the input data into a more desirable output format. For example, a grayscale picture of the planet Saturn will be transformed into a color image to emphasize the differences in its rings. A classic example of reducing run-time computations using lookup tables is to obtain the result of a trigonometry calculation, such as the sine of a value.
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József Kürschák (14 March 1864 – 26 March 1933) was a Hungarian mathematician noted for his work on trigonometry and for his creation of the theory of valuations. He proved that every valued field can be embedded into a complete valued field which is algebraically closed. In 1918 he proved that the sum of reciprocals of consecutive natural numbers is never an integer. Extending Hilbert's argument, he proved that everything that can be constructed using a ruler and a compass, can be constructed by using a ruler and the ability of copying a fixed segment.
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The graphical method of designing an in-line slider-crank mechanism involves the usage of hand-drawn or computerized diagrams. These diagrams are drawn to scale in order for easy evaluation and successful design. Basic trigonometry, the practice of analyzing the relationship between triangle features in order to determine any unknown values, can be used with a graphical compass and protractor alongside these diagrams to determine the required stroke or link lengths. When the stroke of a mechanism needs to be calculated, first identify the ground level for the specified slider-crank mechanism.
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The calculator can be set to display values in binary, octal, or hexadecimal form, as well as the default decimal. When a non-decimal base is selected, calculation results are truncated to integers. Regardless of which display base is set, non- decimal numbers must be entered with a suffix indicating their base, which involves three or more extra keystrokes. When hexadecimal is selected, the row of six keys normally used for floating-point functions (trigonometry, logarithms, exponentiation, etc.) are instead allocated to the hex digits A to F (although they are physically labelled to ).
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Graphical projection was once commonly taught, though this has been superseded by trigonometry, logarithms, sliderules and computers which made arithmetical calculations increasingly trivial/ Graphical projection was once the mainstream method for laying out a sundial but has been sidelined and is now only of academic interest. The first known document in English describing a schema for graphical projection was published in Scotland in 1440, leading to a series of distinct schema for horizontal dials each with characteristics that suited the target latitude and construction method of the time.
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The HP 20b contains functions similar to the HP 10bII, with financial functions including: TVM, IRR, NPV, NUS ("Net Uniform Series"), amortization, depreciation, bonds, yield and accrued interest, interest conversion, list-based cashflow analysis, cashflows, break-even analysis. Math/Statistics functions include: list-base, 1 and 2 variable statistics, mean, standard deviation, population deviation, standard error, forecasting, correlations and covariance, +, -, ×, ÷, %, 1/x, +/-, scientific notation, n!, combinations, permutations, rounding, random numbers, LOG, LN, 10×, PL, square root, trigonometry, probability. For input modes, it supports RPN, Chain and Algebraic input.
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While Greek astronomy probably influenced Indian learning, to the point of introducing trigonometry, it seems to be the case that Indian mathematics is otherwise an indigenous tradition;Any early contact between Babylonian and Indian mathematics remains conjectural . in particular, there is no evidence that Euclid's Elements reached India before the 18th century. Āryabhaṭa (476–550 CE) showed that pairs of simultaneous congruences n\equiv a_1 \bmod m_1, n\equiv a_2 \bmod m_2 could be solved by a method he called kuṭṭaka, or pulveriser;Āryabhaṭa, Āryabhatīya, Chapter 2, verses 32–33, cited in: . See also .
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HM offers twenty-six Honors courses and seven foreign languages. Students in the Upper Division are required to study English, world history, United States history, biology, chemistry, or physics or both, geometry, algebra, and trigonometry, and also meet various requirements in the arts, computer science, health and counseling, and physical education. Students must go beyond these basic requirements in at least some, if not all, subjects. They are also required to take at least through the levels-three courses of either Chinese, French, Italian, Japanese, Latin, or Spanish.
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Some of the elective classes are athletics, Spanish and Choctaw languages, Keyboarding and Computer Applications I and II, Personal Financial Literacy, Current Events, Family and Consumer Sciences, ACT Prep, Web Design, Into To Computers, Desktop Publishing, AG Education I and II, AG Education Power and Technology, Animal Sciences, AG Communication, Music Appreciation, Music Theory, Drama, Art, and Competitive Academics. Other offered courses are, Pre AP Biology, Environmental Science, Trigonometry, and Algebra III. Silo encourages students to take concurrent classes at the local colleges. This will count as dual credit for high school and college.
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In 1895, at the age of 27, Chisholm became the first woman to be awarded a doctorate in any field in Germany. Again government approval had to be obtained to allow her to take the examination, which consisted of probing questions by several professors on sections such as geometry, differential equations, physics, astronomy, and the area of her dissertation, all in German. Along with her test she was required to take courses showing broader knowledge as well as prepare a thesis which was entitled Algebraisch-gruppentheoretische Untersuchungen zur sphärischen Trigonometrie (Algebraic Groups of Spherical Trigonometry).
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In 1839 he published a work entitled A Practical and Theoretical Essay on Oblique Bridges in which he was the first to apply trigonometry to the design of the skew arch railway bridge. It was used as a standard reference work on the subject until the early 20th century, its last reprinting being in 1895. He was an active member of the Institution of Civil Engineers from 1821. He was extremely busy during the railway mania years, but his health broke and he became deaf in the mid-1840s, retiring to the Isle of Man.
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A triangle in the plane In the case of the Euclidean plane, the symmetry group is the Euclidean motion group, the semidirect product of the two dimensional group of translations by the group of rotations., Chapter I, Euclidean geometry. Geodesics are straight lines and the geometry is encoded in the elementary formulas of trigonometry, such as the cosine rule for a triangle with sides , , and angles , , : : c^2 = a^2 +b^2 -2ab \,\cos \gamma. Flat tori can be obtained by taking the quotient of by a lattice, i.e.
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De triangulis planis et sphaericis libri Title page for Qvesta opra da ogni parte e un libro doro, 1476 During his time in Italy he completed Peuerbach's Almagest abridgement, Epytoma in almagesti Ptolemei. In 1464, he completed De triangulis omnimodis ("On Triangles of All Kinds"). De triangulis omnimodis was one of the first textbooks presenting the current state of trigonometry and included lists of questions for review of individual chapters. In it he wrote: His work on arithmetic and algebra, Algorithmus Demonstratus, was among the first containing symbolic algebra.
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In 2001, Big Finish Productions launched a series of new audio plays based on the original series, produced by Nigel Fairs. Nicholas Young and Philip Gilbert reprised their roles as John and TIM, with Helen Goldwyn and James Daniel Wilson appearing as Elena and Paul, the new Tomorrow People. Some releases also feature other original cast members, such as Peter Vaughan-Clarke, Elizabeth Adare and Mike Holoway (notably Trigonometry). Trevor Littledale took over the role of TIM in the audio series from The Warlock's Dance onwards after Philip Gilbert's death in 2004.
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Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their side lengths are proportional. Proportionality constants are written within the image: , , , where is the common measure of five acute angles. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.
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In 1919, she began work as a teacher of chemistry, biology, geometry and trigonometry at Englewood High School. McConnell applied to the University of Colorado School of Medicine in 1920 and was accepted. Although her father had previously paid for 17 men to attend medical school, he refused to pay for Frances' tuition because he deemed medicine to be "too hard a life for a woman". She therefore supported herself through medical school by working as a musician in local bars and theaters, as a tutor, and as a laboratory assistant.
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The theodolite constructed for Roy by Ramsden is called the Royal Society theodolite. See The Great Theodolites The theodolite was the largest ever constructed but, despite its massive size, it was carried from London to the Channel coast and employed on hills, steeples and a moveable tower. At each location the angles to other vertices of the triangulation mesh were measured many times, often at night time using newly devised lights. Finally the angle data was used to calculate the sides of the triangles by using spherical trigonometry.
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In Odisha, as elsewhere in India, children are enrolled in school at the age of five. The core subjects taught in schools include Science (including Physics, Chemistry and Biology), Mathematics (Arithmetic, Algebra, Geometry, Trigonometry, Computer Science, and Set theory), Social Studies (Geography, History, Civics and Economics), and three languages, which are usually Odia, Hindi and English. Additionally, school children receive training in sports and physical education, as well as vocational training. After ten years of schooling, children at the end of class X must appear in one of the three school examinations; 1\.
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Several later Islamic authors were influenced by Jābir, including Ibn Rushd (Averroes) and Nur ad-Din al-Betrugi, both of whom worked in Andalusia. The work was transmitted to Egypt in the 12th century by Maimonides and further east by the end of the 13th century. The work was translated from the Arabic into both Hebrew and Latin, the latter by Gerard of Cremona, who Latinized his name as "Geber". Through that channel it had a wide influence on later European mathematicians and astronomers and helped to promote trigonometry in Europe.
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Fig. 1 Isosceles skinny triangle A skinny triangle in trigonometry is a triangle whose height is much greater than its base. The solution of such triangles can be greatly simplified by using the approximation that the sine of a small angle is equal to the angle in radians. The solution is particularly simple for skinny triangles that are also isosceles or right triangles: in these cases the need for trigonometric functions or tables can be entirely dispensed with. The skinny triangle finds uses in surveying, astronomy, and shooting.
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A page from al- Khwārizmī's Algebra Al-Khwārizmī's contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his book on the subject, "The Compendious Book on Calculation by Completion and Balancing". On the Calculation with Hindu Numerals written about 820, was principally responsible for spreading the Hindu–Arabic numeral system throughout the Middle East and Europe. It was translated into Latin as Algoritmi de numero Indorum.
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There are ten departments at St. Mary's from which students choose their required and elective courses: Theology, English, Social Studies, Mathematics, Physical Education & Health, Science, Computer, Foreign Language, and Fine Arts. In addition, students may take courses for high school and college credit at San Joaquin Delta Community College or University of the Pacific. Advanced Placement courses are offered in American Literature, English Literature, Chemistry, European History, U.S. History, U.S. Government, Psychology, Calculus and Biology. Honors courses are offered in Algebra, Biology, Chemistry, English, Geometry/Trigonometry, Physical Science, Pre-Calculus and World Literature.
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Simple trigonometry can calculate the angle that the target would appear when the aircraft was at the drop point. This is known as the range angle or drop angle, and was typically looked up from a set of pre-computed tables or using a simple mechanical calculator. The bombsight is then set to that angle, and the bomb aimer drops the bombs when the target passes through the sights. In the presence of a cross-wind, as the aircraft flies forward the wind will push it sideways, away from the drop point.
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The new larger tower was built by Telstra with the ownership reverting to Wollongong City Council on completion. There was a campaign to paint it green so it would blend with the summit plateau canopy but this failed and it remains grey. In 2006 binocular telescopes were fitted, and after several tests, vandalism and malfunctioning being a problem, they are currently in use for gold coin donation to the rotary club. With these it is possible to see up close places like Stanwell Park in the distance and Brokers Nose trigonometry station.
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In the school year 1999-2000, the Mathematics department proposed an amendment to the Math curriculum of UPRHS. To be implemented starting school year 2000-2001 are the courses Math 3-A (Advanced Algebra, formerly Math IV-A and IV-B) and Math 3-B (Geometry, formerly Math III). On the other hand, 4th year Math courses such as Math 4-A (Trigonometry with Introductory Calculus, formerly Math V & VI) and Math 4-B (Introduction to Statistics, formerly Math VII) will be offered starting school year 2001-2002.
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In 1342, Levi ben Gershon, known as Gersonides, wrote On Sines, Chords and Arcs, in particular proving the sine law for plane triangles and giving five-figure sine tables. A simplified trigonometric table, the "toleta de marteloio", was used by sailors in the Mediterranean Sea during the 14th-15th Centuries to calculate navigation courses. It is described by Ramon Llull of Majorca in 1295, and laid out in the 1436 atlas of Venetian captain Andrea Bianco. Regiomontanus was perhaps the first mathematician in Europe to treat trigonometry as a distinct mathematical discipline,Boyer, p.
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In every beginning trigonometry course, one learns of the 30°–60°–90° triangle with sides of length 1, 2, and . When two such triangles are placed in the positions shown in the illustration, the smallest rectangle that can enclose them has width 1 + and height . Drawing a line connecting the original triangles' top corners creates a 45°–45°–90° triangle between the two, with sides of lengths 2, 2 and (by the Pythagorean theorem) 2. The remaining space at the top of the rectangle is a right triangle with small angles of 15° and 75°.
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The math collection of the library holds many rare collections and older printed books. There is information available about items in the collection from the early 19th century and their substantial connection with the teaching of mathematics. Ciaran Mac an Bhaird, A Guide to the Mathematics Collection in the Russell Library (College Collection) In the mathematics collection there is an example of André Darré’s Elements of Geometry with both Plane and Spherical Trigonometry (Dublin, 1813). Darré produced the book to help reform the study of mathematics in the college at that time.
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While a Penn State undergraduate, Urschel was involved in teaching integral vector calculus, trigonometry and analytic geometry, and introduction to econometrics. In 2015, Urschel co-authored a paper in the Journal of Computational Mathematics titled "A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians". It includes "a cascadic multigrid algorithm for fast computation of the Fiedler vector of a graph Laplacian, namely, the eigenvector corresponding to the second smallest eigenvalue." Urschel began a Ph.D. in mathematics at MIT in 2016, focusing on spectral graph theory, numerical linear algebra, and machine learning.
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The Jesuits made significant contributions to scientific knowledge in China. Under the Qing Dynasty, the Jesuits' knowledge of observational astronomy and spherical trigonometry was welcomed by the imperial court. The Manchus who conquered the Ming Dynasty also welcomed the Jesuit scientists and employed their help due to their expert knowledge of mathematical astronomy, which aided the ruling class in predicting celestial events, thus, displaying that this dynasty retained the Mandate of Heaven. In addition to reinforcing the Mandate of Heaven, the Jesuits separated two fields of science that were thought by the Chinese to be the same, cosmology and cosmography.
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Various types of equations can be solved using trigonometry. For example, a linear difference equation or linear differential equation with constant coefficients has solutions expressed in terms of the eigenvalues of its characteristic equation; if some of the eigenvalues are complex, the complex terms can be replaced by trigonometric functions of real terms, showing that the dynamic variable exhibits oscillations. Similarly, cubic equations with three real solutions have an algebraic solution that is unhelpful in that it contains cube roots of complex numbers; again an alternative solution exists in terms of trigonometric functions of real terms.
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Tate was the author of numerous educational works on mathematics, mechanics, drawing, and natural science, all tending to promote intellectual methods of instruction. His 'Principles of Geometry, Mensuration, Trigonometry, Land Surveying, and Levelling' (London, 1848, 12mo) was translated into: Hindustani. His 'Philosophy of Education' (London, 1854, 8vo) reached a third edition in 1860; it showed Tate's debts to Francis Bacon, John Locke, Johann Pestalozzi and faculty psychology; it is noted for its advocacy of the inductive method. From 1853 to 1855, with Tilliard, he edited the Educational Expositor, a work designed to assist schoolmasters and teachers.
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Oriani devoted significant time to observations of Uranus, calculating its orbital properties which he published as a booklet of tables in 1793.Alexandro Malaspina Research Centre After others had shown that Uranus was not on a parabolic orbit but rather in a roughly circular orbit, he calculated the orbit in 1783. In 1789, Oriani improved his calculations by accounting for the gravitational effects of Jupiter and Saturn. In addition to his continual contributions to the Effemeridi, he published a series of memoirs on spherical trigonometry: the Memorie dell' Istituto Italiano, 1806–10, and the Istruzione suelle misure e sui pesi, 1831.
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Most employers prefer to hire electronics technicians with an associate degree or other post-secondary training in engineering technology. Training is available at technical institutes, at community colleges, at extension divisions of colleges and universities, at public and private vocational-technical schools, and in the Armed Forces. Naval electronics technicians are the largest group of engineering technicians in the military (see Electronics Technician (US Navy)). Many 2-year associate degree programs accredited by the Technology Accreditation Commission of the Accreditation Board for Engineering and Technology (ABET) include at least college algebra and trigonometry and one or two basic science courses.
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He recorded an album called Trigonometry under the alias Mr. No No before returning as Saafir in The Hit List (1999). The Hit List was considered Saafir's attempt at commercial acceptance. The album featured production by Stevie J (made famous for his work with P. Diddy's Hitmen production team) and guest vocals from West Coast heavyweights Kam and Jayo Felony and controversial East Coast lyricist Chino XL. In 2006, he released his fourth album, Good Game: The Transition (ABB Records, 2006). The album covers the major transitions throughout his life, most notably his spinal tumor, and his conversion to Islam.
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In 2016, Napoli was nominated for Outstanding Individual Performance in the Theatre for Young Audiences division of the Dora Mavor Moore Awards for her performance in Roseneath Theatre's The Incredible Speediness of Jamie Cavanaugh. In 2017, Napoli starred as math teacher Gabriella in Rob Kempson's Trigonometry. In 2018, Napoli was Celia in the St Lawrence Shakespeare Festival's production of As You Like It. Napoli played Beatrice in the 2019 Shakespeare in High Park production of Much Ado About Nothing as directed by Liza Balkan. In Nightwood Theatre's 2019 premiere of Grace, Napoli played the titular Grace's older sister Sarah.
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The resulting Hipparcos Catalogue, a high-precision catalogue of more than 118,200 stars, was published in 1997. The lower-precision Tycho Catalogue of more than a million stars was published at the same time, while the enhanced Tycho-2 Catalogue of 2.5 million stars was published in 2000. Hipparcos follow-up mission, Gaia, was launched in 2013. The word "Hipparcos" is an acronym for HIgh Precision PARallax COllecting Satellite and also a reference to the ancient Greek astronomer Hipparchus of Nicaea, who is noted for applications of trigonometry to astronomy and his discovery of the precession of the equinoxes.
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The school offers two academic sequences: career prep and college prep. College prep is for students planning on attending either two or four year college degree programs. This sequence offers the typical courses that would be encountered to prepare a student for college, including four years of English; four years of science, including biology and chemistry; four years of social studies, including American history and world cultures; and four years of mathematics, including algebra, geometry, trigonometry, and elementary functions. Foreign language classes in Spanish and French are also offered, in addition to classes in the arts, including band, chorus, and painting classes.
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For example, astronomy was useful for determining the Qibla, the direction in which to pray, botany had practical application in agriculture, as in the works of Ibn Bassal and Ibn al-'Awwam, and geography enabled Abu Zayd al-Balkhi to make accurate maps. Islamic mathematicians such as Al-Khwarizmi, Avicenna and Jamshīd al-Kāshī made advances in algebra, trigonometry, geometry and Arabic numerals. Islamic doctors described diseases like smallpox and measles, and challenged classical Greek medical theory. Al-Biruni, Avicenna and others described the preparation of hundreds of drugs made from medicinal plants and chemical compounds.
