Jhabvala is an artful geometer, and she skews her angles boldly.
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His work as a geometer influenced artists like MC Escher and Buckminster Fuller.
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Compass drawn designs are also linked to sacred geometry, and the belief that god is the "geometer of the world".
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I knew that Euclid and Mandelbrot had to do with geometry, but was unable until almost the end to get my head around GEOMETER.
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Around 1,600 years ago, the Chinese geometer Zu Chongzhi pondered polygons having an incredible 24,576 sides to squeeze pi out to eight digits: 3.1415926 < π < 3.1415927.
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As a ratio, pi has been around since Babylonian times, but it was the Greek geometer Archimedes, some 2,300 years ago, who first showed how to rigorously estimate the value of pi.
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"I think there's still a lot more to discover about geometry based on the quaternions," said Nigel Hitchin, a geometer at the University of Oxford, "but if you want a new frontier, then it's the octonions."
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Before Süss was an interactive widget, it was a member of the Gallery of Singularities, a collection of algebraic surfaces created and curated in 2006 by Herwig Hauser, a geometer at the University of Vienna, and a master at resolving singularities.
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Similar species in the false crocus geometer's range include the crocus geometer (Xanthotype sospeta) and the rufous geometer (Xanthotype rufaria). The crocus geometer is larger, is pale yellow, and has little or no brown spotting. The rufous geometer is a deeper yellow and has a reddish fringe.
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Cingilia is a monotypic moth genus in the family Geometridae erected by Francis Walker in 1862. Its only species, Cingilia catenaria, the chain-dotted geometer, chain dot geometer, chainspotted geometer or chain-spotted geometer, was first described by Dru Drury in 1773. It is found in North America from Nova Scotia south to Maryland and west to Kansas and Alberta. The wingspan is 30–40 mm.
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Stamnodini is a tribe of geometer moths under subfamily Larentiinae.
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Cataclysmiini is a tribe of geometer moths in subfamily Larentiinae.
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He was called "the Apostle of Carinthia" and "the geometer".
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Operophterini is a tribe of geometer moths under subfamily Larentiinae.
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Rheumapterini is a tribe of geometer moths under subfamily Larentiinae.
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Solitaneini is a tribe of geometer moths under subfamily Larentiinae.
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Electrophaes is a genus of geometer moths in the Larentiinae subfamily.
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Baptini is a tribe of geometer moths in the subfamily Ennominae.
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Ophthalmitis is a genus of geometer moths in the Boarmiini tribe.
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The Comibaenini are a tribe of geometer moths in the subfamily Geometrinae.
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Amraica solivagaria is a species of geometer moths in the Ennominae subfamily.
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Diocles (; c. 240 BC – c. 180 BC) was a Greek mathematician and geometer.
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John Arthur Todd FRS (23 August 1908 – 22 December 1994) was a British geometer.
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Xanthotype urticaria, the false crocus geometer, is a North American moth in the family Geometridae.
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The Boarmiini (also often called Cleorini) are a large tribe of geometer moths in the Ennominae subfamily.
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Ozola liwana is a geometer moth in the subfamily Desmobathrinae first described by Manfred Sommerer in 1995.
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Eudulini is a tribe of geometer moths under the subfamily Larentiinae."Tribus Eudulini". BioLib.cz. Retrieved April 26, 2019.
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Chesiadini is a tribe of geometer moths under subfamily Larentiinae. The tribe was described by Stephens in 1850.
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For example the geometer Jakob Steiner (1796 – 1863) hated analytic geometry, and always gave preference to synthetic methods.
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Emmanuel Giroux is a blind French geometer known for his research on contact geometry and open book decompositions...
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Trichopterygini is a tribe of geometer moths under subfamily Larentiinae. The tribe was described by Warren in 1894.
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In this, they seem to be convergent to certain geometer moths, such as Caripeta piniata or Sabulodes niveostriata.
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Notoreas is a genus of geometer moths endemic to New Zealand. The genus was described by Edward Meyrick in 1885.
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Though small in absolute diversity, the Nemoriini are nonetheless among the larger tribes of geometer moths in the subfamily Geometrinae.
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Tea leaves are eaten by some herbivores, such as the caterpillars of the willow beauty (Peribatodes rhomboidaria), a geometer moth.
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André Lichnerowicz (January 21, 1915 – December 11, 1998) was a noted French differential geometer and mathematical physicist of Polish descent.
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Melanthiini is a tribe of geometer moths under subfamily Larentiinae. The tribe was described by Philogène Auguste Joseph Duponchel in 1845.