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Back-conversion from Cartesian to torsion angles is simple trigonometry and has no risk of cumulative errors. They are used for creating input geometries for molecular systems in many molecular modelling and computational chemistry programs. A skillful choice of internal coordinates can make the interpretation of results straightforward. Also, since Z-matrices can contain molecular connectivity information (but do not always contain this information), quantum chemical calculations such as geometry optimization may be performed faster, because an educated guess is available for an initial Hessian matrix, and more natural internal coordinates are used rather than Cartesian coordinates.
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Guo worked on spherical trigonometry, using a system of approximation to find arc lengths and angles. He stated that pi was equal to 3, leading to a complex sequence of equations which came up with an answer more accurate than the answer that would have resulted if he did the same sequence of equations, but instead having pi equal to 3.1415. As people began to add onto his work, the authenticity of his work was questioned. Some believe that he took Middle Eastern mathematical and theoretical ideas and used them as his own, taking all the credit.
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Abū al-Wafāʾ, Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al- Būzjānī or Abū al-Wafā Būzhjānī () (10 June 940 – 15 July 998) was a Persian mathematician and astronomer who worked in Baghdad. He made important innovations in spherical trigonometry, and his work on arithmetics for businessmen contains the first instance of using negative numbers in a medieval Islamic text. He is also credited with compiling the tables of sines and tangents at 15 ' intervals. He also introduced the secant and cosecant functions, as well studied the interrelations between the six trigonometric lines associated with an arc.
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The calculated qibla is therefore 295°, or 25° north of west. This formula was derived by modern scholars, but equivalent methods have been known to Muslim astronomers since the 9th century (3rd century ), developed by various scholars, including Habash al-Hasib (active in Damascus and Baghdad ), Al- Nayrizi (Baghdad, ), Ibn Yunus (10th–11th century), Ibn al-Haytham (11th century), and Al-Biruni (11th century). Today spherical trigonometry also underlies nearly all applications or websites which calculate the qibla. When the qibla angle with respect to the north, \angle q, is known, true north needs to be known to find the qibla in practice.
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Richard of Wallingdorf, inventor of the rectangulus The rectangulus was an astronomical instrument made by Richard of Wallingford around 1326. Dissatisfied with the limitations of existing astrolabes, Richard developed the rectangulus as an instrument for spherical trigonometry and to measure the angles between planets and other astronomical bodies. This was one of a number of instruments he created, including the Albion, a form of equatorium, and a famously complicated and expensive horologium (astronomical clock). His Tractus Rectanguli, describing the rectangulus, was an influential text in medieval astronomy and at least thirty copies were known to survive.
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His father was a philosophy professor at the University of Illinois at Urbana–Champaign. His mother was an English professor at Parkland College, a community college in Champaign, which recognized her work with a "Professor of the Year" award in 1996. As an adolescent, Wallace was a regionally ranked junior tennis player, an experience he wrote about in the essay "Derivative Sport in Tornado Alley", originally published in Harper's Magazine as "Tennis, Trigonometry, Tornadoes". Although his parents were atheists, Wallace twice attempted to join the Roman Catholic Church, but "flunk[ed] the period of inquiry"; he later attended a Mennonite church.
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He showed how, although the number 1 can be approximated by adding a half plus a quarter plus an eighth plus a sixteenth, etc., (as even the ancient Egyptians and Greeks had known), the exact total of 1 can only be achieved by adding up infinitely many fractions. But Madhava went further and linked the idea of an infinite series with geometry and trigonometry. He realized that, by successively adding and subtracting different odd number fractions to infinity, he could home in on an exact formula for pi (this was two centuries before Leibniz was to come to the same conclusion in Europe).
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An ivory set of Napier's Bones from around 1650 A set of Napier's calculating tables from around 1680 His work, Mirifici Logarithmorum Canonis Descriptio (1614) contained fifty-seven pages of explanatory matter and ninety pages of tables of numbers related to natural logarithms (see Napierian logarithm). The book also has an excellent discussion of theorems in spherical trigonometry, usually known as Napier's Rules of Circular Parts. See also Pentagramma mirificum. Modern English translations of both Napier's books on logarithms and their description can be found on the web, as well as a discussion of Napier's bones and Promptuary (another early calculating device).
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Howson, Keitel, and Kilpatrick, Curriculum Development in Mathematics, pp. 196–197. However, SSMCIS was one of the direct inspirations for the New York State Education Department, in the late 1970s and 1980s, adopting an integrated, three-year mathematics curriculum for all its students, combining algebra, geometry, and trigonometry with an increased emphasis in probability and statistics. Given the differences in subject matter and approach, how SSMCIS- taught students would perform on College Entrance Examination Board tests became a major concern of parents and students and teachers. A 1973 report compared the test performance of such students with those from traditional mathematics curricula.
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At Funchal in Madeira in November, FitzGerald returns to England, carrying a letter from Peter to his father, and many gifts for his siblings. Mr Elliot, midshipman, teaches Peter the trigonometry, by the example of a stick of known height and its shadow, a tree whose shadow is paced out, thus the height of the tree is calculated; Peter understands it and succeeds in his classes on board. Before the equator, Peter gets a delirious fever, lasting until they land at Saint Catherine's island off Brazil, where they stay past Christmas. Many die of tropical diseases.
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MCPS is a college preparatory school, offering both an honors and regular program to its students. In the high school honors program, students may take upper level electives, such as Advanced Placement courses in American History, Calculus, English, Biology, Physics, Computer Science, and Fine Arts, as well as honors courses in Chemistry, British Literature, Algebra II, Trigonometry, Latin II and Spanish III, among others. Between thirty and forty percent of its graduates receive scholarship offers to colleges around the United States. Four years of Religion, Social Studies, Science, Mathematics and English are required for all students.
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It was a field in which "the physicist has so far played little part" and in which the practitioner "gropes dimly in the fog" relying mostly on empirical methods supplemented by elementary trigonometry and algebra that tended to give a deceptive authority to what was often little more than educated guesswork. By the time of the third edition of Gears in 1954, knowledge had moved on somewhat but Merritt was obliged to admit that empiricism still ruled and that "the behaviour of mating tooth surfaces and their lubricant still awaits a full understanding."Merritt, H. E. (1954) Gears. Third edition, 1962 reprint.
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The most notable brand is the Casio Databank series, though watches made by Timex were also popular. Most calculator watches contain only a few number of functions such as +, -, x, / and percents. However, there are several models with additional functions: scientific, including transcendent and trigonometry, in models Casio CFX-200, CFX-400, Citizen 49–9421, financial functions (in the Casio CBA-10) and also TV remote control functions (CMD-40B and CMD-30B). Usually calculator watches operate with eight-digit numbers; however, calculator watches can operate with 6 digits (for example, Casio C-801) or 10 digits (Casio CBA-10).
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Elisabeth Miller Bardwell (December 4, 1831 in Colrain, Massachusetts - May 27, 1899 in Greenfield, Massachusetts) was an American astronomer whose main area of study was meteor showers. She graduated from Mount Holyoke College in 1866, and continued on at the college as an instructor until her death. During those 33 years, she taught a mixture of algebra, trigonometry, physics, and astronomy for the first twenty years, and eventually only astronomy after 1886. She also oversaw the development of the observatory at the college which included invited visits to the Washington, Princeton, Lick, Berlin, and Potsdam observatories.
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Rheticus read Copernicus' manuscript and immediately wrote a non-technical summary of its main theories in the form of an open letter addressed to Schöner, his astrology teacher in Nürnberg; he published this letter as the Narratio Prima in Danzig in 1540. Rheticus' friend and mentor Achilles Gasser published a second edition of the Narratio in Basel in 1541. Due to its friendly reception, Copernicus finally agreed to publication of more of his main work—in 1542, a treatise on trigonometry, which was taken from the second book of the still unpublished De revolutionibus. Rheticus published it in Copernicus' name.
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During the Islamic Golden Age, certain advances were made in scientific fields, notably in mathematics and astronomy (algebra, spherical trigonometry), and in chemistry, etc. which were later also transmitted to the West.Fielding H. Garrison, An Introduction to the History of Medicine: with Medical Chronology, Suggestions for Study and Bibliographic Data, p. 86 Stefan of Pise translated into Latin around 1127 an Arab manual of medical theory. The method of algorism for performing arithmetic with the Hindu-Arabic numeral system was developed by the Persian al-Khwarizmi in the 9th century, and introduced in Europe by Leonardo Fibonacci (1170–1250).
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The calculations involve some basic trigonometry but these calculations can easily be done on any inexpensive scientific calculator. Sine height measurement Situations where the top of the tree being measured is above eye level and the base of the tree being measured is below eye level is the most common situation encountered in the field. The other two cases are those where both the top of the tree and the base of the tree are above eye level, and where both the top of the tree and base of the tree are located below eye level.
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The first measurement is taken from the Earth on one side of the Sun, and the second is taken approximately half a year later, when the Earth is on the opposite side of the Sun. The distance between the two positions of the Earth when the two measurements were taken is twice the distance between the Earth and the Sun. The difference in angle between the two measurements is twice the parallax angle, which is formed by lines from the Sun and Earth to the star at the distant vertex. Then the distance to the star could be calculated using trigonometry.
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Anders Johan Lexell (24 December 1740 - ) was a Finnish-Swedish astronomer, mathematician, and physicist who spent most of his life in Imperial Russia, where he was known as Andrei Ivanovich Leksel (Андрей Иванович Лексель). Lexell made important discoveries in polygonometry and celestial mechanics; the latter led to a comet named in his honour. La Grande Encyclopédie states that he was the prominent mathematician of his time who contributed to spherical trigonometry with new and interesting solutions, which he took as a basis for his research of comet and planet motion. His name was given to a theorem of spherical triangles.
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Islamic astronomy gained a good reputation in China for its theory of planetary latitudes, which did not exist in Chinese astronomy at the time, and for its accurate prediction of eclipses. Some of the astronomical instruments constructed by the famous Chinese astronomer Guo Shoujing shortly afterwards resemble the style of instrumentation built at Maragheh. In particular, the "simplified instrument" (jianyi) and the large gnomon at the Gaocheng Astronomical Observatory show traces of Islamic influence. While formulating the Shoushili calendar in 1281, Shoujing's work in spherical trigonometry may have also been partially influenced by Islamic mathematics, which was largely accepted at Kublai's court.
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Nevertheless, in the 20th and 21st centuries, mathematicians and computer scientists have pursued new approaches that, when combined with increasing computational power, extended the decimal representation of to many trillions of digits. The primary motivation for these computations is as a test case to develop efficient algorithms to calculate numeric series, as well as the quest to break records. The extensive calculations involved have also been used to test supercomputers and high- precision multiplication algorithms. Because its most elementary definition relates to the circle, is found in many formulae in trigonometry and geometry, especially those concerning circles, ellipses, and spheres.
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Because of the small RAM capacity of most systems originally used to run BASIC interpreters, clever memory management techniques had to be employed. Altair BASIC let users reclaim the space for trigonometry functions if those weren't being used during a session. PATB placed the start of the most common subroutines at the front of the program for use by the 1-byte 8080 opcode instead of the 3-byte opcode. In LLL BASIC, some variables occupied the same memory locations, in cases where the different variables were used only in command mode or only at runtime.
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Constantin Climescu Constantin Climescu (November 30, 1844 – August 6, 1926) was a Moldavian, later Romanian mathematician and politician. Born in Bacău, he attended the princely academy in Iași, followed by the sciences faculty of Iași University. He then left for the École Normale Supérieure in Paris, and in 1870, took his undergraduate degree from the University of Paris, in mathematics and physical sciences. He was a professor of analytic geometry and spherical trigonometry at Iași University from 1871 to 1909, served as dean of the sciences faculty from 1880 to 1901, and as rector of the university from 1901 to 1907.
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Jacqueline was severely injured in a crash of a SCAN 30 in which she was a passenger in 1949—many of the bones in her face were broken—and spent nearly three years in hospitals undergoing 33 reconstructive operations. To occupy her mind she studied algebra, trigonometry, aerodynamics, and other subjects necessary to obtain advanced pilot certification. She earned a military pilot license in 1950 then qualified as one of the first female test pilots. She was among the first women to break the sound barrier and set five world speed records in the 1950s and 1960s.
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The castle clock, a hydropowered mechanical astronomical clock invented by Al-Jazari in 1206, was the first programmable analog computer.Howard R. Turner (1997), Science in Medieval Islam: An Illustrated Introduction, p. 184, University of Texas Press, Donald Routledge Hill, "Mechanical Engineering in the Medieval Near East", Scientific American, May 1991, pp. 64–69 (cf. Donald Routledge Hill, Mechanical Engineering) The sector, a calculating instrument used for solving problems in proportion, trigonometry, multiplication and division, and for various functions, such as squares and cube roots, was developed in the late 16th century and found application in gunnery, surveying and navigation.
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His main work was probably done about the beginning of the eleventh century, and seems to have taken an important part in the elaboration of trigonometry. For example, he continued the investigations of Abul Wáfa, and devoted much space to this in his zij (or collection of tables) az-Zīj al-Jamī wal-Baligh ("the comprehensive and mature tables"), which incorporated the improved values of the planetary apogees observed by al-Battani.E. S. Kennedy, A Survey of Islamic Astronomical Tables, (Transactions of the American Philosophical Society, New Series, 46, 2), Philadelphia, 1956, pp. 3, 34-5.
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Many detailers would add another classification for those using 3-D Modeling applications specifically designed for steel detailing, as the process for the production of drawings using these applications is markedly different from a 2-D drafting approach. The detailer literally builds the project in 3D before producing detailed shop drawings from the model. Structural steel detailing requires skills in drafting, mathematics (including geometry and trigonometry), logic, reasoning, spatial visualization, and communication. A basic knowledge of general engineering principles and the methods of structural and miscellaneous steel fabrication, however acquired, is essential to the practice of this discipline.
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Tappan was the author of a number of mathematical textbooks, including Treatise on Plane and Solid Geometry (1964), Treatise on geometry and trigonometry (1868), Notes and Exercises on Surveying (1878), and Elements of Geometry (1884). Other works include "Inaugural address of Eli T. Tappan, President of the Ohio Teachers' Association," at Zanesville (1866), "School Legislation," a history of the subject in Ohio through 1873, published as part of A History of Education in the State of Ohio (1876), and "On the Complexity of Causes," an address before the Department of Higher Instruction of the National Educational Association at Chautauqua (1880).
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Set square The side lengths of a 30°–60°–90° triangle This is a triangle whose three angles are in the ratio 1 : 2 : 3 and respectively measure 30° (), 60° (), and 90° (). The sides are in the ratio 1 : : 2\. The proof of this fact is clear using trigonometry. The geometric proof is: :Draw an equilateral triangle ABC with side length 2 and with point D as the midpoint of segment BC. Draw an altitude line from A to D. Then ABD is a 30°–60°–90° triangle with hypotenuse of length 2, and base BD of length 1.
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These are standard results in spherical, hyperbolic and high school trigonometry (see below). Gauss generalised these results to an arbitrary surface by showing that the integral of the Gaussian curvature over the interior of a geodesic triangle is also equal to this angle difference or excess. His formula showed that the Gaussian curvature could be calculated near a point as the limit of area over angle excess for geodesic triangles shrinking to the point. Since any closed surface can be decomposed up into geodesic triangles, the formula could also be used to compute the integral of the curvature over the whole surface.
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This relies on the fact that the stars of a cluster share a common motion through space. Measuring the proper motions of cluster members and plotting their apparent motions across the sky will reveal that they converge on a vanishing point. The radial velocity of cluster members can be determined from Doppler shift measurements of their spectra, and once the radial velocity, proper motion and angular distance from the cluster to its vanishing point are known, simple trigonometry will reveal the distance to the cluster. The Hyades are the best known application of this method, which reveals their distance to be 46.3 parsecs.
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Illustratiom from De ichnographica campi published in Acta Eruditorum, 1763 La perspective affranchie de l'embarras du plan géometral, French edition, 1759 Lambert was the first to introduce hyperbolic functions into trigonometry. Also, he made conjectures regarding non-Euclidean space. Lambert is credited with the first proof that π is irrational by using a generalized continued fraction for the function tan x. Euler believed the conjecture but could not prove that π was irrational, and it is speculated that Aryabhata also believed this, in 500 CE. Lambert also devised theorems regarding conic sections that made the calculation of the orbits of comets simpler.
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Organized each year by the Advantage Testing Foundation, the competition is considered to be the preeminent female math competition for young women in North America. The single-day annual contest is open to female high-school students in 12th grade or below, from the United States and Canada who have attained a qualifying score on the American Mathematics Competitions Exams, specifically the AMC 10 or AMC 12 given in February each year. Up to 300 participants are then selected each year for the competition. Participants must complete 20 short-answer problems in geometry, algebra, trigonometry, and other math topics in 150 minutes.
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Programs can be entered manually on the calculators by the users, where they can select control functions from function key menu tips at the bottom of the screen. In addition to functions appeared in BASIC programming, the calculators support usages of many mathematical functions in many areas, such as exponentials, trigonometry, linear algebra, and calculus. Correspondingly, the calculators can store different types of data, including lists, tables, graphs, and matrices, in the main memories so that users can recall them later. Apart from displaying texts as outputs on the screen, the calculators are able to illustrate graphics.
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According to Kristine Louise Haugen, "The ambiguous phrases and extravagant circumlocutions necessitated by Manilius's hexameter verse must often have made the Astronomica seem, as it does today, rather like a trigonometry textbook rendered as a Saturday The New York Times crossword."Haugen (2011), p. 213. Scholars have noted the irony of Manilius's relative obscurity, because he wrote the Astronomica in the hope of attaining literary immortality. Housman voiced this sentiment in a dedicatory Latin poem written for the first volume of his edition that contrasted the movement of celestial objects with mortality and the fate of Manilius's work.
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Years later he declined to join Mensa International, saying that his IQ was too low. Physicist Steve Hsu stated of the test: When Feynman was 15, he taught himself trigonometry, advanced algebra, infinite series, analytic geometry, and both differential and integral calculus. Before entering college, he was experimenting with and deriving mathematical topics such as the half-derivative using his own notation. He created special symbols for logarithm, sine, cosine and tangent functions so they did not look like three variables multiplied together, and for the derivative, to remove the temptation of canceling out the d's.
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During her career, Gounden has taught science and mathematics at secondary school level from grades 8 to 12and has authored and published the smartphone interactive Mathematics Workbooks I DO U DO MATHS in 2017. The books are divided into two, with Book 1 covering algebra (grades 8 to 12), calculus (grade 12) and number patterns (grades 8 to 12), and Book 2 covering trigonometry (grades 10 to 12), geometry (grades 8 to 12) and functions (grades 8 to 12). During the COVID-19 coronavirus pandemic, Gounden created free online mathematics interactive timetables for grade 8 to 12 learners.