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Archiearis notha Archiearinae is a subfamily of the geometer moth family (Geometridae). It was described by David Stephen Fletcher in 1953.
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"The Blind Geometer" is a 1986 science fiction story by American writer Kim Stanley Robinson. It was published by Asimov's Science Fiction.
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Larentiini is a tribe of geometer moths under subfamily Larentiinae. The tribe was first described by Philogène Auguste Joseph Duponchel in 1845.
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Perizoma curvilinea in Oregon Hydriomenini is a tribe of geometer moths under subfamily Larentiinae. The tribe was erected by Edward Meyrick in 1872.
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A related result on conics was first proved by the French geometer Michel Chasles and later generalized to cubics by Arthur Cayley and .
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Eupitheciini is a tribe of geometer moths under subfamily Larentiinae, often referred to as pugs. The tribe was described by Tutt in 1896.
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400px In geometry, Clifford's theorems, named after the English geometer William Kingdon Clifford, are a sequence of theorems relating to intersections of circles.
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Sterrhinae is a large subfamily of geometer moths (family Geometridae) with some 2,800 described species. This subfamily was described by Edward Meyrick in 1892.
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Epirrita is a genus of geometer moths first described by Jacob Hübner in 1822. They are on the wing from late August to November.
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Perizoma bifaciata, the barred rivulet, is a moth in the family of geometer moths (Geometridae). It was first described by Adrian Hardy Haworth in 1809.
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Charles Haros was a geometer (mathematician) in the French Bureau du Cadastre at the end of the eighteenth century and the beginning of the nineteenth century.
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Xanthorhoini is a tribe of geometer moths under subfamily Larentiinae. The tribe was described by Pierce in 1914."Tribus Xanthorhoini Pierce, 1914". BioLib.cz. Retrieved May 16, 2019.
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George Phillips Odom Jr. (1941 – 18 December 2010) was an American artist and amateur geometer, who is primarily known for his work on the golden ratio (\Phi).
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Perseus (; c. 150 BC) was an ancient Greek geometer, who invented the concept of spiric sections, in analogy to the conic sections studied by Apollonius of Perga.
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Perizomini is a tribe of geometer moths under subfamily Larentiinae. It was first proposed by Claude Herbulot in 1961. It contains four genera, including the eponymous Perizoma.
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The Cidariini are the largest tribe of geometer moths in the subfamily Larentiinae (possibly a distinct familyYoung (2008)). The Cidariini include many of the species known as "carpets" or, ambiguously, "carpet moths" (most other "carpets" are in the Xanthorhoini), and are among the few geometer moths that have been subject to fairly comprehensive cladistic study of their phylogeny. The tribe was described by Philogène Auguste Joseph Duponchel in 1845.
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Scopulini is a tribe of the geometer moth family (Geometridae), with about 900 species in seven genera. The tribe was described by Philogène Auguste Joseph Duponchel in 1845.
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Hyposidra picaria is a geometer moth in the Ennominae subfamily first described by Francis Walker in 1866. It is found throughout Sundaland. Larvae have been reared on Acacia mangium.
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Hypochrosis hyadaria is a geometer moth in the subfamily Ennominae described by Achille Guenée in 1857. The species has a wide range from India, Sri Lanka through Southeast Asia.
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Hypochrosis subrufa is a geometer moth in the subfamily Ennominae first described by Max Bastelberger in 1908. The species can be found in lowland forests in Borneo and Palawan.
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Drepanogynis is a genus in the geometer moth family (Geometridae). Long considered to hold about 5 dozen species, this number has been doubled after the last major revision. They are stout-bodied and hairy by geometer moth standards, usually have pale hindwings and rest with their wings angled upwards like a roof, as Nacophorini do. The genus is by and large restricted to Africa south of the Equator, with most species occurring in southern Africa.
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Hippocrates of Chios (; c. 470 - c. 410 BC) was an ancient Greek mathematician, geometer, and astronomer. He was born on the isle of Chios, where he was originally a merchant.
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Her cousins are actresses Rani Mukerji, Kajol and Tanisha, director Ayan Mukerji and noted MIT algebraic geometer Davesh Maulik. Her brother Samrat Mukerji is also a Bollywood and Bengali actor.
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Harold Scott MacDonald "Donald" Coxeter, (February 9, 1907 - March 31, 2003) was a British-born Canadian geometer. He is regarded as one of the greatest geometers of the 20th century.