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The Math B Regents was often considered one of the most difficult New York State Regents. Math B covered concepts that can be found in trigonometry and advanced algebra, and prepared students for pre-calculus and calculus and reviewed past topics. During their year of study, students learned different theorems, graphed complex numbers and vectors, as well as reviewed topics such as exponential functions, systems of inequalities, and radicals. As the year progressed, students were expected to relate these functions to the real world, create conjectures through their own research, and begin a classroom discussion about these topics.
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In the US, a student in the eleventh grade is typically referred to as a student in the eleventh grade or as a junior. The vast majority of students who are classified as juniors take the SAT Reasoning Test and/or ACT in the second semester of their third year of high school. Math students usually take Algebra II, but classes like Trigonometry or Precalculus are sometimes offered for students who wish to take Advanced Placement math classes in their fourth, or senior year of high school. Depending on the location there may be a combination of any of the listed subjects.
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Her high school mathematics teacher, Mr. Frank Holley, further cultivated her interest. He came back after school and taught trigonometry (a course not offered in the curriculum) to her and a group of committed students. Bozeman graduated from Edward Bell High School in Camp Hill in 1964 and enrolled for her undergraduate studies in mathematics at Alabama A&M; University, during which she also worked on summer projects at NASA and Harvard University. She graduated in 1968 as salutatorian and moved with her husband Robert, also a mathematician, to non-segregated Vanderbilt University, where they both began their graduate studies.
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This work is a commentary and reworking of Ptolemy's Almagest and is the first criticism of it in the Islamic West. He particularly criticized the mathematical basis of the work. For example, he replaced the use of Menelaus' theorem with ones based on spherical trigonometry, in what seems to be an attempt to increase the mathematical precision of the work. These theorems had been developed by a group of 10th century Islamic mathematicians who included Abū al-Wafā' Būzjānī and then also by Abu Abd Allah Muhammad ibn Muadh Al- Jayyani who worked in Andalusia during the 11th century.
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Moldenhauer won the Edyth May Sliffe Award for Distinguished High School Mathematics Teaching of the Mathematical Association of America twice, in 1990 and 2001. She was also a winner of Stanford University's Frederick Emmons Terman Engineering Award, given annually by the graduating engineering students at Stanford to a distinguished high school teacher. She was a two- time winner of Harvey Mudd College's Distinguished Teaching Award. Unusually for a high school mathematics teacher, Moldenhauer has an Erdős number of 2, from her collaboration with mathematician Sherman K. Stein and mechanical engineer Anthony S. Wexler on "Trigonometry and a Wood Bowl".
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William J. Matthews writes that part of The Bell Curve's analysis is based on the AFQT "which is not an IQ test but designed to predict performance of certain criterion variables".William J. Matthews, Ph.D. (1998) A Review of the Bell Curve: Bad Science Makes for Bad Conclusions The AFQT covers subjects such as trigonometry. Heckman observed that the AFQT was designed only to predict success in military training schools and that most of these tests appear to be achievement tests rather than ability tests, measuring factual knowledge and not pure ability. He continues:Cracked Bell James J. Heckman.
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Bergen Tech - Teterboro offers a wide range of mathematics courses. These include: Algebra I, Geometry, Math Analysis I & II (a highly rigorous 2-year Precalculus with Limits course with a heavy emphasis on Algebra II and Trigonometry), AP Calculus AB, AP Calculus BC, Multivariable Calculus, and AP Statistics. Based on the number of students who choose to take the class, some years there will be an Algebra II class, or a Calculus Honors course. Incoming students can take a summer Pre-Algebra or Algebra I course if they feel necessary, or to be placed in another math class.
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"Infinity's end: Time to ditch the never-ending story?" by Amanda Gefter, New Scientist, 15 August 2013 Wildberger draws inspiration from mathematicians predating Georg Cantor's infinite set-theory, like Gauss and Euclid, who he claims were far more wary of using infinite sets than modern mathematicians.For Wildberger's views on the history of infinity, see the Gefter New Scientist article, but also see Wildberger's History of Mathematics and Math Foundations lectures, University of New South Wales, circa 2009–2014 in more than 120 videos and lectures, available online @youtube To date, rational trigonometry is largely unmentioned in mainstream mathematical literature.
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Using this method there was no need for the two stations to compare measurements or perform any trigonometry to determine an actual location in space, both performed simple range measurements directly off their screen and sent their separate corrections to the aircraft. In practice, ranges were not sent by voice to the aircraft. Instead, a tone generator produced Morse code dots or dashes under the control of the operators. This was similar to the beam systems like Lorenz, which the UK aircrew were already familiar with using as a blind landing aid in the pre-war period.
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If the Earth is treated as a sphere, the geodesics are great circles (all of which are closed) and the problems reduce to ones in spherical trigonometry. However, showed that the effect of the rotation of the Earth results in its resembling a slightly oblate ellipsoid: in this case, the equator and the meridians are the only simple closed geodesics. Furthermore, the shortest path between two points on the equator does not necessarily run along the equator. Finally, if the ellipsoid is further perturbed to become a triaxial ellipsoid (with three distinct semi- axes), only three geodesics are closed.
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The passing grade in each subject is 70%. Subjects offered at Notre Dame include English, where students study a range of famous classics from American Literature, British Literature, and World Literature, Religious Studies, where students are taught about the Catholic religion and World religions, Science, which include Biology, Chemistry, and Physics, Mathematics, consisting of Algebra, Geometry, and Trigonometry, Social Studies, American Studies, The Arts, Physical Education, Health Education, and Languages, which consists of French, Spanish, and Latin. Electives are also available. Advanced Placement courses and Honors courses are also available to students in their Sophomore, Junior, and Senior year.
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Thus C=2\pi R=\pi D is seen to be true as a theorem. Several of the arguments that follow use only concepts from elementary calculus to reproduce the formula A=\pi r^2, but in many cases to regard these as actual proofs, they rely implicitly on the fact that one can develop trigonometric functions and the fundamental constant in a way that is totally independent of their relation to geometry. We have indicated where appropriate how each of these proofs can be made totally independent of all trigonometry, but in some cases that requires more sophisticated mathematical ideas than those afforded by elementary calculus.
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The SAT Subject Test in Mathematics Level 1 (formerly known as Math I or MathIC (the "C" representing the use of a calculator)) is the name of a one- hour multiple choice test given on algebra, geometry, basic trigonometry, algebraic functions, elementary statistics and basic foundations of calculus by The College Board. A student chooses whether to take the test depending upon college entrance requirements for the schools in which the student is planning to apply. Until 1994, the SAT Subject Tests were known as Achievement Tests; and from 1995 until January 2005, they were known as SAT IIs. Mathematics Level 1 was taken 109,048 times in 2006.
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Thābit ibn Qurra (known as Thebit in Latin) (born 836) contributed to a number of areas in mathematics, where he played an important role in preparing the way for such important mathematical discoveries as the extension of the concept of number to (positive) real numbers, integral calculus, theorems in spherical trigonometry, analytic geometry, and non-Euclidean geometry. In astronomy Thabit was one of the first reformers of the Ptolemaic system, and in mechanics he was a founder of statics. An important geometrical aspect of Thabit's work was his book on the composition of ratios. In this book, Thabit deals with arithmetical operations applied to ratios of geometrical quantities.
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Euler worked in almost all areas of mathematics, such as geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, lunar theory and other areas of physics. He is a seminal figure in the history of mathematics; if printed, his works, many of which are of fundamental interest, would occupy between 60 and 80 quarto volumes. Euler's name is associated with a large number of topics. Euler is the only mathematician to have two numbers named after him: the important Euler's number in calculus, e, approximately equal to 2.71828, and the Euler–Mascheroni constant γ (gamma) sometimes referred to as just "Euler's constant", approximately equal to 0.57721.
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In trigonometry and mathematics in general, plane angles are conventionally measured counterclockwise, starting with 0° or 0 radians pointing directly to the right (or east), and 90° pointing straight up (or north). However, in navigation, compass headings increase clockwise around the compass face, starting with 0° at the top of the compass (the northerly direction), with 90° to the right (east). A circle defined parametrically in a positive Cartesian plane by the equations and is traced counterclockwise as the angle t increases in value, from the right-most point at . An alternative formulation with sin and cos swapped gives a clockwise trace from the upper-most point.
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Maaseh Hoshev is sometimes mistakenly referred to as Sefer Hamispar (The Book of Number), which is an earlier and less sophisticated work by Rabbi Abraham ben Meir ibn Ezra (1090–1167). In 1342, Levi wrote On Sines, Chords and Arcs, which examined trigonometry, in particular proving the sine law for plane triangles and giving five-figure sine tables. One year later, at the request of the bishop of Meaux, he wrote The Harmony of Numbers in which he considers a problem of Philippe de Vitry involving so-called harmonic numbers, which have the form 2m·3n. The problem was to characterize all pairs of harmonic numbers differing by 1.
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Statue of Spiru Haret by Ion Jalea, located in University Square, Bucharest Haret was born in Iaşi, Moldavia, to an old Armenian family, and showed an early talent for mathematics, publishing two textbooks (one in algebra and one in trigonometry) when he was still a high school student. In 1869 he entered the University of Bucharest, where he studied physics and mathematics. In 1870, while a student in his second term, he became teacher of mathematics at Nifon Seminary in Bucharest, but quit the following year in order to continue his studies. In 1874, at age 23, he graduated with a degree in physics and mathematics.
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It was based on the SR16 design from Kinpo Electronics. Power sources come from smaller solar cells than the 1994 TI-34, and CR2025 battery. Feature set was based on TI-36X II, but without unit conversions and constants, base calculations, boolean algebra, complex value functions (abs now only works in real numbers), integral calculation, engineering notation display modes, gradian angle mode, percentage sign, three 2-variable statistic modes (logarithmic, exponent, power), hyperbolic trigonometry. Functions added over TI-36X II (primarily coming from the TI-32 Math Explorer Plus) include rounding by digits, min/max, lcm/gcd, cube/cubic root, remainder, integer division, percentage conversion, unsimplified fraction, adjustable fraction simplification factor.
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Hipparchus was the first to show that the stereographic projection is conformal, and that it transforms circles on the sphere that do not pass through the center of projection to circles on the plane. This was the basis for the astrolabe. Besides geometry, Hipparchus also used arithmetic techniques developed by the Chaldeans. He was one of the first Greek mathematicians to do this, and in this way expanded the techniques available to astronomers and geographers. There are several indications that Hipparchus knew spherical trigonometry, but the first surviving text discussing it is by Menelaus of Alexandria in the 1st century, who on that basis is now commonly credited with its discovery.
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The Secondary School Mathematics Curriculum Improvement Study (SSMCIS) was the name of an American mathematics education program that stood for both the name of a curriculum and the name of the project that was responsible for developing curriculum materials. It is considered part of the second round of initiatives in the "New Math" movement of the 1960s. The program was led by Howard F. Fehr, a professor at Columbia University Teachers College. The program's signature goal was to create a unified treatment of mathematics and eliminate the traditional separate per-year studies of algebra, geometry, trigonometry, and so forth, that was typical of American secondary schools.
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Astronomy, as it was an eminent centre of Astronomical Observatory (Khagoliya Vedhashala) established by Aryabhata or Aryabhatta for Astronomical Studies and Astronomical Research. Aryabhatta is called Father of Algebra, Geometry and Trigonometry, Concept of Zero (0) and decimal system. Aryabhata, also called Aryabhata I or Aryabhata the Elder (born in the year 476 AD, at Kusumapura, near Pataliputra or present day Patna in India) was astronomer and the earliest Indian mathematician whose work and history are available to modern scholars. He is also known as Aryabhata I or Aryabhata the Elder to distinguish him from a 10th-century Indian mathematician of the same name.
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Computer literacy was integrated in the THE 1 and 2, while Educational Computing was offered as a specialized course in the THE 3 and 4; likewise, Computer-Aided Instructions in English, Science and Mathematics were introduced. Advanced Computer courses were also offered as enrichment subjects for high school students while Values Education 3 and 4 were replaced by Trigonometry and Calculus. Keeping up with recent developments in early childhood education, SY 1998–1999 saw the expansion of the pre-school program with the inclusion of Development Kindergarten room in Roosevelt College Marikina, similar to the one in Cainta was started. It was opened formally, SY 1999–2000.
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John Doyle was born in South Africa where his father was the chaplain to the Governor of Cape Province. He was employed at the Bank of South Africa for two years but left in mid-1914 because he saw a recruiting advertisement for the Royal Naval Air Service. He was not taken due to a lack of trigonometry and then, since the war had started on 4 August, he applied to the Royal Flying Corps where he was told the war would be over by Christmas and anyway they had plenty of applicants. He then joined the Inns of Court Officers' Training Corps as a cavalry officer candidate.
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Even the urbane Captain JAG Troup, Royal Navy, in his truly excellent 1934 work "On the Bridge", has a chuckle at the expense of those who don't observe ordinary caution and good practice at sea. And in our own day, the sharp-witted, stressed out guardian of bridge standards can be a formidable teacher of would-be officers of the watch. There is, it seems, a style of instruction common to didactic, experienced navigators and Harris belongs in the mainstream of this convention. It is not clear why he refrains from burdening his readers with spherical trigonometry, a knowledge of which is so essential to successful astro-navigation.
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Iriññāttappiḷḷi Mādhavan Nampūtiri known as Mādhava of Sangamagrāma () was an Indian mathematician and astronomer from the town believed to be present-day Aloor, Irinjalakuda in Thrissur District, Kerala, India. He is considered the founder of the Kerala school of astronomy and mathematics. One of the greatest mathematician-astronomers of the Middle Ages, Madhava made pioneering contributions to the study of infinite series, calculus, trigonometry, geometry, and algebra. He was the first to use infinite series approximations for a range of trigonometric functions, which has been called the "decisive step onward from the finite procedures of ancient mathematics to treat their limit-passage to infinity".
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He graduated from Cornell University in 1983. Before entering graduate school in the Fall of 1984, he spent a year teaching algebra, geometry, and trigonometry to inmates at the Tompkins County Jail in Ithaca, NY. He received his M.S. in Social Psychology from the University of Washington in 1986, and his Ph.D. in Social Psychology from the University of Michigan in 1990. He was hired as an Assistant Professor of Psychology at the University of Texas at Austin in 1990 and is now a Full Professor. He is a Member of the Institute For Neuroscience, and the Institute for Mental Health Research, both located in Austin, Texas.
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Among Roberts's earlier lectures were a series on the Theory of Invariants and Covariants, on which he published papers. Next he took an interest in hyperelliptic integrals, a subject developed by Jacobi, Riemann, and Weierstrass. In 1871 he published a "Tract on the Addition of Elliptic and Hyperelliptic Integrals", constructing a trigonometry of hyperelliptic functions on the analogy of that of elliptic functions. Roberts discovered many properties of geodesic lines and lines of curvature on the ellipsoid, especially in relation to umbilics, and from 1845 published papers in the Journal de Mathématiques, the Proceedings of the Royal Irish Academy, Cambridge and Dublin Mathematical Journal, Nouvelles Annales de Mathématiques.
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Restivo (1992), 32. In his formula "technique of intersecting circles", he created an approximation of the arc of a circle s given the diameter d, sagitta v, and length of the chord c subtending the arc, the length of which he approximated as s = c + 2v2/d. Restivo writes that Shen's work in the lengths of arcs of circles provided the basis for spherical trigonometry developed in the 13th century by Guo Shoujing (1231–1316). He also simplified the counting rods technique by outlining short cuts in algorithm procedures used on the counting board, an idea expanded on by the mathematician Yang Hui (1238–1298).
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The English Department instructed the third grade and offered studies in geography and English; and the second grade was also taught by the English Department with courses in history and natural philosophy. First grade, the school's highest, was instructed by the Classical and Mathematical Department and offered studies in Greek, Latin, French, geometry, algebra, trigonometry, surveying, mensuration, navigation, astronomy, and bookkeeping. According to an advertisement for a female teacher in the Baltimore Sun on November 9, 1853, William C. Clayton was serving as the institute's principal by late 1853. Clayton stated in the advertisement that the institute was seeking an experienced female teacher to lead the school's Female Department.
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This was largely because the names of the bays were swapped around and displayed incorrectly on maps for many years. However, it was officially corrected in 1972 by the Surveyor-General’s Trigonometry Surveys and Mapping Office. Vleesbaai and its surrounding region proved to be good agricultural land for livestock, and as result it saw an increase of nomadic farmers from the Cape region creating farm settlements in the area during the greater part of the nineteenth century. It was only towards the first part of the twentieth century that the first informal settlements started in the bay as a holiday camping site for the local farmers.
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The square, massive Norman tower has three-arched belfry windows on each face, surmounted by corner turrets, and a conically-shaped tower of octagonal proportions, topped again by a short steeple. The tower was a main viewing point for the Anglo-French Survey (1784–1790) which linked the Paris Observatory with the Royal Greenwich Observatory using trigonometry. Cross- channel sightings were made of signal lights at Dover Castle and Fairlight, East Sussex. The church was assigned as a historic monument by decree of 10 September 1913, only to have its stained glass smashed during a Zeppelin bombardment on 15 January 1915, falling through the roof.
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Flickinger (1914), pp 136–140 In the early days, focus was on vocational training and the educational portion was minimal, as schooling beyond an eighth grade education was not offered. Shortly after Oklahoma's statehood, the school implemented a public school model for classes which included algebra, arithmetic, astronomy, bookkeeping, botany, chemistry, civics, composition, economics, geography, geology, geometry, grammar, history, literature, rhetoric, stenography, surveying, telegraphy, trigonometry, typewriting and zoology. In addition to the classroom studies, technical trades offered included agriculture, animal husbandry, apiculture, carpentry, cobbling, concrete work, domestics, gardening, laundry work, poultry raising, and sewing.Flickinger (1914), p 270 Though standardization of education was required, so was segregation.
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The tenth and final chapter describes practical geometry (including basic trigonometry) in 151 pages. The book's mathematical content draws heavily on the traditions of the abacus schools of contemporary northern Italy, where the children of merchants and the middle class studied arithmetic on the model established by Fibonacci's Liber Abaci. The emphasis of this tradition was on facility with computation, using the Hindu–Arabic numeral system, developed through exposure to numerous example problems and case studies drawn principally from business and trade. Pacioli's work likewise teaches through examples, but it also develops arguments for the validity of its solutions through reference to general principles, axioms and logical proof.
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The oldest picture of the Brittenburg is a woodcut (identified by Leiden professor Jan Hendrik Holwerda, curator of the Rijksmuseum van Oudheden) by Abraham Ortelius in 1562 for Lodovico Guicciardini's first edition of The Low Countreys, printed in 1589 by Christophe Plantin in Antwerp. This woodcut was replaced in later editions with an engraving. The oldest picture was used later by Zacharias Heyns (1598, 1599) and Hermann Moll (1734, 1736). It concerns a land surveyor's draft (trigonometry), in which the distance from the ruins (by that time in the North Sea and only visible at low tide) westward to the church of Katwijk is mentioned, namely 1,200 'schreden' (= 1,080 meters).
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At the 1769 Census, Kongsberg was the second largest city in Norway (after Bergen), with more than 8,000 inhabitants, and the number of employees at the Kongsberg Silver Mines exceeded 4,000. In 1757, after an initiative from mining engineer Michael Heltzen and chemist and physician Johan Heinrich Becker, Det Kongelige Norske Berg-Seminarium was established by an Order in Council from Frederick V of Denmark dated 19 September 1757. The institution combined both practical and theoretical education related to mining. Among the theoretical subjects were mathematics (in particular geometry and trigonometry), mechanics (for construction of buildings and machinery), hydrostatics, hydraulics, physical chemistry, mineralogy, metallurgy and pyrotechnics.
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Lexell is mainly known for his works in astronomy and celestial mechanics, but he also worked in almost all areas of mathematics: algebra, differential calculus, integral calculus, geometry, analytic geometry, trigonometry, and continuum mechanics. Being a mathematician and working on the main problems of mathematics, he never missed the opportunity to look into specific problems in applied science, allowing for experimental proof of theory underlying the physical phenomenon. In 16 years of his work at the Russian Academy of Sciences, he published 62 works, and 4 more with coauthors, among whom are Leonhard Euler, Johann Euler, Wolfgang Ludwig Krafft, Stephan Rumovski, and Christian Mayer.
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Computer literacy was integrated in the THE 1 and 2, while Educational Computing was offered as a specialized course in the THE 3 and 4; likewise, Computer-Aided Instructions in English, Science and Mathematics were introduced. Advanced Computer courses were also offered as enrichment subjects for high school students while Values Education 3 and 4 were replaced by Trigonometry and Calculus. Keeping up with recent developments in early childhood education, SY 1998–1999 saw the expansion of the pre-school program with the inclusion of Development Kindergarten room in Roosevelt College Marikina, similar to the one in Cainta was started. It was opened formally, SY 1999–2000.
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The new school, its headmaster announced, would "offer instruction in the various grades usually taught in academies.... No pains will be spared on the part of the instructor to render the acquisition of useful knowledge easy and pleasant to those young gentlemen and ladies who may attend the School." The "reasonable" board would cost $3.00 for each quarter's enrolment, Leavitt announced in his initial advertisement, and would cover most fields of study, except "Algebra, Navigation, Gunnery, or the Science of Projectiles, &c.;, Spherick Geometry & Trigonometry, Astronomy & Philosophy." For study in those more complicated fields Leavitt proposed to charge an additional 50 cents tuition for each quarter of enrolment.
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De revolutionibus, 1543, title page Copernicus was still working on De revolutionibus orbium coelestium (even if not certain that he wanted to publish it) when in 1539 Georg Joachim Rheticus, a Wittenberg mathematician, arrived in Frombork. Philipp Melanchthon, a close theological ally of Martin Luther, had arranged for Rheticus to visit several astronomers and study with them. Rheticus became Copernicus's pupil, staying with him for two years and writing a book, Narratio prima (First Account), outlining the essence of Copernicus's theory. In 1542 Rheticus published a treatise on trigonometry by Copernicus (later included as chapters 13 and 14 of Book I of De revolutionibus).
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When the scientific expedition of the Morea landed at Navarino in the Peloponnese on March 3, 1829, Peytier was attached to it. Trigonometry of the Morea (by Peytier, Puillon Boblaye and Servier) As soon as March, a base of 3,500 meters had been traced in the Argolis, from one point at the ruins of Tiryns to a point at a ruined house in the village of Aria."Notice sur les opérations géodésiques exécutées en Morée, en 1829 et 1830, par MM. Pierre Peytier, Puillon-Boblaye et Servier" in Bulletin de la Société de géographie, vol. 19, nr. 117-122, January – June 1833, p. 91.
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At high school level, in most of the U.S., algebra, geometry and analysis (pre-calculus and calculus) are taught as separate courses in different years. Mathematics in most other countries (and in a few U.S. states) is integrated, with topics from all branches of mathematics studied every year. Students in many countries choose an option or pre-defined course of study rather than choosing courses à la carte as in the United States. Students in science-oriented curricula typically study differential calculus and trigonometry at age 16–17 and integral calculus, complex numbers, analytic geometry, exponential and logarithmic functions, and infinite series in their final year of secondary school.
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The Flower Mound High School Math Club participates in several state and national competitions, including the AMC and AIME tests, the Trig-Star competition, UIL Mathematics, UIL Number Sense, UIL Calculator, the Best of Texas competition, TMSCA tests, and the UT Arlington Calculus Bowl. The Math Club annually sponsors the AMC and AIME tests and invites many of the school's students to participate. In 2006 and 2007, the school achieved the AMC 12 Merit Roll. The Trig-Star competition, a nationally held trigonometry competition sponsored by the Texas Society of Professional Surveyors and the National Society of Professional Surveyors, is also open to the student body and by invitation.
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It comprises a core set of ideas from Pure Mathematics. These ideas reflect those that would be met early on in a typical A Level Mathematics course: algebra, basic functions, sequences and series, coordinate geometry, trigonometry, exponentials and logarithms, differentiation, integration, graphs of functions. In addition, knowledge of the GCSE curriculum is assumed Test of Mathematics for University Admission - Specification for October 2018 retrieved 22 April 2019 . Paper 2: Mathematical Reasoning Paper 2 has 20 multiple-choice questions, with 75 minutes allowed to complete the paper. The second paper assesses a candidate’s ability to justify and interpret mathematical arguments and conjectures, and deal with elementary concepts from logic.
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He had also set up a boarding school which taught trigonometry and navigation as extra subjects, as well as running a shop which sold books, stationery, barometers, thermometers, and philosophical and mathematical instruments. He was a well-respected professional and valued advisor to the Rev'd Nevil Maskelyne, the Astronomer Royal. Andrews predicted the annular solar eclipse in 1791: :To the north of Scotland it will be a very great eclipse; but nowhere total on account of the apparent diameter of the sun. The spectators will be entertained with a beautiful annulus, or ring of light encompassing the opaque body of the Moon on every side.
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Nicolaus Copernicus' teacher, Domenico Maria Novara da Ferrara, referred to Regiomontanus as having been his own teacher. There is speculation that Regiomontanus had arrived at a theory of heliocentrism before he died; a manuscript shows particular attention to the heliocentric theory of the Pythagorean Aristarchus, mention was also given to the motion of the earth in a letter to a friend.Arthur Koestler, The Sleepwalkers, Penguin Books, 1959, p. 212. Much of the material on spherical trigonometry in Regiomontanus' On Triangles was taken directly from the twelfth-century work of Jabir ibn Aflah otherwise known as Geber, as noted in the sixteenth century by Gerolamo Cardano.
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Astronomers had to make thousands of such calculations, and because the best method of multiplication available was long multiplication, most of this time was spent taxingly multiplying out products. Mathematicians, particularly those who were also astronomers, were looking for an easier way, and trigonometry was one of the most advanced and familiar fields to these people. Prosthaphaeresis appeared in the 1580s, but its originator is not known for certain; its contributors included the mathematicians Ibn Yunis, Johannes Werner, Paul Wittich, Joost Bürgi, Christopher Clavius, and François Viète. Wittich, Yunis, and Clavius were all astronomers and have all been credited by various sources with discovering the method.
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Alexander Hamilton Preparatory Academy offers major courses for students such as English I, II, II, Geometry, Algebra II, Pre-Calculus, Probability and Statistics, Trigonometry and plenty of Science classes such as Biology, Chemistry, Physics and Forensic Science. As a new independent high school, the academy is beginning to offer a few Advanced Placement Programs (AP) classes for students who wish take them for Course credit also known as college credits. Elective classes are also offered such as the fine arts, music, and business. Advanced Placement courses offered include AP English Literature, AP Spanish Literature, AP French Literature, AP United States History, AP Chemistry and AP Biology.
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As slide rule development progressed, added scales provided reciprocals, squares and square roots, cubes and cube roots, as well as transcendental functions such as logarithms and exponentials, circular and hyperbolic trigonometry and other functions. Slide rules with special scales are still used for quick performance of routine calculations, such as the E6B circular slide rule used for time and distance calculations on light aircraft. In the 1770s, Pierre Jaquet-Droz, a Swiss watchmaker, built a mechanical doll (automaton) that could write holding a quill pen. By switching the number and order of its internal wheels different letters, and hence different messages, could be produced.
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Adding the latter two equations gives :a^2 + b^2 = ac\cos\beta + bc\cos\alpha + 2ab\cos\gamma. Subtracting the first equation from the last one results in :a^2 + b^2 - c^2 = ac\cos\beta + bc\cos\alpha + 2ab\cos\gamma - ( ac\cos\beta + bc\cos\alpha ) which simplifies to :c^2 = a^2 + b^2 - 2ab\cos\gamma. This proof uses trigonometry in that it treats the cosines of the various angles as quantities in their own right. It uses the fact that the cosine of an angle expresses the relation between the two sides enclosing that angle in any right triangle.
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The high school follows a block schedule and students have a full day of classes for their entire stay at the school. Graduation requires four years of English and History, three years of Math and Science, and two years of foreign language (Spanish or Mandarin). The Senior Institute is a division of the school consisting of grades 11 and 12; classes in the Senior Institute are sometimes taught through a two-year curriculum; students may have some of their teachers for two academic years. The Math sequence consists of Algebra I, Geometry, Algebra II/Trigonometry, and Statistics/Calculus; the Science sequence includes Biology, Chemistry, AP Environmental Science, Food Science and Physics.
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Many students consider the twelfth grade also known as the senior year of high school a year to relax and prepare for the transition out of their old lives into college/university or the workplace. Others take advantage of the opportunity to complete additional higher-level courses, such as Advanced Placement and International Baccalaureate, to earn credits for college/university. Mathematics courses normally include Precalculus, Trigonometry, Advanced Placement Calculus, Advanced Placement Statistics, or Probability. Science courses include Advanced Placement Chemistry, Advanced Placement Biology, Advanced Placement Environmental Science, or Advanced Placement Physics B, Advanced Placement Physics C: Mechanics, or Advanced Placement Physics C: Electricity and Magnetism.
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Murderous Maths is a series of British educational books by author Kjartan Poskitt. Most of the books in the series are illustrated by illustrator and author Philip Reeve, with the exception of "The Secret Life of Codes", which is illustrated by Ian Baker, "The Essential Arithmetricks: How to plus, minus, times and divide." illustrated by Daniel Postgate and Rob Davis, and "The Murderous Maths of Everything", also illustrated by Rob Davis. The Murderous Maths books have been published in over 25 countries. The books, which are aimed at children aged 8 and above, teach maths, spanning from basic arithmetic to relatively complex concepts such as the quadratic formula and trigonometry.
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František Wolf (1904–1989) was a Czech mathematician known for his contributions to trigonometry and mathematical analysis, specifically the study of the perturbation of linear operators. Wolf was born 1904 in Prostějov, then part of the Austro-Hungarian empire and now part of the Czech Republic, the elder of two children of a furniture maker. He studied physics at Charles University in Prague, and then mathematics at Masaryk University in Brno under the supervision of Otakar Borůvka; he was awarded a doctorate in 1928 (degree Rerum Naturum Doctor). He then taught mathematics at the high school level until 1937, when he obtained a faculty position at Charles University.
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The second half of the book contains Arab-Islamic contributions to the fields of logic, philosophy, geometry, the development of Ptolemaic astronomy, observational methods, calculations in trigonometry and mathematics to determine the length of the year, the eccentricity of the sun's orbit, and the construction of astronomical tables, etc. The Ṭabaqāt al-ʼUmam has been transcribed and translated into many different languages in many periods and cultures. The original document is not extant and discrepancies in the translations creates problems for historians, including variations in the title of the book. Discrepancies in the content of the editions appear with some versions omitting words, sentences, paragraphs or entire sections.
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By the Second World War, all sides had developed automatic electro-mechanical calculators, exemplified by the U.S. Navy's Torpedo Data Computer.The British called theirs the "fruit machine". Submarine commanders were still expected to be able to calculate a firing solution by hand as a backup against mechanical failure, and because many submarines existing at the start of the war were not equipped with a TDC; most could keep the "picture" in their heads and do much of the calculations (simple trigonometry) mentally, from extensive training. Against high-value targets and multiple targets, submarines would launch a spread of torpedoes, to increase the probability of success.
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Core curriculum includes the Mathematical Investigations (MI) series, from MI I to MI IV, which is a four-semester series covering topics in Algebra II/Trigonometry to Pre- Calculus, and the AB and BC Calculus series. Students may be placed into either the AB or the BC Calculus tracks depending on performance in the MI courses or based on a placement test. Many elective options are offered including popular ones such as Multi-Variable Calculus, Differential Equations, Discrete Mathematics, Number Theory, and Statistics. However, there are also various others on a which cover a variety of mathematical topics including Graph Theory, Problem Solving, and Modern Geometries.
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In the 8th century, Transoxiana, the territory between the Amudarya and Syrdarya rivers, was conquered by the Arabs (Ali ibn Sattor) becoming a focal point soon after of the Islamic Golden Age. Many notable scientists lived there and contributed to its development after the conquest. Among the achievements of the scholars during this period were the development of trigonometry into its modern form (simplifying its practical application to calculate the phases of the moon), advances in optics, in astronomy, as well as in poetry, philosophy, art, calligraphy and many others, which set the foundation for the Muslim Renaissance. In the 9th and 10th centuries, Transoxiana was included into the Samanid State.
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He also read James Ferguson's Astronomy explained upon Sir Isaac Newton's principles and made easy to those who have not studied mathematics (1756) and William Emerson's The elements of trigonometry (1749), The elements of optics (1768) and The principles of mechanics (1754). Herschel took lessons from a local mirror-builder and having obtained both tools and a level of expertise, started building his own reflecting telescopes. He would spend up to 16 hours a day grinding and polishing the speculum metal primary mirrors. He relied on the assistance of other family members, particularly his sister Caroline and his brother Alexander, a skilled mechanical craftsperson.
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James Gregory FRS (November 1638 – October 1675) was a Scottish mathematician and astronomer. His surname is sometimes spelled as Gregorie, the original Scottish spelling. He described an early practical design for the reflecting telescope – the Gregorian telescope – and made advances in trigonometry, discovering infinite series representations for several trigonometric functions. In his book Geometriae Pars Universalis (1668) Gregory gave both the first published statement and proof of the fundamental theorem of the calculus (stated from a geometric point of view, and only for a special class of the curves considered by later versions of the theorem), for which he was acknowledged by Isaac Barrow.
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There are three available diplomas a student can earn by graduation: a Regents Diploma Advanced Regents Diploma, or a Local Diploma A Regents Diploma can be earned by completing the core classes and passing the English, U.S. history, algebra, biology, and earth science regents courses, which are mandatory by New York State. An Advanced Regents Diploma is earned after taking and passing more than one regents examination given by NYS. For example, instead of only taking an algebra regents exam, a student must also take a trigonometry regents exam and pass it. Every graduate must earn 22 high school credits, which means completing 22 classes with a 65 or better grade.
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Van Brummelen earned his PhD degree from Simon Fraser University in 1993, and served as a professor of mathematics at Bennington College from 1999 to 2006. He then transferred to Quest University Canada as a founding faculty member. In 2020, he became the dean of the Faculty of Natural and Applied Sciences at Trinity Western University in Langley, BC. Glen Van Brummelen has published the first major history in English of the origins and early development of trigonometry, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry.McRae, Alan S. (2009), Review of The Mathematics of the Heavens and the Earth, .
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Optical interferometers are extremely complex, unfilled aperture photon-collecting telescopes in the visual (sometimes the near infrared, too), which produce synthesized images and fringe data "on the fly" (unlike radio interferometers which are privileged to record the data for later synthesis), essentially by taking an inverse Fourier transform of the incoming data. Astrometry is understood by precisely measuring delay line additions while fringing, to match the light path differences from baseline ends. Using essentially trigonometry the angle and position of where the array is 'pointed' can be determined, thus inferring a precise position on the sphere of the sky. Only a few exist that can be considered operational.
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Throughout the 1980s and 1990s, John Saxon spoke out against mathematics education reform efforts that he believed would lead to a disaster in math and science education. He wrote or co-wrote a series of nine mathematics textbooks for kindergarten through high school which use an incremental teaching method often called "Saxon math". According to Saxon in media interviews in the 1980s and early 1990s and documentation coming with the high-school level textbooks, the inclusion of specialised and/or somewhat uncommon words such as "sciolist" in the story problems is intended as a vocabulary builder in preparation for the verbal section of the SAT and similar tests.Book Review: Algebra III- Geometry-Trigonometry The Meadowood Economist, 25.
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The Canadarm2 robotic manipulator on the International Space Station is operated by controlling the angles of its joints. Calculating the final position of the astronaut at the end of the arm requires repeated use of trigonometric functions of those angles. Amongst the lay public of non- mathematicians and non-scientists, trigonometry is known chiefly for its application to measurement problems, yet is also often used in ways that are far more subtle, such as its place in the theory of music; still other uses are more technical, such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions and find application in a number of areas, including statistics.
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Alexander S. Leidholdt, Showdown on Mr. Jefferson's Lawn, Virginia Magazine of History & Biography Vol 122 Issue 3 (2014) Blackford attended Virginia's elite Episcopal High School, although he failed to finish a required trigonometry course and thus did not graduate, and then the University of Virginia. He participated in the Experiment in International Living in Madrid, living with a former Republican who had fought against Francisco Franco in the Spanish Civil War and who been imprisoned by the Franco regime for a decade. This experience fostered the young man's lifelong identification with underdogs. Blackford, a Rhodes Scholar, regarded by many of his professors as one of the university's top students, edited the student newspaper, The Cavalier Daily.
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FDR High School also has a rigorous honors program, for example, Honors Algebra 1, Honors Chemistry, Honors Geometry, Honors Sophomore English, Honors Physics, Honors Algebra 2/Trigonometry, Honors Participation in Government, Honors Economics, and a special class called "Pre-Calculus for Juniors only" a class offered to students who have taken Algebra 1 in eighth grade. FDR is also home to an alternative program called the Young Adult Borough Center (YABC) that provides over-aged and under-credited high school students with alternative means to obtain their high school diploma. Classes are offered in the evenings Monday through Thursday and students in good academic standing are provided a paid internship during the day.
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But when the functionality of calculators improved beyond simple arithmetic operations, most people realized that the suanpan could never compute higher functions - such as those in trigonometry - faster than a calculator. Nowadays, as calculators have become more affordable, suanpans are not commonly used in China, but many parents still send their children to private tutors or school- and government- sponsored after school activities to learn bead arithmetic as a learning aid and a stepping stone to faster and more accurate mental arithmetic, or as a matter of cultural preservation. Speed competitions are still held. Suanpans are still being used elsewhere in China and in Japan, as well as in some few places in Canada and the United States.