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Hubert Lewis Bray is a mathematician and differential geometer. He is known for having proved the Riemannian Penrose inequality. He works as professor of mathematics and physics at Duke University.
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A young geometer, who was doing survey work in the area for the Cassini maps, the first modern maps of France, was hacked to death by suspicious villagers in the 1740s.
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' (c. 800 Baghdad? - c. 860 Baghdad?) was a geometer who worked at the House of Wisdom in Baghdad and for in a short time in Damascus where he made astronomical observations.
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Dinostratus (; c. 390 – c. 320 BCE) was a Greek mathematician and geometer, and the brother of Menaechmus. He is known for using the quadratrix to solve the problem of squaring the circle.
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Xanthotype rufaria, the rufous geometer moth, is a species of geometrid moth in the family Geometridae. It is found in North America. The MONA or Hodges number for Xanthotype rufaria is 6742.
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The Pseudoterpnini are a tribe of geometer moths in the subfamily Geometrinae. The tribe was described by Warren in 1893. It was alternatively treated as subtribe Pseudoterpniti by Jeremy Daniel Holloway in 1996.
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In sharp contrast, the nocturnal species are generally small, pale-colored insects. The Uraniidae are similar to the geometer moths, to which they are related, but a different wing veining pattern distinguishes them.
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Orthofidonia flavivenata, the yellow-veined geometer moth, is a species of geometrid moth in the family Geometridae. It is found in North America. The MONA or Hodges number for Orthofidonia flavivenata is 6430.
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Peterson, Ivars. Fragments of Infinity: A Kaleidoscope of Math and Art. New York: John Wiley & Sons, Inc, 2001. Some of his sculptures portray minimal surfaces, which were named after German geometer Alfred Enneper.
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Agnesi's 1748 illustration of the curve and its construction The curve was studied by Pierre de Fermat in his 1659 treatise on quadrature. In it, Fermat computes the area under the curve and (without details) claims that the same method extends as well to the cissoid of Diocles. Fermat writes that the curve was suggested to him "ab erudito geometra" [by a learned geometer]. speculate that the geometer who suggested this curve to Fermat might have been Antoine de Laloubère.
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Hyposidra aquilaria is a geometer moth in the Ennominae subfamily. It is found in Northwestern Himalaya, Western, Southern and Eastern China, Peninsular Malaysia, Sumatra, and Borneo. It is a rare species of lowland forests.
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Hyposidra violescens is a geometer moth in the Ennominae subfamily. It is found in Northwestern Himalaya, Northern Vietnam, Northern Thailand, Peninsular Malaysia, Sumatra, and Borneo. The species is infrequent in lowlands and lower montane forests.
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Zamarada exigua is a geometer moth species first described by David Stephen Fletcher in 1974. Its name has only been provisionally accepted. It is found in both the Democratic Republic of the Congo and Uganda.
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The wingspan of this species is between 29 and 41 mm. Adults are quite variable but tend to be yellow to tan with gray smudging, some specimens look exceptionally dark compared to lighter variants. Uncommonly individuals will have dark spotting in the subterminal area of the forewing. There are several species that are easily confused with E. confusaria including the dark-edged eusarca (Eusarca fundaria), juniper geometer (Patalene olyzonaria), curve-toothed geometer (Eutrapela clemataria), large maple spanworm (Prochoerodes lineola) and the rose hooktip (Oreta rosea).
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Mileva Prvanović (born July 16, 1929 - 2016) was a Serbian differential geometer. She is a retired professor of mathematics at the University of Novi Sad and a member of the Serbian Academy of Sciences and Arts.
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Thus, Kepler could reason that his relationships gave evidence for God acting as a grand geometer, rather than a Pythagorean numerologist.Field, J. V. (1984). A Lutheran astrologer: Johannes Kepler. Archive for History of Exact Sciences, Vol.
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Shafarevich opposed political interference in universities. The algebraic geometer Miles Reid gave the example of Shafarevich in asserting that plagiarism and poor work were ignored in a doctorate that was obtained by a Communist Party functionary.
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Krananda lucidaria is a geometer moth in the subfamily Ennominae first described by John Henry Leech in 1897. It is found in Western and Southern China, Northern Thailand, Peninsular Malaysia, Sumatra, and Borneo in lower montane forests.
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Hirst was a projective geometer in the style of Poncelet and Steiner. He was not an adherent of the algebraic geometry approach of Cayley and Sylvester, despite being a friend of theirs. His speciality was Cremona transformations.