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REA was founded by Max Fogiel in 1959 as an educational publisher, concentrating on problems and solutions, or what's known as test preparation today. The company produced the iconic "Problem Solver" series of comprehensive solution guides. The Problem Solver series eventually encompassed over 30 topics with more than 28,000 problem/solution sets, covering differential equations, electric circuits, electronic circuits, precalculus, calculus, advanced calculus, algebra and trigonometry, physics, linear algebra, statistics, organic chemistry, mechanics, thermodynamics, electromagnetics, geometry, chemistry, probability, materials strength, heat transfer, economics, robotics, discrete math, fluid mechanics and dynamics, numerical analysis, optics, topology, electronic communications, operations research, and several others. Recently REA has focused on providing digital test banks through its online study center.
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The Academy for Mathematics, Science, and Engineering, a satellite academy of Morris County School of Technology located in Rockaway, New Jersey, has the highest combined SAT scores in the country and is one of the most difficult high schools to get into in the country. On average over a thousand middle school students apply to the Math, Science and Engineering Academy and only 7% are accepted. The school only accepts multiples of 22/23 and only if 44/46 people meet the demanding qualifications for the school, making it an incredibly difficult school to get into. AP classes are mandatory, and students take advanced classes such as Trigonometry and Physics freshman year.
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Isaac Israeli ben Joseph or Yitzhak ben Yosef (often known as Isaac Israeli the Younger) was a Spanish-Jewish astronomer/astrologer who flourished at Toledo in the first half of the fourteenth century. He was a pupil of Asher ben Yehiel, at whose request (in 1310) he wrote the astronomical work Yesod Olam, the finest contribution on the subject in Hebrew literature. The book includes chapters on: geometry and trigonometry; the structure and position of the globe; the number and movements of celestial spheres; the time differences in days and nights in various parts of the Earth; the movements of sun and moon; solstices, neomeniæ, eclipses, and leap-years. It also contains astronomical tables (ephemeris) and a perpetual calendar.
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While he noticed that no contradictions can be found in his logarithmic-spherical geometry, he remained convinced of the special role of Euclidean geometry. According to Paul Stäckel and Friedrich Engel, as well as Zacharias, Taurinus must be given credit as a founder of non-Euclidean trigonometry (together with Gauss), but his contributions cannot be considered as being on the same level as those of the main founders of non-Euclidean geometry, Nikolai Lobachevsky and János Bolyai. Taurinus corresponded with Gauss about his ideas in 1824. In his reply, Gauss mentioned some of his own ideas on the subject, and encouraged Taurinus to further investigate this topic, but he also told Taurinus not to publicly cite Gauss.
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American public schools traditionally teach biology in the first year of high school, chemistry in the second, and physics in the third. The belief is that this order is more accessible, largely because biology can be taught with less mathematics, and will do the most toward providing some scientific literacy for the largest number of students. In addition, many scientists and educators argue that freshmen do not have an adequate background in mathematics to be able to fully comprehend a complete physics curriculum, and that therefore quality of a physics education is lost. While physics requires knowledge of vectors and some basic trigonometry, many students in the Physics First program take the course in conjunction with geometry.
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They were provided with large maps of their operational area printed on light paper so they could be stored for future reference. A rotating straightedge with the centrepoint at the radar's location on the map was fixed on top, so when the operator called an angle the plotter would rotate the straightedge to that angle, look along it to pick off the range, and plot a point. The range called from the operator is the line- of-sight range, or slant range, not the over-ground distance from the station. To calculate the actual location over the ground, the altitude also had to be measured (see below) and then calculated using simple trigonometry.
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For reasons which seem inadequate now, he confines himself to an explanation of "plain trigonometry" and one can only speculate that the true reason is that before Mr. Harrison did his famous work on sea-going chronometers, the navigator's need for spherical trig was relatively undeveloped. On the other hand Harris's evident delight in the new chart projection "commonly called Mercator's" is clearly and amusingly explained in the text. This is probably not a book for the general reader, and even for the historian of the 18th century it is specialist stuff. The navigator, however, is bound to read him with respect and admiration; he describes many enduring maritime truths in an engaging and entertaining style.
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While trigonometry can be codified—as was clear already to expert mathematicians of the eighteenth century (if not before)—the search for a complete and unified theory of special functions has continued since the nineteenth century. The high point of special function theory in the period 1800–1900 was the theory of elliptic functions; treatises that were essentially complete, such as that of Tannery and Molk, could be written as handbooks to all the basic identities of the theory. They were based on techniques from complex analysis. From that time onwards it would be assumed that analytic function theory, which had already unified the trigonometric and exponential functions, was a fundamental tool.
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Early attempts to measure the distance to the Moon exploited observations of a lunar eclipse combined with knowledge of Earth's radius and an understanding that the Sun is much further than the Moon. By observing the geometry of a lunar eclipse, the lunar distance can be calculated using trigonometry. The earliest accounts of attempts to measure the lunar distance using this technique were by Greek astronomer and mathematician Aristarchus of Samos in the 4th century BC and later by Hipparchus, whose calculations produced a result of (376,000-427,000 km or 233,000-265,000 mi). This method later found its way into the work of Ptolemy, who produced a result of (409,000 km or 253,000 mi) at its farthest point.
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Spanish "technical engineers" have full competency in their respective professional field of engineering, being the difference that the three or four year Engineers have competence only in their speciality (Mechanical, Electrical, Chemical, etc.)and the "Engineering Superior School" Engineers have wider competences. In the United States, the Technology Accreditation Commission of the Accreditation Board for Engineering and Technology (ABET) grants 2-year associate degree programs to students that meet a set of specified standards. These programs include at least a college algebra and trigonometry course and, if needed, one or two basic science courses at any accredited school. The number of math and science prerequisite courses depends on the branch of engineering that the student chooses.
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The sin and cos functions of trigonometry, were important mathematical concepts, imported from the Gupta period of Indian astronomy namely the jyā and koṭi-jyā functions via translation of texts like the Aryabhatiya and Surya Siddhanta, from Sanskrit to Arabic, and then from Arabic to Latin, and later to other European languages.Uta C. Merzbach, Carl B. Boyer (2011), A History of Mathematics, Hoboken, N.J.: John Wiley & Sons, 3rd ed., p. 189. Abu'l-Hasan al-Uqlidisi a scholar in the Abbassid caliphate wrote al-Fusul fi al-Hisab al-Hindi ("chapters in Indian calculation") to address the difficulty in procedures for calculation from the Euclid's Elements and endorsed the use of Indian calculation.
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Describing, in detail, an advanced universal astrolabe of Blagrave's design - incorporating the designs of earlier astrolabists. The 'jewel' consisted of four movable parts - Mater, Rete, Label, and Rule - which were lavishly illustrated in the book's frontispiece and engraved plates. The 'jewel's' uses were described in the third book as being used for anything from trigonometry, to navigation, to astrology; in Blagrave's words from the 'jewel' one could draw "so infinite a number of conclusions, more than I thinke I shall ever have time to write". The astrolabe contains some significant similarities to the universal astrolabe of Andalusian astrolabist Ali ibn Khalaf and David A. King has suggested that Blagrave copied his design for the 'Jewel' from ibn Khalaf.
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Entrance to the Pharmacy and Medicine classrooms of the Colegio de San José A Nautical School was created on January 1, 1820 which offered a four-year course of study (for the profession of pilot of merchant marine) that included subjects such as arithmetic, algebra, geometry, trigonometry, physics, hydrography, meteorology, navigation and pilotage. A School of Commercial Accounting and a School of French and English Languages were established in 1839. The Don Honorio Ventura College of Arts and Trades (DHVCAT) in Bacolor, Pampanga is said to be the oldest official vocational school in Asia. Augustinian Friar Juan Zita and civic leader Don Felino Gil established the vocational school on November 4, 1861.
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Mr. Bean is late for a mathematics exam and speeds past a blue Reliant Regal in his Mini (which would become a running gag later throughout the series), running it off the road and nearly overturning it in the process. Arriving at the college he has been attending, Bean finds himself sitting next to a fellow student (Paul Bown) who asks him if he did his revision. Bean replies that he has been concentrating on trigonometry, to which the student says that he has studied calculus. Bean then says he believes calculus was the focus of the test last year, rendering the other student worried while Bean snickers to himself for deceiving him.
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A German manuscript page teaching use of Arabic numerals (Hans Talhoffer, 1459) The translation of Al-Khwarizmi's work greatly influenced mathematics in Europe. As Professor Victor J. Katz writes: "Most early algebra works in Europe in fact recognized that the first algebra works in that continent were translations of the work of al-Khwärizmï and other Islamic authors. There was also some awareness that much of plane and spherical trigonometry could be attributed to Islamic authors". The words algorithm, deriving from Al-Khwarizmi's Latinized name Algorismi, and algebra, deriving from the title of his AD 820 book Hisab al-jabr w’al-muqabala, Kitab al-Jabr wa-l-Muqabala are themselves Arabic loanwords.
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Mathematics in China emerged independently by the 11th century BC.Chinese overview The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system (base 2 and base 10), algebra, geometry, number theory and trigonometry. In the Han Dynasty, the Chinese made substantial progress on finding the nth root of positive numbers and solving linear congruence equations. The major texts from the period, The Nine Chapters on the Mathematical Art and the Book on Numbers and Computation gave detailed processes to solving various mathematical problems in daily life. All procedures were computed using a counting board in both texts, and they included inverse elements as well as Euclidean divisions.
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Avicenna created an extensive corpus of works during what is commonly known as the Islamic Golden Age, in which the translations of Greco-Roman, Persian, and Indian texts were studied extensively. Greco-Roman (Mid- and Neo-Platonic, and Aristotelian) texts translated by the Kindi school were commented, redacted and developed substantially by Islamic intellectuals, who also built upon Persian and Indian mathematical systems, astronomy, algebra, trigonometry and medicine. The Samanid dynasty in the eastern part of Persia, Greater Khorasan and Central Asia as well as the Buyid dynasty in the western part of Persia and Iraq provided a thriving atmosphere for scholarly and cultural development. Under the Samanids, Bukhara rivaled Baghdad as a cultural capital of the Islamic world.
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Alhazen's The Model of the Motions of Each of the Seven Planets was written 1038. Only one damaged manuscript has been found, with only the introduction and the first section, on the theory of planetary motion, surviving. (There was also a second section on astronomical calculation, and a third section, on astronomical instruments.) Following on from his Doubts on Ptolemy, Alhazen described a new, geometry-based planetary model, describing the motions of the planets in terms of spherical geometry, infinitesimal geometry and trigonometry. He kept a geocentric universe and assumed that celestial motions are uniformly circular, which required the inclusion of epicycles to explain observed motion, but he managed to eliminate Ptolemy's equant.
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S. and world history), English literature, and mathematics (algebra, geometry, and trigonometry), among other subjects. For fifth-grade science and sixth-grade world history, however, Chabad educators eschew state-mandated booklets and textbooks and instead use material that they collect from a variety of sources in order to comply with the Hasidic movement's religious beliefs. In high school, where students are required by the New York Board of Regents to study from specific textbooks, teachers append their own notations to pages describing theories such as the Big Bang and evolution to inform students of the Torah point of view on these topics. Novels read in English literature classes are also vetted for compliance with Chabad philosophy and religious belief.
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The nocturnal revolutionized long distance seafaring by complementing the use of the astrolabe and ephemerides by now giving sailors an accurate tool with which to discover the time at their position. Both Zacuto and Cortes were respected mathematicians and had determined in their respective publications the trigonometric measurements concerning the degrees of latitude and longitude. If a ship's pilot or navigator used the nocturnal to read their time, and then consulted an astrolabe in concert with astronomical charts they could determine the time distance between themselves and a fixed location. The trigonometry, dictated particularly in Zacuto's work, then allowed a sailor to calculate the degree difference east or west of the fixed position.
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However, the curriculum was continuously improved and by 1927–1928 it was comparable to those of similar military schools in other countries. Many officers of the General Staff were assigned a teaching position. In 1924, classes included religious education, tactics, military equipment, machine guns, mortars, shooting range, military administration, military law, military history, topography, fortifications, artillery, Lithuanian language and literature, knowledge of the homeland, physics and chemistry, algebra, trigonometry, typology, hygiene, world history, French and German languages, physical education (gymnastics). In 1932, classes included religious education, general tactics, infantry tactics, military history, military law, military psychology, military organisation, commissariat, topography, pioneer subjects, chemistry, artillery, cavalry, aviation, mortars, heavy machine guns, communications, German language, physical education, dance and singing.
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Peter Vaughan-Clarke is a British actor, born in Wandsworth, London on 11 June 1957. Vaughan-Clarke is best known for his portrayal of Stephen Jameson in the TV series The Tomorrow People in the 1970s, a character he returned to later in life in the audio continuation of the series by Big Finish Productions, most notably in the episode "Trigonometry". He has also appeared on TV in The Pallisers, Shoestring (as "Fred"), The Duchess of Duke Street (as "Jamie"), and appeared in the 1975 British film It Could Happen to You (aka Intimate Teenage Secrets), along with his Tomorrow People co-star Nicholas Young. No longer regularly acting, he now works as a lighting technician and key grip.
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The basic problem in bombing is the calculation of the trajectory of the bomb after it leaves the aircraft. Due to the effects of air drag, wind and gravity, bombs follow a complex path that changes over time – the path of a bomb dropped from 100 meters looks different from the one when the same bomb is dropped from 5,000 meters. The path was too complex for early systems to calculate directly, and was instead measured experimentally at a bombing range by measuring the distance the bomb traveled forward during its fall, a value known as the range. Using simple trigonometry, this distance can be converted into an angle as seen from the bomber.
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In January 1810 he obtained an engagement at Mr. Rainhall's school as teacher of arithmetic, at a salary of 20l., and there commenced calculating the times of the eclipses and exhibiting their mode of occurrence by diagrams. He opened a school of his own in the summer of 1811 in James Street, Old Street; in the following year moved into a better house in Lizard Street, Bartholomew Square, St. Luke's, and joined the Mathematical Society in Crispin Street, Spitalfields, where the extensive library was of much use to him. Meanwhile, he corrected the press of a Welsh magazine then published, and wrote his ‘Key to Bonnycastle's Trigonometry’ (1814), which established his character as a mathematician.
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The term "trigonometry" was derived from Greek τρίγωνον trigōnon, "triangle" and μέτρον metron, "measure". The modern word "sine" is derived from the Latin word sinus, which means "bay", "bosom" or "fold" is indirectly, via Indian, Persian and Arabic transmission, derived from the Greek term khordḗ "bow-string, chord". The Hindu term for sine in Sanskrit is jyā "bow-string", the Hindus originally introduced and usually employed three trigonometric functions jyā, koti-jyā, and utkrama-jyā. The Hindus defined these as functions of an arc of a circle, not of an angle, hence their association with a bow string, and hence the "chord of an arc" for the arc is called "a bow" (dhanu, cāpa).
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The Hindus had given the name jiva to the half-chord in trigonometry, and the Arabs had taken this over as jiba. In the Arabic language there is also the word jaib meaning "bay" or "inlet". When Robert of Chester came to translate the technical word jiba, he seems to have confused this with the word jaib (perhaps because vowels were omitted); hence, he used the word sinus, the Latin word for "bay" or "inlet". This was then interpreted as the genuine Arabic word jayb, meaning "bosom, fold, bay", either by the Arabs or by a mistake of the European translators such as Robert of Chester, who translated jayb into Latin as sinus.
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He published Essay on the Education of Youth, in which he wrote that he did not "study the interest of the boy but the embryo Man". To a non- specialist, he would have seemed deeply knowledgeable in science and mathematics, but a close inspection of his essay and curriculum revealed that the extent of his mathematical teachings was limited to algebra, trigonometry and logarithms. Thus, Green's later mathematical contributions, which exhibited knowledge of very modern developments in mathematics, could not have resulted from his tenure at the Robert Goodacre Academy. He stayed for only four terms (one school year), and it was speculated by his contemporaries that he had exhausted all they had to teach him.
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Together, they come upon a theory to explain the unusual measurements: they actually live on a very large sphere, and the Triangles have more than 180 degrees due to being inscribed on a non-planar surface. With help from the sphere from the first novel, they are able to prove this theory. However, the established scientific community is not able to comprehend the idea proposed by the two, and thus they do not attempt to enlighten Flatland. Furthermore, as the residents of Flatland advance, they begin to travel in space; they see distant worlds like their own, and the surveyor tries to find the distance between their world and these distant worlds, using trigonometry and radar.
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It was a highly challenging program, focusing on preparating of students to achieve success in AP coursesand for entry into college. The magnet included differentiated instruction and a competency-based curriculum, and served as an educational partnership linking the personnel and resources of the University of Maryland, College Park and Northwestern. Students had access to Pre-Advanced Placement courses and AP Government at the ninth grade level; major emphasis on analytical writing in English classes, computer-intensive mathematics classes; scientific research in trigonometry and calculus classes; and a host of other magnet-exclusive instructional methods. Due to the court-ordered restructuring of PGCPS magnet programs, several magnets were eliminated in between 2003 and 2004, including the programs at Northwestern and Nicholas Orem.
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His first textbook was published in 1981 and had a very distinctive cover with a blue background and orange letters spelling out the word algebra. Saxon came into national prominence by conservative thinker and publisher William F. Buckley. Buckley announced Saxon's success on the front page of the National Review magazine in 1981 with the headline "Supply-side Algebra." After his first book was published, Saxon published more books: Algebra 1 1/2, Algebra 1/2 and Geometry, Trigonometry and Algebra 3. (He later renamed his book Algebra 1 1/2 simply Algebra 2). His reasoning for titling his second textbook Algebra 1 1/2 is that a good part of the book was a review of Algebra 1 topics.
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Verbiest claimed that the studying of celestial patterns was of great practical importance to the dynasty and that whether the astronomer in question was Muslim, Jesuit or Chinese didn't matter. He argued that ensuring the observations were impartial and that applying Tycho's ideas to the observations to verify said observations were the two most important factors. Verbiest also claimed that Western ways of measuring data were the most accurate and dismissed the older findings of Chinese astronomers. While these claims did little to convince the Chinese that their old measurements were inaccurate, Verbiest's pushing of spherical trigonometry would go on to have the greatest impact on Chinese astronomy, as they saw it as being connected to when the Mongols brought Islamic astronomy to China during their conquest.
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Four directions and Political divisions of Iran by Abū Rayḥān al-Bīrūnī Bīrūnī devised a novel method of determining the earth's radius by means of the observation of the height of a mountain. He carried it out at Nandana in Pind Dadan Khan (present-day Pakistan). He used trigonometry to calculate the radius of the Earth using measurements of the height of a hill and measurement of the dip in the horizon from the top of that hill. His calculated radius for the Earth of 3928.77 miles was 2% higher than the actual mean radius of 3847.80 miles. His estimate was given as 12,803,337 cubits, so the accuracy of his estimate compared to the modern value depends on what conversion is used for cubits.