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Stenoporpia polygrammaria, known generally as the faded gray or faded gray geometer, is a species of geometrid moth in the family Geometridae. It is found in North America. The MONA or Hodges number for Stenoporpia polygrammaria is 6459.
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Asthenini is a tribe of geometer moths under subfamily Larentiinae first described by Warren in 1893. The tribe has been combined with Eupitheciini in the past, most notably by Jeremy Daniel Holloway in his work The Moths of Borneo.
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Hyposidra apioleuca is a geometer moth in the Ennominae subfamily. It is found in Peninsular Malaysia, Sumatra, and Borneo. The species prefers lower montane forests at 1000-1200m, but has been collected as low as 500m and at 1930m.
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Geometry Expert (GEX) is a Chinese software for dynamic diagram drawing and automated geometry theorem proving and discovering. There's a new Chinese version of Geometry Expert, called MMP/Geometer. Java Geometry Expert is free under GNU General Public License.
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Selenia kentaria, commonly known as Kent's thorn or Kent's geometer, is a moth of the family Geometridae. It is found in eastern and central North America. The wingspan is 32–52 mm. Adults are on wing from March to August.
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Eucyclodes gavissima, the Oriental orange banded green geometer moth, is a species of moth of the family Geometridae described by Francis Walker in 1861. It is found in the Indian subregion, Sri Lanka, Bhutan, western China, Taiwan, Sumatra and Borneo.
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Apodasmia rufonigraria is the sole species of Apodasmia, a monotypic genus of geometer moths. It was first described in 1862 (as Fidonia rufonigraria) by Francis Walker, and transferred to Apodasmia by Alfred Jefferis Turner. The species is found in Australia.
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Coxeter decompositions are named after Harold Scott MacDonald Coxeter, an accomplished 20th century geometer. He introduced the Coxeter group, an abstract group generated by reflections. These groups have many uses, including producing the rotations of Platonic solids and tessellating the plane.
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Hypochrosis cryptopyrrhata is a geometer moth in the subfamily Ennominae first described by Francis Walker in 1863. The species can be found in lowland and lower montane forests in Borneo and Sumatra. The larvae feed on Paraserianthes falcataria (= Falcataria moluccana).
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Morphological and DNA sequence data indicate that they are a very ancient lineage of geometer moths; they might even be distinct enough to warrant elevation to full family status in the superfamily Geometroidea. They share numerous plesiomorphic traits - for example at least one areola in the forewing, a hammer-shaped ansa of the tympanal organ and the lack of a gnathos - with the Sterrhinae which are either somewhat less distant from other geometer moths or are part of the same distinct lineage; the Lythriini were until recently placed in the Larentiinae but are apparently Sterrhinae.Õunap et al. (2008), Young (2008) But the Larentiinae characteristically tend to have much longer foreleg tarsi and hindleg tibiae than their relatives, and also have hairy or toothed extensions on the upperside sections of the transtilla; their caterpillars often have the abdominal prolegs reduced already (as is typical for the more advanced geometer moths), and the Larentiinae's tympanal organs have a unique and characteristic structure.
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Ectropis is a genus in the geometer moth family (Geometridae). They are mostly paleotropical, but also plentiful in Australia and extend into Asia. Only one species - or cryptic species complex - (the engrailed/small engrailed, E. bistortata/E. crepuscularia) is found in Europe.
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Patalene olyzonaria, the juniper-twig geometer, is a moth of the family Geometridae. It is found from Quebec and New Hampshire to Florida, west to Texas, north to Wisconsin. The wingspan is 21–25 mm. Adults are on wing from April to November.
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Otherwise, the forewings are generally unpatterned and brown to blackish-grey in color. Hyalospila is a synonym. The snout moth genus Zonula (moth) was invalidly described by Ragonot in 1888; the geometer moth genus Locha was invalidly described by Warren in 1894.
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Anthemius of Tralles (, Medieval Greek: , Anthémios o Trallianós; – 533 558) was a Greek from Tralles who worked as a geometer and architect in Constantinople, the capital of the Byzantine Empire. With Isidore of Miletus, he designed the Hagia Sophia for Justinian I.
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London: Duckworth, pages 52-55. Meton appears briefly as a character in Aristophanes' play The Birds (414 BC). He comes on stage carrying surveying instruments and is described as a geometer. What little is known about Meton is related by ancient historians.
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Leptostales laevitaria, the raspberry wave moth, is a species of moth in the family Geometridae (the geometer moths). It was first described by Geyer in 1837 and it is found in North America. The MONA or Hodges number for Leptostales laevitaria is 7177.