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Beautiful Jim Key and his trainer periodically toured the United States in a special railroad car to promote the fledgling cause of the humane treatment of animals. They performed in venues in most of the larger American cities, including New York’s Madison Square Garden. The horse was among the most popular attractions at the 1904 St. Louis World's Fair. Beautiful Jim Key was supposedly intelligent enough that he could calculate mathematical problems, possibly even trigonometry. William Key President William McKinley saw Beautiful Jim Key perform at an exposition in Tennessee and declared, “This is the most astonishing and entertaining exhibition I have ever witnessed.” The President also commented that it was an example of what “kindness and patience” could accomplish.
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Mīrzā Muhammad Tāraghay bin Shāhrukh (, ), better known as Ulugh Beg () (22 March 1394 – 27 October 1449), was a Timurid sultan, as well as an astronomer and mathematician. Ulugh Beg was notable for his work in astronomy-related mathematics, such as trigonometry and spherical geometry, as well as his general interests in the arts and intellectual activities.Science in Islamic civilisation: proceedings of the international symposia: "Science institutions in Islamic civilisation", & "Science and technology in the Turkish and Islamic world" It is thought that he spoke five languages: Arabic, Persian, Turkic, Mongolian, and a small amount of Chinese. During his rule (first as a governor, then outright) the Timurid Empire achieved the cultural peak of the Timurid Renaissance through his attention and patronage.
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A surveyor using a total station A student using a Theodolite in field Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial or three-dimensional positions of points and the distances and angles between them. A land surveying professional is called a land surveyor. These points are usually on the surface of the Earth, and they are often used to establish maps and boundaries for ownership, locations, such as the designed positions of structural components for construction or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales. Surveyors work with elements of geometry, trigonometry, regression analysis, physics, engineering, metrology, programming languages, and the law.
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A chair in hydrography has been in place since 1704." "In the faculties, it is the mathematics in the sixteenth century, and the reshaping of this chair by the Marquis de Pommereuil in 1705 that gives new shine to optics, geometry, astronomy, architecture, military use of alloy chemistry, trigonometry, so as to train good officers. Mathematics and science in Douai were illustrated by the mathematician Charles Malapert in the early seventeenth century, who discovered sunspots probably before Kirchner, whom he met in Ingolstadt, and in the second half of the century by Anthony Thomas, a Jesuit successor of Verbiest in China, to chair the tribunal of Mathematics in Beijing. This correspondent of the Academy of Sciences has left a major work.
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An 1891 ad for "Jonas-Gibbs & Co.", a real estate firm owned by Frank B. Jonas and George Gibbs in Washington, D.C. Following in his father's footsteps, George Gibbs entered the U.S. Naval Academy in 1886, but he resigned in 1888. According to critic Grant Overton, Gibbs "generally neglected trigonometry in favor of a sketch book and the writing of verses." While at Annapolis, he contributed drawings, poems and songs to Junk, the Naval Academy yearbook of that era (forerunner of the Lucky Bag, which began publication in 1894 and continues to today), and he edited a collection of material from past editions of Junk after he left the Academy. Gibbs also played football at the Academy, "in the gridiron days of skull caps and padless knickers".
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He had Euclid's "Elements of Geometry" translated into Sanskrit as also several works on trigonometry, and Napier's work on the construction and use of logarithms. Relying primarily on Indian astronomy, these buildings were used to accurately predict eclipses and other astronomical events. The observational techniques and instruments used in his observatories were also superior to those used by the European Jesuit astronomers he invited to his observatories. Termed as the Jantar Mantar they consisted of the Ram Yantra (a cylindrical building with an open top and a pillar in its center), the Jai Prakash (a concave hemisphere), the Samrat Yantra (a huge equinoctial dial), the Digamsha Yantra (a pillar surrounded by two circular walls), and the Narivalaya Yantra (a cylindrical dial).
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In applied mathematics as used in the engineering field of robotics, an arm solution is a solution of equations that allow the calculation of the precise design parameters of a robot's arms in such a way as to enable it to make certain movements. A typical industrial robot is built with fixed length segments that are connected either at joints whose angles can be controlled, or along linear slides whose length can be controlled. If each angle and slide distance is known, the position and orientation of the end of the robot arm relative to the base can be computed with the simple trigonometry in robot control. Going the other way -- calculating the angles and slides needed to achieve a desired position and orientation -- is much harder.
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The academic program follows a classical liberal arts model with particular attention to classical (Latin and Greek) and modern foreign languages, British and American literature, mathematics and the natural sciences, history, theology, cultural studies, and the fine arts (vocal music, theater arts/communication). The Latin and Greek courses, in particular, encourages all students to be able to read Virgil's Aeneid in the original Latin and be able to translate the Gospel of John from the original Greek by their senior year. The mathematics program begins with pre-algebra and extends to Trigonometry and Calculus with emphasis in theory rather than application. Students are required to take Spanish as a modern foreign language. Each student is also required to participate in the school’s band and choir program.
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The parsec is defined as being equal to the length of the adjacent leg (opposite leg being 1 AU) of an extremely elongated imaginary right triangle in space. The two dimensions on which this triangle is based are its shorter leg, of length one astronomical unit (the average Earth-Sun distance), and the subtended angle of the vertex opposite that leg, measuring one arcsecond. Applying the rules of trigonometry to these two values, the unit length of the other leg of the triangle (the parsec) can be derived. One of the oldest methods used by astronomers to calculate the distance to a star is to record the difference in angle between two measurements of the position of the star in the sky.
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The length of the opposite side to the parallax angle is the distance from the Earth to the Sun (defined as one astronomical unit, au), and the length of the adjacent side gives the distance from the sun to the star. Therefore, given a measurement of the parallax angle, along with the rules of trigonometry, the distance from the Sun to the star can be found. A parsec is defined as the length of the side adjacent to the vertex occupied by a star whose parallax angle is one arcsecond. The use of the parsec as a unit of distance follows naturally from Bessel's method, because the distance in parsecs can be computed simply as the reciprocal of the parallax angle in arcseconds (i.e.
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The first edition was published in 1754, and The Elements of Navigation went through seven editions in fifty years. The first volume included sections on logarithms, Euclidean geometry, plane trigonometry, spherics, geography, plane sailing, oblique sailing, current sailing, globular sailing, parallel sailing, middle latitudes and Mercator's sailing, great circular sailing, astronomy, use of globes, as well as estimating distances and fortification. Pupils were prepared for the Royal Navy and the standards of mathematics at the Royal Mathematical School was high. A similar curriculum was followed at the Royal Navy Academy, of which Robertson became a mathematics master in 1755. His edition of The Elements of Navigation was used by Royal Mathematical School pupils on a daily basis between 1755 and 1775.
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Triana worked as an engineer for the train line of Puerto Wilches, finished in 1883, the central northern highway and train tracks in Cúcuta and on irrigation projects in the Valley of Sogamoso as part of a study to dewater Lake Tota. From 1890 Triana was director of public works in Nariño and from 1917 manager of the Municipal Tramway of Bogotá. Miguel Triana was professor in physics, hydraulics, geometry, trigonometry and drawing at the faculty of Engineering of the Universidad Nacional in Bogotá. He was affiliated with various organisations in Colombia, among others: Sociedad Físico-Literaria de Bogotá, El Ateneo, Sociedad de Ingenieros Civiles de los Estados Unidos, Sociedad Colombiana de Ciencias Naturales and the Sociedad Colombiana de Ingenieros, founded by Triana in 1887.
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As slide rule development progressed, added scales provided reciprocals, squares and square roots, cubes and cube roots, as well as transcendental functions such as logarithms and exponentials, circular and hyperbolic trigonometry and other functions. Aviation is one of the few fields where slide rules are still in widespread use, particularly for solving time–distance problems in light aircraft. In 1831–1835, mathematician and engineer Giovanni Plana devised a perpetual-calendar machine, which, through a system of pulleys and cylinders could predict the perpetual calendar for every year from AD 0 (that is, 1 BC) to AD 4000, keeping track of leap years and varying day length. The tide- predicting machine invented by Sir William Thomson in 1872 was of great utility to navigation in shallow waters.
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But they used his philosophy and proved it untrue by being able to calculate things such as temperature and power.Agutter, Paul S.; Wheatley, Denys N. (2008) "Thinking About Life" They developed Al-Battani's work on trigonometry and their most famous work was the development of the mean speed theorem, (though it was later credited to Galileo) which is known as "The Law of Falling Bodies".Gavroglu, Kostas; Renn, Jurgen (2007) "Positioning the History of Science" Although they attempted to quantify these observable characteristics, their interests lay more in the philosophical and logical aspects than in natural world. They used numbers to philosophically disagree and prove the reasoning of "why" something worked the way it did and not only "how" something functioned the way that it did.
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Shortly after TELCOMP was created, Wally decided to introduce it to children as a tool to teach mathematics and in 1965–66, under U.S. Office of Education support, explored its use as an auxiliary resource in eight elementary and secondary schools served by the BBN time-sharing system. Students were introduced to TELCOMP and then worked on standard arithmetic, algebra, and trigonometry problems by writing TELCOMP programs. The project strongly confirmed expectations that the use of interactive computation with a high- level interpretive language would be highly motivating to students. Wally's collaborators in this research were Daniel Bobrow, Richard Grant, and Cynthia Solomon from BBN and consultant Seymour Papert, who had recently arrived at MIT from Jean Piaget's Institute in Geneva.
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World History, on the other hand, is now being offered to the juniors. In 1979, Agriculture and Home Economics periods were further reduced to four hours a week. A change in the Mathematics curriculum was also implemented with the replacement of the traditional Mathematics courses with Math I (Modern Math), Math II (First Course in Algebra), Math III (Geometry), Math IV-A (Second Course in Algebra, part I), Math IV-B (Second Course in Algebra, part II), Math V (Introduction to Trigonometry), Math VI (Advanced Algebra), and Math VII (Introduction to Statistics). Advanced Mathematics classes have been offered starting school year 1980-81 to students who rate high in the math test of the entrance exam and later qualify in a test given to them.
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Quadratino was published by the children magazine Il Corriere dei Piccoli from 1910 to 1911.Franco Fossati, "Quadratino", in Fumetto - characters e disegnatori, cured by Luigi F. Bona, Electa, 2005. An early version of the character had previously appeared in 1909, in the same magazine, in the story La tragica istoria del triangolo e del quadrato. It depicts the surreal stories of the naughty Quadratino ("Little Square"), her grandmother Nonna Matematica ("Grandma Maths") and the tutor Trigonometria ("Trigonometry"); in every episode the title character is punished for his bad behaviour with the transformation of his head in a rectangle, a triangle or in another geometric shape; at the end of the story, after he understood his faults, the head returns to normal.
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For simplicity, consider that 5% to be a 5 degree angle. Using simple trigonometry, 5 degrees at 20,000 feet is approximately 1,750 feet, an error that would place the bombs far outside their lethal radius. In tests, accuracies of 3 to 4 degrees were considered standard, and angles as high as 15 degrees were not uncommon. Given the seriousness of the problem, systems for automatic levelling of bombsights was a major area of study before World War II, especially in the US.All of the USAAC's pre-war bombsights featured some system for automatically levelling the sight; the Estopery D-series used pendulums, Sperry designs used gyroscopes to stabilize the entire sight, and the Norden used gyroscopes to stabilize the optics.
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Important in fields such as surveying, railway engineering (for example to lay out railroad curves and superelevation), civil engineering, astronomy, and spherical trigonometry up into the 1980s, the exsecant function is now little-used. Mainly, this is because the broad availability of calculators and computers has removed the need for trigonometric tables of specialized functions such as this one. The reason to define a special function for the exsecant is similar to the rationale for the versine: for small angles θ, the sec(θ) function approaches one, and so using the above formula for the exsecant will involve the subtraction of two nearly equal quantities, resulting in catastrophic cancellation. Thus, a table of the secant function would need a very high accuracy to be used for the exsecant, making a specialized exsecant table useful.
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As theoretical statistics developed into a modern discipline, its practitioners were using geometrical representation in their presentations. The cross pollination of statistics with geometry led to increased interest in geometric theory. Professor Karl Pearson proposed that a specialist in geometry work out the trigonometry of higher-dimensioned plane space for all the relations between multiple correlation and partial correlation coefficients when variates are properties of the angles, edges and perpendiculars of sphero-polyhedron multiple space. A pure mathematician was needed to write, in effect, a treatise on “Spherical Polyhedrometry.”Karl Pearson, "Some Novel Properties of Partial and Multiple Correlation Coefficient in a Universe of Manifold Characteristics," 11 Biometrika 231, 237 (1916) cited in Raj Chandra Bose, "On the Application of Hyperspace Geometry to the Theory of Multiple Correlation," Sankhya (Indian Statistical Institute 1934) at 338.
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The academic program followed a classical liberal arts model with particular attention to classical (Latin and Greek) and modern foreign languages, British and American literature, mathematics and the natural sciences, history, theology, cultural studies, and the fine arts (vocal music, theater arts/communication, and mass media and video production). The Latin and Greek courses, in particular, encouraged all students to be able to read Virgil's Aeneid in the original Latin and be able to translate the Gospel of John from the original Greek by senior year. The mathematics program begins with pre- algebra and extends to Trigonometry and Calculus with emphasis in theory rather than application. Students were required to take Spanish as a modern foreign language. Each student was also required to participate in the school’s band and choir program.
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Al-Jabr wa-al-Muqabilah By the beginning of the 9th century, the "Islamic Golden Age" flourished, the establishment of the House of Wisdom in Baghdad marking a separate tradition of science in the medieval Islamic world, building not only Hellenistic but also on Indian sources. Although the Islamic mathematicians are most famed for their work on algebra, number theory and number systems, they also made considerable contributions to geometry, trigonometry and mathematical astronomy, and were responsible for the development of algebraic geometry. Al-Mahani (born 820) conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra. Al-Karaji (born 953) completely freed algebra from geometrical operations and replaced them with the arithmetical type of operations which are at the core of algebra today.
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In the applications of mathematics, there are often situations where an affine plane without the Euclidean metric is used instead of the Euclidean plane. For example, in a graph, which can be drawn on paper, and in which the position of a particle is plotted against time, the Euclidean metric is not adequate for its interpretation, since the distances between its points or the measures of the angles between its lines have, in general, no physical importance (in the affine plane the axes can use different units, which are not comparable, and the measures also vary with different units and scalesSee also the books of Mandelbrot, "Gaussian Self-Affinity and Fractals", of Levi, "Foundations of Geometry and Trigonometry", and of Yaglom, "A Simple Non-Euclidean Geometry and its Physical Basis".).
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Aryabhata's general solution for linear indeterminate equations, which Bhaskara I called kuttakara ("pulverizer"), consisted of breaking the problem down into new problems with successively smaller coefficients—essentially the Euclidean algorithm and related to the method of continued fractions. With Kala-kriya Aryabhata turned to astronomy—in particular, treating planetary motion along the ecliptic. The topics include definitions of various units of time, eccentric and epicyclic models of planetary motion (see Hipparchus for earlier Greek models), planetary longitude corrections for different terrestrial locations, and a theory of "lords of the hours and days" (an astrological concept used for determining propitious times for action). Aryabhatiya ends with spherical astronomy in Gola, where he applied plane trigonometry to spherical geometry by projecting points and lines on the surface of a sphere onto appropriate planes.
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In vector analysis, a vector with polar coordinates and Cartesian coordinates can be represented as the sum of orthogonal components: Similarly in trigonometry, the angle sum identity expresses: : And in functional analysis, when is a linear function of some variable, such as time, these components are sinusoids, and they are orthogonal functions. A phase-shift of changes the identity to: :, in which case is the in-phase component. In both conventions is the in-phase amplitude modulation, which explains why some authors refer to it as the actual in-phase component. IQ phasor diagram IQ modulation and demodulation block diagram Phase shifter using IQ modulator When a sinusoidal voltage is applied to either a simple capacitor or inductor, the resultant current that flows is "in quadrature" with the voltage.
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It was bundled together with the Encomium PrussiaeNicolaus Copernicus Gesamtausgabe (complete edition), Akademie Verlag, Letters of Copernicus, which praised the spirit of humanism in Prussia. During his two year stay in Prussia, Rheticus published works of his own, and in cooperation with Copernicus, in 1542 a treatise on trigonometry which was a preview to the second book of De revolutionibus. Under strong pressure from Rheticus, and having seen the favorable first general reception of the Narratio Prima, Copernicus finally agreed to give the book to his close friend, bishop Tiedemann Giese, to be delivered to Nuremberg for printing by Johannes Petreius under Rheticus's supervision. Later editions of Narratio Prima were printed in Basel, in 1541 by Robert Winter, and in 1566 by Henricus Petrus in connection with the second edition of De revolutionibus.
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The Garfield Building served as the Pottsville High School from 1894 to 1916Pottsville High School Centennial: 1853-1953, page 14 After the Civil War, a committee comprising Peter W. Sheafer, William B. W ells, Christopher Little, John W . Roseberry, and David A. Smith accomplished the reorganization of the high school and it was again placed on a firm basis. The P. H. S. Annual of 1905 said of the reorganization, "At this time a curriculum was adopted which has suffered little change." The then prevailing three-year course offered the following subjects: First (Junior Year) ~ History, algebra, geometry, foundation of Latin, Caesar, elocution; Second (Middle Year) ~ Geometry, physiology, literature, botany, composition, Cicero, Latin prose, Caesar, elocution, physical geography; Third (Senior Year ) ~ Physics, Cicero, Virgil, rhetoric, civics, astronomy, trigonometry, chemistry, geology, elocution.
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Fairview High School offers academic classes for reading and writing in the English language, basic mathematics, general science, general social studies, physical education, and career education for students in grades 6-8. Fairview High School also offers academic classes for reading and writing in the English language, reading and writing in the Spanish language, algebra, geometry, trigonometry, chemistry, biology, forensics, anatomy, United States history, United States government, geography, concert choir, art, humanities, marketing, career education, and advanced physical education for students in grades 9-12. Fairview High School's academic instruction is regulated by the Kentucky Department of Education. As of the 2014-2015 school year, Fairview High School earned a "Needs Improvement" classification for middle school instruction (grades 6-8) and a "Distinguished" classification for high school instruction (grades 9-12).
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Part of a 20th-century table of common logarithms in the reference book Abramowitz and Stegun. Before the advent of computers, lookup tables of values were used to speed up hand calculations of complex functions, such as in trigonometry, logarithms, and statistical density functions. In ancient (499 AD) India, Aryabhata created one of the first sine tables, which he encoded in a Sanskrit-letter-based number system. In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144"Maher, David.