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Hypochrosis pyrrhophaeata is a geometer moth in the subfamily Ennominae first described by Francis Walker in 1863. It is found in the north eastern Himalayas and Sundaland. The species is common, often abundant, in lowlands and hill forests up to 2000 m.
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The species has larvae which live near plants such as Odontites and large specimens of Euphrasia, both in the figwort family (Scrophulariaceae). This species hibernates as pupae, sometimes for many years, which is unusual for geometer moths. The grown butterflies fly in July and August.
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Helen Elizabeth Moore is an American mathematician. Originally a differential geometer, she moved from academia to industry and from pure to applied mathematics, and in particular the applications of control theory to combination therapy in the health industry. She is affiliated with pharmaceutical company AstraZeneca.
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The Angeronini are a small tribe of geometer moths in the subfamily Ennominae. The tribe was first described by William Trowbridge Merrifield Forbes in 1948. As numerous ennomine genera have not yet been assigned to a tribe,See references in Savela (2008) the genus list is preliminary.
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Bobillier is a tiny, cup-shaped lunar impact crater in the southwest part of Mare Serenitatis. It was named after French geometer Étienne Bobillier in 1976. It lies to the north-northwest of the crater Bessel. To the south and west is a wrinkle ridge designated Dorsum Buckland.
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Parectropis is a genus in the geometer moth family (Geometridae). A small Old World genus, it contains only a good dozen species altogether, though new ones are still being discovered. Only one species (P. similaria) is found in Europe; most others live in Asia though some occur in Africa.
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Idaea, sometimes called Hyriogona (among other synonyms), is a large genus of geometer moths. It was erected by Georg Friedrich Treitschke in 1825. They are found nearly worldwide, with many native to the Mediterranean, the African savannas, and the deserts of western Asia.Choi, S. W. & Kim, S. S. (2013).
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Probole is a genus of moths in the family Geometridae, the geometer moths. It is a Nearctic genus distributed throughout Canada and much of the United States.Tomon, T. J. A revision of the genus Probole Herrich-Schäffer (Lepidoptera: Geometridae). Ten-Minute Papers, Section A. Systematics, Morphology and Evolution.
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When the larvae emerge they eat the flowers' ovaries, and the plant is unable to create seeds. The larvae usually proceed to hollow out the flower buds and use them as safe places to pupate. Caterpillars of the engrailed moth (Ectropis crepuscularia), a polyphagous geometer moth, also feed on purple loosestrife.
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S.) 4(3): 312. The closest relatives of Callidulidae are not known, but they are currently placed in a group that includes the three butterfly superfamilies, the "hook-tip moths" Drepanoidea and the "geometer moths" Geometroidea and also possibly Axioidea which share some structural characteristics.Minet, J. (1999 [1988]). The Axioidea and Calliduloidea.
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In geometry, the Parry point is a special point associated with a plane triangle. It is a triangle center and it is called X(111) in Clark Kimberling's Encyclopedia of Triangle Centers. The Parry point is named in honor of the English geometer Cyril Parry, who studied them in the early 1990s.
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Sterrhini is a tribe of the geometer moth family (Geometridae), with about 825 species in 19 genera. There are also 6 genera with 36 species tentatively associated with the tribe. The tribe was erected by Edward Meyrick in 1892."Phylogeny and tribal classification of Sterrhinae with emphasis on delimiting Scopulini (Lepidoptera: Geometridae)".
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Anthonisz served as burgomaster (mayor) of Alkmaar in the Netherlands from 1582. Adriaan fathered two sons, and named them both Metius (from the Dutch word meten, meaning 'measuring', 'measurer', or surveyor). They each became prominent members of society. Adriaan Metius (9 Dec 1571 – 6 Sep 1635) was a Dutch geometer and astronomer.
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The Bistonini are a tribe of geometer moths in subfamily Ennominae. As numerous ennomine genera have not yet been assigned to a tribe,See references in Savela (2010) the genus list is preliminary. In addition, the entire tribe is sometimesFollowing Holloway (1994) merged into a much-expanded Boarmiini. In other treatments,See e.g.
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Ennominae is the largest subfamily of the geometer moth family (Geometridae) with some 9,700 described species in 1,100 genera. They are usually a fairly small moths, though some (such as the peppered moth) grow to be considerably large. This subfamily has a global distribution. It includes some species that are notorious defoliating pests.
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He began his studies at the collège at Caen, discovering Euclid's Elements aged around 18 and soon moving to study mathematics alone. He made such progress in this area that the geometer Alexis Fontaine, whom he met in Paris, offered to become his patron. They edited several papers for the Académie des sciences.
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Haematopis is a monotypic moth genus in the family Geometridae erected by Jacob Hübner in 1823. Its only species, Haematopis grataria, the chickweed geometer, was first described by Johan Christian Fabricius in 1823. It is found throughout the United States. In Canada it is found from Quebec to Alberta, north to the Northwest Territories.
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Eugonobapta is a monotypic moth genus in the family Geometridae described by Warren in 1894. Its only species, Eugonobapta nivosaria, the snowy geometer, was first described by Achille Guenée in 1857. It is found in North America from Manitoba to New Brunswick, south to North Carolina and Tennessee. The wingspan is 21–33 mm.
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Hyposidra infixaria is a geometer moth in the Ennominae subfamily. It is found in Northwestern Himalaya, Southern China, Taiwan and Sundaland, mainly in lowland forests. There is great variation in wing color, presence or absence of the subcostal line. The larvae has been reared from Psidium guajava (Myrtaceae), Desmos (Annonaceae), Buchanania (Anacardiaceae) and Punica (Punicaceae).
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In the south, the Bulgarians marched throughout Epirus and in the west they seized the area of modern Durrës (medieval Dyrrhachium or Drach) on the Adriatic Sea.Zlatarski, pp. 645–647.Ioannes Geometer. Carmina, col. 920A. In 989, Phocas was killed and his followers surrendered, and the following year Basil II reached an agreement with Skleros.
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With a wingspan of 43–55 mm, E. hortaria is one of the larger geometer moths. There are two forms, one being "Dendraria" and the other being "Carbonaria". The Dendraria has a broader median with subterminal lines while the Carbonaria is darker with white edging. The thick bodied caterpillar has a swollen 3rd thoracic segment.
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Although the circle appears to be an obvious solution to the problem, proving this fact is rather difficult. The first progress toward the solution was made by Swiss geometer Jakob Steiner in 1838, using a geometric method later named Steiner symmetrisation.J. Steiner, Einfacher Beweis der isoperimetrischen Hauptsätze, J. reine angew Math. 18, (1838), pp.
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Walem was born in Soignies, Belgium. His former clubs are Molenbeek (as a youngster), Anderlecht, Udinese, Parma (on loan), Standard Liège, Torino and Catania. At Udinese, he was nicknamed Il Geometra (The Geometer) as he was very precise in his passes. His partnership with German striker Oliver Bierhoff was also praised at that time.
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Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was long considered the first rigorous proof of the theorem, many now also consider Camille Jordan's original proof rigorous.
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Entephria is a genus in the geometer moth family (Geometridae). There is no unambiguous common name for these moths; like many other members of their subfamily Larentiinae, they are sometimes called "carpets". The genus was erected by Jacob Hübner in 1825. Most of its roughly 50 species occur across the Holarctic; from Europe alone, 10 species have been recorded.
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Adult hedylids resemble geometer moths. They share many morphological and genetic characteristics with both the superfamilies Papilionoidea and the Hesperioidea. The abdomen is very long and slim, like many Neotropical butterflies of the subfamilies Ithomiinae and Heliconiinae, hence the name of one Macrosoma species "heliconiaria". Unlike other butterflies, however, the antennae are un-clubbed, but rather filiform or bipectinate.
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Nacophorini are generally robust and quite hairy geometer moths, though some species are more delicate. Exceptional among their subfamily, many have slim wings. They typically rest with the hindwings tucked under the forewings. Nacophorini have long antennae, and most if not all have terminal sensillae shaped like stout pegs and sensillae basiconicae on the flagellomeres or rami.
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P. curvilinea in Oregon Perizoma is a genus in the geometer moth family (Geometridae). It is the type genus of tribe Perizomini in subfamily Larentiinae. The tribe is considered monotypic by those who include the genera Gagitodes, Martania and Mesotype in Perizoma. Some other less closely related species formerly placed here are now elsewhere in the Larentiinae, e.g.
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A special case of a toric section is the spiric section, in which the intersecting plane is parallel to the rotational symmetry axis of the torus. They were discovered by the ancient Greek geometer Perseus in roughly 150 BC.. Well-known examples include the hippopede and the Cassini oval and their relatives, such as the lemniscate of Bernoulli.