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Schultz used Christian Wolff's Treatise of Algebra and Leonhard Euler Elements of Algebra (French: Élémens ďalgebre) and his own text for arithmetic, geometry and trigonometry. Schultz first met the philosopher Johann Gottlieb Fichte between July to October 1791 when Schultz helped Fichte acquire a teaching position close to Danzig. Fichte described Schultz in correspondence as: :He has an angular Prussian face, but honesty and kindness shine forth from it They continued to write to each other to discuss ideas, even when Fichte left Danzig.Fichte also discusses Schulz at some length in the 2nd Introduction [1797] to his Wissenschaftslehre (Science Teaching) The relationship between Schultz and Fichte was more convoluted than it would otherwise be, as Johanna Eleonore, née Büttner (1751–1795), Schultz’s wife, was romantically linked to Fichte.
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Ahmad ibn 'Abdallah Habash Hasib Marwazi (766 - d. after 869 in Samarra, Iraq ) was a PersianGeneral Cartography : "The Iranian geographers Abū Muhammad al- Hasan al-Hamdānī and Habash al-Hasib al-Marwazi set the Prime Meridian of their maps at Ujjain, a center of Indian astronomy" : "Additionally in the ninth century, the Persian mathematician and geographer, Habash al-Hasib al- Marwazi, utilized the utilization circular trigonometry and guide projection strategies keeping in mind the end goal to change over polar directions to an alternate arrange framework fixated on a particular point on the circle, in this the Qibla, the course to Mecca. Abū Rayhān Bīrūnī (973– 1048) later created thoughts which are viewed as a reckoning of the polar organize framework." astronomer,Islamic Desk Reference, ed. E. J. Van Donzel, (Brill, 1994), 121.
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It offered courses in penmanship, map- drawing, ancient and modern geography, American and world history, "evidences of Christianity", mental "phylosophy", trigonometry, astronomy, geology, botany, physiology, English, rhetoric, and Latin; all of these were required to complete a degree, except that French, German, art, or music could be substituted for Latin. Students were also required to take "physical culture". The college closed in 1895 for financial reasons; it may have been over- extended by its recent expansion and affected by the 1893 financial depression in the US. Add-Ran Christian University, a precursor of Texas Christian University, then bought the buildings and 15 acres of land from the Christian Church of Waco, which added a cash incentive and moving funds.Eric S. Ames, Waco, Images of America, Charleston, South Carolina: Arcadia, 2009, , p. 118.
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Rational trigonometry is otherwise broadly based on Cartesian analytic geometry, with a point defined as an ordered pair of rational numbers :(x,y) and a line :ax + by + c = 0, as a general linear equation with rational coefficients , and . By avoiding calculations that rely on square root operations giving only approximate distances between points, or standard trigonometric functions (and their inverses), giving only truncated polynomial approximations of angles (or their projections) geometry becomes entirely algebraic. There is no assumption, in other words, of the existence of real number solutions to problems, with results instead given over the field of rational numbers, their algebraic field extensions, or finite fields. Following this, it is claimed, makes many classical results of Euclidean geometry applicable in rational form (as quadratic analogs) over any field not of characteristic two.
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In Monastir, under the influence of his trigonometry teacher and deputy principal of the school, Bajo Topulli, Menduh got soon in contact with the patriotic circles. Though still young, he had developed a personality that won their respect and often attended their private meetings. The leading Albanian nationalists were striving to establish a new political organization that would fight for more cultural and political freedom, in a time when the policies of the declining Ottoman Empire towards the Albanian people were fluctuating between giving more cultural freedom and then restraining it by regarding them as Ottomans, not Albanians, considering that the majority of the population was Muslim. The League of Peja in 1899, the last significant political organization to express the demand for autonomy, had no substantial results; the Ottoman government shut it down and in 1902 its leader Haxhi Zeka was executed.
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One of the first resolutions adopted was to procure reports on the state and progress of particular sciences, to be drawn up from time to time by competent persons for the information of the annual meetings, and the first to be placed on the list was a report on the progress of mathematical science. Whewell, the mathematician and philosopher, was a Vice-president of the meeting: he was instructed to select the reporter. He first asked William Rowan Hamilton, who declined; he then asked Peacock, who accepted. Peacock had his report ready for the third meeting of the Association, which was held in Cambridge in 1833; although limited to Algebra, Trigonometry, and the Arithmetic of Sines, it is one of the best of the long series of valuable reports which have been prepared for and printed by the Association.
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Most textbooks of astronomy written in the medieval Islamic World contain a chapter on the determination of the qibla, considered one of the many things connecting astronomy with Islamic law (sharia). According to David A. King, various medieval solutions for the determination of the qibla "bear witness to the development of mathematical methods from the 3rd/9th to the 8th/14th centuries and to the level of sophistication in trigonometry and computational techniques attained by these scholars". The first mathematical methods developed in the early 9th century were approximate solutions to the mathematical problem, usually using a flat map or two-dimensional geometry. Since in reality the earth is spherical, the directions found were inexact, but they were sufficient for locations relatively close to Mecca (including as far away as Egypt and Iran) because the errors were less than 2°.
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Homestead High School teaches courses in business, computer science, cooperative education, engineering and technology, English, family and consumer education, fine arts, foreign language, mathematics, physical education, science, and social studies. Honors courses include algebra 1, algebra 2/trigonometry, American literature, American studies-English, American studies-social studies, biology, British literature, business organization and management, calculus AB I, chemistry, English 9/argumentation, English 9, expository writing, French 4, geometry, German 4, independent study, Latin 4, multi-variable calculus, physics, pre-calculus, product development project, Spanish 4, and world studies. Homestead offers A.P. classes in French, German, calculus AB, calculus BC, physics, Spanish, statistics, United States history, American government, biology, chemistry, macroeconomics, microeconomics, psychology, English language, and English literature. The graduation rate for the school has been 99% or better for at least the past 10 consecutive years.
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Bellevue College campus in 2005 Bellevue College was established in 1966, originally under the auspices of the Bellevue School District, as an institution of higher education for residents of the Eastside of Lake Washington. The college opened with a total of 464 students and 37 instructors, with a curriculum that included classes in the social sciences, trigonometry, physics, botany, and English, among others. Vocational classes initially offered included nursing, basic aircraft blueprint reading, and food service management. Dr. Merle E. Landerholm was appointed the college's first president. The college graduated its first class in June 1967, with 10 students earning degrees and certificates, and 15 earning high school diplomas. Also in 1967, the Washington State Legislature passed the Community College Act, which created a statewide community college system and separated Bellevue Community College from the Bellevue School District.
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The O.B. Montessori Professional High School Curriculum is composed of 4 core subjects: Communication Arts (Filipino, English, Public Speaking, Logic/Argumentation and Debate, Spanish/Italian/Nihonggo/French); Science and Technology (Physical Science, Biology, Chemistry, Physics); Mathematics (Algebra, Geometry with Logic, Trigonometry with Calculus and Statistics); and Makabayan Subjects (Social Studies, Law on Persons, Technology, Home Economics and Livelihood Education, Computer, Accounting, Values Education, Music, Physical Education, Health, Leadership Training and the Revitalized Homeroom Guidance Program) Co-curricular activities complement the classroom activities. Field trips are regularly scheduled through the year. High school joint school-endorsed clubs include: OBMC Leadership Corps, Women's Volleyball Varsity, Marching Band, Show Band, Taekwondo Club, Men's and Women's Basketball Varsity, Glee Club, Dance Club, Rainbow Catering Club, and UNESCO ASPNet Club. To symbolize adolescence, the symbol of knightlihood and chivalry is used for the OBMC Professional High School.
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Military implements, the supply of an army, its organization, tactics, and discipline, have constituted the elements of military science in all ages; but improvement in weapons and accoutrements appears to lead and control all the rest.p. 194, Lodge The breakthrough of sorts made by Clausewitz in suggesting eight principles on which such methods can be based, in Europe, for the first time presented an opportunity to largely remove the element of chance and error from command decision making process.p. 12, Dupuy At this time emphasis was made on the Topography (including Trigonometry), Military art (Military science),taught by a Professor of Military Art at the Staff School in France, p. 248, Barnard Military history, Organisation of the Army in the field, Artillery and Science of Projectiles, Field fortifications and Permanent fortifications, Military legislation, Military administration and Manoeuvres.p.
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Anderson's first journalistic job was on the Hornsey Journal after which he joined the News Chronicle. He then tried to establish a soap manufactury in Trinidad, but after that failed he returned to Britain to work at Manchester's journal of the textile industry, the Textile Recorder. He served in the Indian Army and taught gunners trigonometry by writing a manual in Urdu, that he learned in three months, in which he compared the relationship between the sides of a right-angled triangle to that between cousins of various degrees within a family. He was invalided out of the Indian Army in 1944, from whom he refused to accept a disability pension due to the country's poverty, and was then taken on by The Guardian where he became the paper's correspondent at Eisenhower's headquarters in the later period of the Second World War.
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A gnomon or style is set to point at the celestial north pole, the shadow of the sun is thrown onto the dial plate and will appear at the same position each day of the year, and this position can be calculated using trigonometry, or drawn using geometric construction. In the world of sundials some of the technical terms use an old form of language, so the angle to which the style is set is called the style height. The style height is identical to the geographical latitude, and in London this was 51 degrees 30 minutes or 51.50 degrees, which roughly corresponds with Westminster Bridge. The gnomon has thickness, and thus two shadow throwing edges (the styles) one for the morning and one for the afternoon, there is a gap left on the dialplate the width of the gnomon.
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The coordinates of an unknown point relative to a known coordinate can be determined using the total station as long as a direct line of sight can be established between the two points. Angles and distances are measured from the total station to points under survey, and the coordinates (X, Y, and Z; or easting, northing, and elevation) of surveyed points relative to the total station position are calculated using trigonometry and triangulation. To determine an absolute location, a total station requires line of sight observations and can be set up over a known point or with line of sight to 2 or more points with known location, called free stationing. For this reason, some total stations also have a Global Navigation Satellite System receiver and do not require a direct line of sight to determine coordinates.
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A spherical triangle In sixteenth century Europe, celestial navigation of ships on long voyages relied heavily on ephemerides to determine their position and course. These voluminous charts prepared by astronomers detailed the position of stars and planets at various points in time. The models used to compute these were based on spherical trigonometry, which relates the angles and arc lengths of spherical triangles (see diagram, right) using formulas such as: :\cos a = \cos b \cos c + \sin b \sin c \cos \alpha and :\sin b \sin \alpha = \sin a \sin \beta where a, b and c are the angles subtended at the centre of the sphere by the corresponding arcs. When one quantity in such a formula is unknown but the others are known, the unknown quantity can be computed using a series of multiplications, divisions, and trigonometric table lookups.
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Hilda Dallas was seen in a poster parade encouraging women to come to the demonstration at the House of Commons on 30 June 1908 with Dorothy Hartopp Radcliffe, Charlotte Marsh and Dora Spong in the strand earlier in June 1908. The image is in the Museum of London. Hilda Dallas (third from left) in poster parade in June 1908 Irene Dallas was studying maths whilst already in prison and the prison governor wrote, on 9 October 1908, to the Home Office, for permission for her to be sent an Algebra & Geometry and a Trigonometry book, as she was preparing for the Cambridge University entrance examinations. The governor remarked in his letter that 'A lady who runs the risk of imprisonment has presumably calculated that her action is of more importance to her than her prospects of getting into Cambridge.
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In order to qualify for a diploma, students must complete four years of English, science, social studies, mathematics, physical education, and elective classes; a total of 44 credits are required for graduation. In addition, students are required to complete at least one year of foreign language; one credit each of music and art are also required. LMGHS Programs Offered A New York State Regents Diploma is given to students who pass the Regents Examinations in English, global history, American history, algebra, geometry, advanced algebra, trigonometry, biology, chemistry, and physics and who complete three years of a foreign language. Students who have completed a minimum of nine semesters (9 credits) of arts study, along with a rigorous assessment of their art form, including passing the visual arts or music Regents Examination, will also earn the NYC Chancellor’s Arts Endorsed Diploma.
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Thus his patronage resulted in the refinement of the definition of the mile used by Arabs (mīl in Arabic) in comparison to the stadion used by Greeks. These efforts also enabled Muslims to calculate the circumference of the earth. Al-Mamun also commanded the production of a large map of the world, which has not survived,Edson and Savage-Smith (2004) though it is known that its map projection type was based on Marinus of Tyre rather than Ptolemy. Also in the 9th century, the Persian mathematician and geographer, Habash al-Hasib al-Marwazi, employed spherical trigonometry and map projection methods in order to convert polar coordinates to a different coordinate system centred on a specific point on the sphere, in this the Qibla, the direction to Mecca. Abū Rayhān Bīrūnī (973–1048) later developed ideas which are seen as an anticipation of the polar coordinate system.
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But if rote exercises are the only kinds of problems that students see in their classes, we are doing the students a grave disservice. He advocated setting challenges: :By "real problems" ... I mean mathematical tasks that pose an honest challenge to the student and that the student needs to work at in order to obtain a solution. A similar sentiment was expressed by Marvin Bittinger when he prepared the second editionMarvin L Bittinger (1981) Fundamental Algebra and Trigonometry, 2nd edition, Addison Wesley, of his textbook: :In response to comments from users, the authors have added exercises that require something of the student other than an understanding of the immediate objectives of the lesson at hand, yet are not necessarily highly challenging. The zone of proximal development for each student, or cohort of students, sets exercises at a level of difficulty that challenges but does not frustrate them.
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FLORENCIA CORPUZ, MA cand. College Algebra (SY 1994–1995, 1995–1996) MR. RODRIGO CORPUZ Physical Education (SY 1985–1986 to present) MS. MILA CORTEZ, MA English (SY 1995–1996 to 1997–1998, 1999–2000, 2000–2001) Self-Discovery, Group Processing (SY 1995–1996 to 1999–2000) MR. ARSENIO CRISOSTOMO, BM Music (SY 2000–2001 to present) MRS. LOURDES DALUPAN, MA Spanish and English (SY 1975–1976 to 1979–1980) MS. MARY ANN DALUPAN, MA cand.. Group Dynamics (SY 1990–1991 to 1992–1993) MS. VISITACION R. DE LA TORRE, MA (Lingui) English Composition, Philippine Literature, Drama, Poetry (SY 1974–1975) Mr. JESUS ANGELO DELA CRUZ Religious Education (SY 2000–2001, 2001–2002, 2002–2003) MS. KREMHILDA DIDELES, MAT College Algebra, Physics (SY 1985–1986, 1986–1987) Earth and Universe, Trigonometry (SY 1986–1987) MRS. NANETTE GARCIA-DUNGO, PhD Sociology (SY 2006–2007 to present) Economics (SY 2007–2008 to present) MRS.
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Butthan emphasizes mindfulness training and conscious use of mind to activate the physical movement, thereby maximizing the efficiency and delivery of power which is known as Mon-Chala. The practice of the martial art produces balance through a process of inculcating self- discipline and pragmatic restructuring of personal habits known as Vaz-Sodhon. Butthan also uniquely stages a mental test as a part of the tournament rules to ensure the quality of participants’ mental and physical prowess equally which is called Jhalak Khela. The system of Butthan has the essence of knowledge and scientific principles of psychology, trigonometry, human anatomy, physiology, logic, human nervous system, Vajra Pran, Siddha medical knowledge blended with selected self-defense methods combining the arts such as Bando, Vajra-mushti, Varma kalai, Tibetan and Chinese Kempo, Ming Jing, Bansahy, Lathi khela and other selected strategies of the ancient Indian, Burmese and Tibetan unarmed and weapons systems.
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The great height of this area, however, combined with its unpredictable weather, meant that few useful sightings were obtained before 1847. In an era before the electronic computer, it then took many months for a team of humans to calculate, analyze and extrapolate the trigonometry involved. According to accounts of the time,See report in 'The Illustrated London News', 15 August 1857 it was 1852 when the team's leader of the human computers, Radhanath Sikdar came to Waugh to announce that what had been labeled as "Peak XV" was the highest point in the region and most likely in the world. Sikdar and Waugh checked their calculations again and again in order to make no mistake in them and then sent a message to Royal Geographical Society from their headquarters in Dehradun, where they found that Kangchenjunga is not the highest peak of the world.
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The first attempt at reorganisation was the 1891 scheme which proposed the creation of a 200 pupil school on a 9-acre site on Pen-y-pound. Building of the school was delayed by many problems and was not completed until 1898 at a cost of £6,945. The school at this time was supposed to be a grammar school taking pupils from all over North Monmouthshire with a curriculum of Latin, English, History, Geography, French, Arithmetic, Algebra, Trigonometry and Chemistry.Nelmes (1992), p. 5 In the 1920s there was new building with three classrooms, a gym and a library. The Old Boys' Association was founded at a meeting on 7 November 1923 and was soon thriving, with branches of the Abergavenny Society in both London and Aberystwyth. By 1930 the school had 150 pupils. The new sciences of Physics and Biology were introduced in the period and the increased importance of metalwork and woodwork led to the building of a handicrafts room.
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Its acceptance within the European Space Agency's scientific programme, in 1980, was the result of a lengthy process of study and lobbying. The underlying scientific motivation was to determine the physical properties of the stars through the measurement of their distances and space motions, and thus to place theoretical studies of stellar structure and evolution, and studies of galactic structure and kinematics, on a more secure empirical basis. Observationally, the objective was to provide the positions, parallaxes, and annual proper motions for some 100,000 stars with an unprecedented accuracy of 0.002 arcseconds, a target in practice eventually surpassed by a factor of two. The name of the space telescope, "Hipparcos", was an acronym for High Precision Parallax Collecting Satellite, and it also reflected the name of the ancient Greek astronomer Hipparchus, who is considered the founder of trigonometry and the discoverer of the precession of the equinoxes (due to the Earth wobbling on its axis).
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Masood 2009, pp.49–52 and gave the first known recorded explanation of cryptanalysis and the first description of the method of frequency analysis. Avicenna ( 980–1037) contributed to mathematical techniques such as casting out nines.Masood 2009, pp.104–105 Thābit ibn Qurra (835–901) calculated the solution to a chessboard problem involving an exponential series.Masood 2009, pp.48–49 Al-Farabi ( 870–950) attempted to describe, geometrically, the repeating patterns popular in Islamic decorative motifs in his book Spiritual Crafts and Natural Secrets in the Details of Geometrical Figures.Masood 2009, pp.148–149 Omar Khayyam (1048–1131), known in the West as a poet, calculated the length of the year to within 5 decimal places, and found geometric solutions to all 13 forms of cubic equations, developing some quadratic equations still in use.Masood 2009, pp.5, 104, 145–146 Jamshīd al-Kāshī ( 1380–1429) is credited with several theorems of trigonometry, including the law of cosines, also known as Al-Kashi's Theorem.