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He has been considered the greatest pure geometer since Apollonius of Perga. In his Systematische Entwickelung der Abhängigkeit geometrischer Gestalten von einander he laid the foundation of modern synthetic geometry. In projective geometry even parallel lines have a point in common: a point at infinity. Thus two points determine a line and two lines determine a point.
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Coryphista is a monotypic moth genus in the family Geometridae erected by George Duryea Hulst in 1896. The genus may be considered to be a synonym of Rheumaptera. Its only species, Coryphista meadii, the barberry geometer moth or barberry looper, was first described by Alpheus Spring Packard in 1874. It is found in the United States and southern Canada.
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Though small in absolute diversity of genera, the Hemitheini are nonetheless the largest tribes of geometer moths in the subfamily Geometrinae. Like most Geometrinae, they are small greenish "emerald moths". The tribe was first described by Charles Théophile Bruand d'Uzelle in 1846. In some treatments the Comostolini, Hemistolini, Jodini, Microloxiini, Thalassodini and Thalerini are split off as independent tribes.
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The schools faculty includes a mathematician and professor , an educator, geometer, author of several geometry textbooks Rafail Gordin, director of the , head of development of Unified State Exam Ivan Yashchenko. Former faculty includes poet and novelist Igor Vishnevetsky, mathematician and Soviet dissident Tatyana Velikanova, biologist, founder of the biological classes at School 57 and other Moscow schools .
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Mathematician Terence Tao in 2006 Chinese American mathematicians Shing-Tung Yau and Terence Tao both won the Fields Medal. The geometer Shiing-Shen Chern received the Wolf Prize in Mathematics in 1983. Manjul Bhargava, an American Canadian of Indian origins won the Fields Medal in mathematics in 2014. Yitang Zhang is a Chinese-born American mathematician working in the area of number theory.
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He intended to verify and emend the books, releasing each one as it was completed. Hearing of this plan from Apollonius himself on a subsequent visit of the latter to Pergamon, Eudemus had insisted Apollonius send him each book before release. The circumstances imply that at this stage Apollonius was a young geometer seeking the company and advice of established professionals.
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Eutrapela is a genus of moths in the family Geometridae. It contains only one species, Eutrapela clemataria, the curve-toothed geometer moth or purplish- brown looper, which is found in North America, where it has been recorded from Nova Scotia to Florida, west to Texas and north to Saskatchewan.mothphotographersgroup The habitat consists of deciduous and mixed woodlands. The wingspan is 38–56 mm.
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Siedlungsnamen zwischen Rhein, Main, Neckar und Itter article of Heinrich Tischner. In 1563 Count Wolfgang von Zweibrücken asked the geometer and cartographer Tilemann Stella to assess the offices of Zweibrücken and Kirkel. At that time he documented the name of today's "Bierbach" to be "Beurbach", which would be the linguistic sound evolution from "Bûribach".Tilemann Stella: Beschreibung der Ämter Zweibrücken und Kirkel 1564.
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This was published after Wright's death as A Description of the Admirable Table of Logarithmes (1616). Wright's work influenced, among other persons, Dutch astronomer and mathematician Willebrord Snellius; Adriaan Metius, the geometer and astronomer from Holland; and the English mathematician Richard Norwood, who calculated the length of a degree on a great circle of the earth using a method proposed by Wright.
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Edmund Gunter (158110 December 1626), was an English clergyman, mathematician, geometer and astronomerGuy O. Stenstrom (1967), "Surveying Ready Reference Manual", McGraw–Hill. p. 7 of Welsh descent. He is best remembered for his mathematical contributions which include the invention of the Gunter's chain, the Gunter's quadrant, and the Gunter's scale. In 1620, he invented the first successful analogue deviceTrevor Homer (2012).
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Mark de Berg is a Dutch computational geometer, known as one of the authors of the textbook Computational Geometry: Algorithms and Applications (with Otfried Cheong, Marc van Kreveld, and Mark Overmars, Springer, 1997; 3rd ed., 2008). De Berg completed his Ph.D. in 1992 at Utrecht University. His dissertation, Efficient Algorithms for Ray Shooting and Hidden Surface Removal, was supervised by Mark Overmars.
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Marc Johan van Kreveld is a Dutch computational geometer, known as one of the authors of the textbook Computational Geometry: Algorithms and Applications (with Mark de Berg, Otfried Cheong, and Mark Overmars, Springer, 1997; 3rd ed., 2008). Van Kreveld completed his Ph.D. in 1992 at Utrecht University. His dissertation, New Results on Data Structures in Computational Geometry, was supervised by Mark Overmars.