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A rigorous treatment requires spherical trigonometry, thus those who remain certain that Hipparchus lacked it must speculate that he may have made do with planar approximations. He may have discussed these things in Perí tēs katá plátos mēniaías tēs selēnēs kinēseōs ("On the monthly motion of the Moon in latitude"), a work mentioned in the Suda. Pliny also remarks that "he also discovered for what exact reason, although the shadow causing the eclipse must from sunrise onward be below the earth, it happened once in the past that the Moon was eclipsed in the west while both luminaries were visible above the earth" (translation H. Rackham (1938), Loeb Classical Library 330 p. 207). Toomer (1980) argued that this must refer to the large total lunar eclipse of 26 November 139 , when over a clean sea horizon as seen from Rhodes, the Moon was eclipsed in the northwest just after the Sun rose in the southeast.
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The book is organized historically, and reviewer Robert Bradley divides the topics of the book into three parts. The first part discusses the earlier history of polyhedra, including the works of Pythagoras, Thales, Euclid, and Johannes Kepler, and the discovery by René Descartes of a polyhedral version of the Gauss–Bonnet theorem (later seen to be equivalent to Euler's formula). It surveys the life of Euler, his discovery in the early 1750s that the Euler characteristic V-E+F is equal to two for all convex polyhedra, and his flawed attempts at a proof, and concludes with the first rigorous proof of this identity in 1794 by Adrien-Marie Legendre, based on Girard's theorem relating the angular excess of triangles in spherical trigonometry to their area. Although polyhedra are geometric objects, Euler's Gem argues that Euler discovered his formula through being the first to view them topologically (as abstract incidence patterns of vertices, faces, and edges), rather than through their geometric distances and angles.
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The range of subjects being taught were very advanced, as can be seen from the Syllabus of Education in the Municipal Atheneum of Manila, that included Algebra, Agriculture, Arithmetic, Chemistry, Commerce, English, French, Geography, Geometry, Greek, History, Latin, Mechanics, Natural History, Painting, philosophy, Physics, Rhetoric and poetry, Spanish Classics, Spanish Composition, Topography, and Trigonometry. Among the subjects being taught to girls, as reflected in the curriculum of the Colegio de Santa Isabel, were Arithmetic, Drawing, Dress- cutting, French, Geology, Geography, Geometry, History of Spain, Music, Needlework, Philippine History, Physics, Reading, Sacred History and Spanish Grammar. Contrary to what the Propaganda of the Spanish–American War tried to depict, the Spanish public system of education was open to all the natives, regardless of race, gender or financial resources. The Black Legend propagation, black propaganda and yellow journalism were rampant in the last two decades of Spanish Colonial Period and throughout the American Colonial Period.
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Instead, Arabian and Persian cartography followed Al-Khwārizmī in adopting a rectangular projection, shifting Ptolemy's Prime Meridian several degrees eastward, and modifying many of Ptolemy's geographical coordinates. Having received Greek writings directly and without Latin intermediation, Arabian and Persian geographers made no use of T-O maps. In the 9th century, the Persian mathematician and geographer, Habash al-Hasib al-Marwazi, employed spherical trigonometry and map projection methods in order to convert polar coordinates to a different coordinate system centred on a specific point on the sphere, in this the Qibla, the direction to Mecca. Abū Rayhān Bīrūnī (973–1048) later developed ideas which are seen as an anticipation of the polar coordinate system. Around 1025, he describes a polar equi-azimuthal equidistant projection of the celestial sphere. However, this type of projection had been used in ancient Egyptian star-maps and was not to be fully developed until the 15 and 16th centuries.
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The next step in applying Rømer's correction would be to calculate the position of Earth and Jupiter in their orbits for each of the eclipses. This sort of coordinate transformation was commonplace in preparing tables of positions of the planets for both astronomy and astrology: it is equivalent to finding each of the positions L (or K) for the various eclipses which might be observable. Finally, the distance between Earth and Jupiter can be calculated using standard trigonometry, in particular the law of cosines, knowing two sides (distance between the Sun and Earth; distance between the Sun and Jupiter) and one angle (the angle between Jupiter and Earth as formed at the Sun) of a triangle. The distance from the Sun to Earth was not well known at the time, but taking it as a fixed value a, the distance from the Sun to Jupiter can be calculated as some multiple of a.
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In 1868 Beltrami published two memoirs (written in Italian; French translations by J. Hoüel appeared in 1869) dealing with consistency and interpretations of non-Euclidean geometry of János Bolyai and Nikolai Lobachevsky. In his "Essay on an interpretation of non-Euclidean geometry", Beltrami proposed that this geometry could be realized on a surface of constant negative curvature, a pseudosphere. For Beltrami's concept, lines of the geometry are represented by geodesics on the pseudosphere and theorems of non-Euclidean geometry can be proved within ordinary three-dimensional Euclidean space, and not derived in an axiomatic fashion, as Lobachevsky and Bolyai had done previously. In 1840, Ferdinand Minding already considered geodesic triangles on the pseudosphere and remarked that the corresponding "trigonometric formulas" are obtained from the corresponding formulas of spherical trigonometry by replacing the usual trigonometric functions with hyperbolic functions; this was further developed by Delfino Codazzi in 1857, but apparently neither of them noticed the association with Lobachevsky's work.
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Even tasks as simple as drawing two angled lines meeting at a point require a number of moves of the T-square and triangles, and in general, drafting can be a time-consuming process. A solution to these problems was the introduction of the mechanical "drafting machine", an application of the pantograph (sometimes referred to incorrectly as a "pentagraph" in these situations) which allowed the drafter to have an accurate right angle at any point on the page quite quickly. These machines often included the ability to change the angle, thereby removing the need for the triangles as well. In addition to the mastery of the mechanics of drawing lines, arcs and circles (and text) onto a piece of paper—with respect to the detailing of physical objects—the drafting effort requires a thorough understanding of geometry, trigonometry and spatial comprehension, and in all cases demands precision and accuracy, and attention to detail of high order.
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In Morpeth, Nicholson started work on a book entitled A Treatise on Dialing in which he described how to prepare and erect sundials, as well as applying trigonometry to the problem of finding the length of the hip of a roof and its rafters from the angle of inclination of its eaves. On 10 August 1832, Nicholson's wife, Jane died, aged 48, and he erected a neat memorial to her in the grounds of the High Church before leaving Morpeth and taking up residence in Carliol Street, Newcastle upon Tyne. At the age of 67, and still financially embarrassed, Nicholson resumed his writing, finally getting his Treatise on Dialing published in Newcastle in 1833, and set up a school in the recently opened Royal Arcade, which he ran for a few years, though it was not a financial success. He was nevertheless highly regarded by the local people and was awarded honorary memberships of a number of local institutions, including the Newcastle Mechanics' Institute.
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In the 19th century, hyperbolic geometry was explored extensively by Nikolai Ivanovich Lobachevsky, János Bolyai, Carl Friedrich Gauss and Franz Taurinus. Unlike their predecessors, who just wanted to eliminate the parallel postulate from the axioms of Euclidean geometry, these authors realized they had discovered a new geometry. Gauss wrote in an 1824 letter to Franz Taurinus that he had constructed it, but Gauss did not publish his work. Gauss called it "non-Euclidean geometry"Felix Klein, Elementary Mathematics from an Advanced Standpoint: Geometry, Dover, 1948 (reprint of English translation of 3rd Edition, 1940. First edition in German, 1908) pg. 176 causing several modern authors to continue to consider "non-Euclidean geometry" and "hyperbolic geometry" to be synonyms. Taurinus published results on hyperbolic trigonometry in 1826, argued that hyperbolic geometry is self consistent, but still believed in the special role of Euclidean geometry. The complete system of hyperbolic geometry was published by Lobachevsky in 1829/1830, while Bolyai discovered it independently and published in 1832.
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Notwithstanding the arduous duties of his professorship, he found time for investigation in various fields of physical science, and he published a very large number of dissertations, some of them of considerable length. Among the subjects were the transit of Mercury, the Aurora Borealis, the figure of the Earth, the observation of the fixed stars, the inequalities in terrestrial gravitation, the application of mathematics to the theory of the telescope, the limits of certainty in astronomical observations, the solid of greatest attraction, the cycloid, the logistic curve, the theory of comets, the tides, the law of continuity, the double refraction micrometre, and various problems of spherical trigonometry. In 1742 he was consulted, with other men of science, by Pope Benedict XIV, as to the best means of securing the stability of the dome of St. Peter's, Rome, in which a crack had been discovered. His suggestion of placing five concentric iron bands was adopted.
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On January 8, 1854, Yan Fu was born in what is modern day Fuzhou, Fujian Province to a respectable scholar-gentry family in the trade of Chinese medicine. In his early years, Yan Fu’s father greatly encouraged Yan Fu to obtain a high education and prepare for the Imperial examination. However, the death of his father in 1866 caused an abrupt change to these plans. A year later, Yan Fu entered the Fujian Arsenal Academy () in Fuzhou, a Western school where he studied a variety of subjects including English, arithmetic, geometry, algebra, trigonometry, physics, chemistry, astrology and navigation. This was a turning point in young Yan Fu’s life as he was able to experience first-hand contact with Western science, thus inspiring the enthusiasm that carried him through the rest of his career. After graduating with high honors in 1871, Yan Fu went on to spend the next five years at sea.
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In Chapter XI of The Age of Reason, the American revolutionary and Enlightenment thinker Thomas Paine wrote: :The scientific principles that man employs to obtain the foreknowledge of an eclipse, or of any thing else relating to the motion of the heavenly bodies, are contained chiefly in that part of science that is called trigonometry, or the properties of a triangle, which, when applied to the study of the heavenly bodies, is called astronomy; when applied to direct the course of a ship on the ocean, it is called navigation; when applied to the construction of figures drawn by a ruler and compass, it is called geometry; when applied to the construction of plans of edifices, it is called architecture; when applied to the measurement of any portion of the surface of the earth, it is called land-surveying. In fine, it is the soul of science. It is an eternal truth: it contains the mathematical demonstration of which man speaks, and the extent of its uses are unknown.
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Discussions on establishing a second post-secondary institution in Ottawa began in the fall of 1938 among a committee of members from the local YMCA chapter, who looked to create a school to meet the educational needs of Ottawa's sizeable non-Catholic population. While the Second World War abruptly ended the committee's activities, a new committee was organized by Henry Marshall Tory as the Ottawa Association for the Advancement of Learning at a meeting held in December 1941, with formal incorporation in June 1942. Established in 1942 as Carleton College, a non-denominational institution, the school began offering evening courses in rented classrooms at the High School of Commerce, now part of the Glebe Collegiate Institute. Classes offered during the first academic year included English, French, history, algebra, trigonometry, chemistry, physics, and biology. With the end of the war in 1945 and return of veterans from the frontlines, the College experienced an unexpected upsurge in student enrolment during the 1945–46 academic year, enrolling about 2,200 new students.
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If a navigator knows how long the ship has sailed on the erroneous course, he can calculate its current distance from its intended course, and estimate how long it must sail back on a new bearing until it recovers its old course. In the Corsica-to-Genoa example, there is an implied triangle ACD, with one side given (AC = 70 miles on actual NW course), a 45° angle at A (angle of difference between actual course NW and intended course N) and another angle of 90° at C (angle of difference between actual course NW and return course NE). The challenge to the navigator is to find how long one must sail on the NE return course (the length of side CD, what is called the ritorno) and how far one has advanced on the intended course by the time one straightens out (the length of the hypotenuse AD, or what is called the total avanzo). This is elementary trigonometry, solving for two sides given one side (70) and two angles (45° and 90°).
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In 1825, Dr. Juan José de Aycinena y Piñol was elected as president of the University, and kept the religious curriculum that the institution had had for decades. However, in 1829, the conservative regime of his brother Mariano de Aycinena y Piñol was defeated by the liberal general Francisco Morazán, and the conservatives - mainly the Aycinena family - and the regular clergy were expelled from Central America and the University was suspended. In 1834, when doctor Mariano Gálvez was head of State of Guatemala, he found the Science Academy in the State, which took the position that the Pontifical University had previously occupied; the new university eliminated religious education altogether and implemented classes of Algebra, Geometry, Trigonometry and Physics; besides, the institution began to offer studies in engineering. The Academy of Science was open until 1840, because in that year the conservatives regained power in Guatemala under the strong leadership of General Rafael Carrera who reopened the old "Pontifical University of San Carlos Borromeo"; Dr. Aycinena was once again named as president of the university.
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"Incognito" included student creative writing and students contributed to You're the Critic which featured critical reviews by Baltimore City High School students. There was also a student government. A number of classes were available to students, such as: English, Geometry, Algebra, Trigonometry, Calculus, Social Studies, Biology, Art, Jewelry-making, photography, reading, Spanish, German, typing, Sociology, Psychology, Drafting, and others. Some community college classes were offered after regular school hours on the Northern High School campus. For the class of 1977, the city comptroller, Hyman Pressman, read a poem for graduation. Due to overcrowding in the 1970s in many Baltimore City Schools, there were 2–3 years when students attended for a half day all year, with juniors and seniors attending 8am to 12 noon and sophomores attending 12 to 4 pm. High School was for 3 years at that time, and many students transferred to Northern High School after Junior High School of grades 7, 8, and 9. During these times freshman who wanted to attend Northern could not and had to wait until their sophomore year due to the over crowding.
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It was during this time—approximately 1774—that he met Charles Messier, and apparently, they became friends. In the same year, he also produced his first astronomical work, a paper on an occultation of Aldebaran by the Moon and presented it as a memoir to the Academy of Sciences. In 1777, he married Barbe-Thérèse Marjou whom he knew from his work in Versailles. They had two sons: Jérôme, born 1780, and Augustin, born 1784, and one daughter. He was admitted to the French Académie des sciences in 1782, and was the editor of Connaissance des Temps from 1785 to 1792; this was the journal which, among other things, first published the list of Messier objects. In 1789 he was elected a Fellow of the Royal Society. He participated in the Anglo-French Survey (1784–1790) to measure by trigonometry the precise distance between the Paris Observatory and the Royal Greenwich Observatory. This project was initiated by Dominique, comte de Cassini, and in 1787 Méchain visited Dover and London with Cassini and Adrien-Marie Legendre to facilitate its progress.
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James E. Gentle, Numerical Linear Algebra for Applications in Statistics, Publisher: Springer, 1998, , 9780387985428, 221 pages, [James E. Gentle page 183] Algebraic operations work in the same way as arithmetic operations,Horatio Nelson Robinson, New elementary algebra: containing the rudiments of science for schools and academies, Ivison, Phinney, Blakeman, & Co., 1866, page 7 such as addition, subtraction, multiplication, division and exponentiation.Ron Larson, Robert Hostetler, Bruce H. Edwards, Algebra And Trigonometry: A Graphing Approach, Publisher: Cengage Learning, 2007, , 9780618851959, 1114 pages, page 6 and are applied to algebraic variables and terms. Multiplication symbols are usually omitted, and implied when there is no space between two variables or terms, or when a coefficient is used. For example, 3 \times x^2 is written as 3x^2, and 2 \times x \times y may be written 2xy.Sin Kwai Meng, Chip Wai Lung, Ng Song Beng, "Algebraic notation", in Mathematics Matters Secondary 1 Express Textbook, Publisher Panpac Education Pte Ltd, , 9789812738820, page 68 Usually terms with the highest power (exponent), are written on the left, for example, x^2 is written to the left of .
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The book only assumes a high-school understanding of algebra, geometry, and trigonometry, but it is primarily aimed at professionals in this area, and some steps in the book's reasoning which a professional could take for granted might be too much for less-advanced readers. Nevertheless, reviewer J. C. P. Miller recommends it to "anyone interested in the subject, whether from recreational, educational, or other aspects", and (despite complaining about the omission of regular skew polyhedra) reviewer H. E. Wolfe suggests more strongly that every mathematician should own a copy. Geologist A. J. Frueh Jr., describing the book as a textbook rather than a monograph, suggests that the parts of the book on the symmetries of space would likely be of great interest to crystallographers; however, Frueh complains of the lack of rigor in its proofs and the lack of clarity in its descriptions. Already in its first edition the book was described as "long awaited", and "what is, and what will probably be for many years, the only organized treatment of the subject".
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Frontispiece of Leslie's A Short Account of Experiments and Instruments, Depending on the Relations of Air to Heat and Moisture 1813 Leslie's home at 62 Queen Street, Edinburgh For the next twelve years (passed chiefly in London or at Largo, with an occasional visit to the continent of Europe) he continued his physical studies, which resulted in numerous papers contributed by him to Nicholson's Philosophical Journal, and in the publication (1804) of the Experimental Inquiry into the Nature and Properties of Heat, a work which gained him the Rumford Medal of the Royal Society of London. In 1805 he was elected to succeed John Playfair in the chair of mathematics at Edinburgh. This despite violent opposition on the part of a party who accused him of heresy. During his tenure of this chair he published two volumes of A Course of Mathematics- the first, entitled Elements of Geometry, Geometrical Analysis and Plane Trigonometry, in 1809, and the second, Geometry of Curve Lines, in 1813; the third volume, on Descriptive Geometry and the Theory of Solids was never completed.
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His method, as Riggs notes, is an inductive one, starting with the study of "sensible things" (52), and progressing to "things invisible" only after mastering the former (Riggs 450). This move effectively inverts the deductive method common in medieval education. The "organic arts" of rhetoric and logic therefore find a place at the end of Milton's curriculum, rather than at the beginning (59). Noteworthy too is Milton's inclusion of poetry amongst the other organic arts: “poetry would be made subsequent, or indeed, rather precedent, as being less subtle and fine, but more simple, sensuous, and passionate” (60). Milton’s proposed curriculum, encompassing as it does grammar, arithmetic, geometry, religion, agriculture, geography, astronomy, physics, trigonometry, ethics, economics, languages, politics, the law, theology, church history as well as the “organic arts” of poetry, rhetoric and logic, is encyclopaedic in scope. His main thrust in the educational enterprise remains, however, on that practical erudition which would serve both the individual in a moral sense and the state in a public sense, equipping people “to be brave men and worthy patriots, dear to God and famous to all ages” (56). This stands in contrast to the contemplative and speculative concerns of medieval education.
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However, there are a number of limitations to the use of radar speed guns. For example, user training and certification are required so that a radar operator can use the equipment effectively, with trainees being required to consistently visually estimate vehicle speed within +/-2 mph of actual target speed, for example if the target's actual speed is 30 mph then the operator must be able to consistently visually estimate the target speed as falling between 28 and 32 mph. Stationary traffic enforcement radar must occupy a location above or to the side of the road, so the user must understand trigonometry to accurately estimate vehicle speed as the direction changes while a single vehicle moves within the field of view. Actual vehicle speed and radar measurement thus are rarely the same, however, for all practical purposes this difference in actual speed and measured speed is inconsequential, generally being less than 1 mph difference, as police are trained to position the radar to minimize this inaccuracy and when present the error is always in the favor of the driver reporting a lower than actual speed.
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