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The wild application of girih on architectures should credit to the close relationship between Islamic architecture, geometry, and craft. Architecture was classified in the field of practical geometry in the early Islamic period, and building projects always involve a muhandis (geometer). In addition, no clear border was established between science and craft; thus, the craftsmen usually followed the mathematicians’ principles and guidelines directly.
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Hodge's home at 1 Church Hill Place, Edinburgh Sir William Vallance Douglas Hodge (; 17 June 1903 – 7 July 1975) was a British mathematician, specifically a geometer. His discovery of far-reaching topological relations between algebraic geometry and differential geometry—an area now called Hodge theory and pertaining more generally to Kähler manifolds—has been a major influence on subsequent work in geometry.
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The point here is that Cortés accomplished the planning and was on his way to finish the building of Mexico City before the royal ordinances addressed specifically to him even arrived. Men like Cortés and Alonso García Bravo (who is also called "the good geometer"), played a crucial role in creating a city scape of New World cities as we know them.
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Sasakian manifolds were introduced in 1960 by the Japanese geometer Shigeo Sasaki. There was not much activity in this field after the mid-1970s, until the advent of String theory. Since then Sasakian manifolds have gained prominence in physics and algebraic geometry, mostly due to a string of papers by Charles P. Boyer and Krzysztof Galicki and their co- authors.
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Nikolai Sergeevich Bakhvalov () (May 29, 1934 - August 29, 2005) was a Soviet and Russian mathematician. Born in Moscow into the family of Sergei Vladimirovich Bakhvalov, a geometer at Moscow State University, N.S. Bakhvalov was exposed to mathematics from a young age. In 1950, Bakhvalov entered the Faculty of Mechanics and Mathematics at Moscow State University. His supervisors there included Kolmogorov and Sobolev.
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Biston robustum is a species of moth belonging to the family Geometridae. This is a large moth and is known in its native range as the giant geometer moth. It is related, and generally similar, to the famous and widespread Peppered Moth. The species is found in China (Shandong, Shaanxi, Shanghai, Jiangsu, Jiangxi), Taiwan, Japan, Russia, North Korea, South Korea and Vietnam.
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Vakil is an algebraic geometer and his research work spans over enumerative geometry, topology, Gromov-Witten theory, and classical algebraic geometry. He has solved several old problems in Schubert calculus. Among other results, he proved that all Schubert problems are enumerative over the real numbers, a result that resolves an issue mathematicians have worked on for at least two decades.
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Christian Heinrich von Nagel (28 February 1803 in Stuttgart, Germany - 27 October 1882 in Ulm, Germany) was a German geometer. After attending the gymnasium, Nagel went in 1817 to Evangelical Seminaries of Maulbronn and Blaubeuren. From 1821 to 1825, he took a four-year course of theology at the Tübinger Stift. Soon after his graduation, he became interested in mathematics.
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While travelling, the couple assists a property dispute and the curious Besian and his wife get closer. A geometer approaches Besian and tells him to write about the difficult life they live in, without having the right to exercise their professions and dubbing all that as a "tragicomedy". Gjorg is counting his remaining days of freedom. He decides to go up the mountains during his remaining days.
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Apollonius was a prolific geometer, turning out a large number of works. Only one survives, Conics. It is a dense and extensive reference work on the topic, even by today's standards, serving as a repository of now little known geometric propositions as well as a vehicle for some new ones devised by Apollonius. Its audience was not the general population, which could not read or write.
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The cathedral's interior surfaces were sheathed with polychrome marbles, green and white with purple porphyry, and gold mosaics. The exterior was clad in stucco tinted yellow and red during restorations in the 19th century at the direction of the Fossati architects. Justinian chose geometer and engineer Isidore of Miletus and mathematician Anthemius of Tralles as architects. The construction is described by Procopius's On Buildings (, ).
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Between 1841 and 1877, the geometer Efferz undertook a cadastral survey. One soldier from Pfeffelbach fell in the Franco-Prussian War in 1870. That same year, Peter Aulenbacher, Jakob Braun and Jakob Heß opened Pfeffelbach's first stone quarry. Paving stones from this quarry and others that were subsequently opened were shipped by horse and cart to Kusel and for a time even to Sankt Wendel.
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Eusarca confusaria trapped by the carnivorous plant Drosera filiformis The Ourapterygini are one of the large tribes of geometer moths in the subfamily Ennominae. The tribe was described by Charles Théophile Bruand d'Uzelle in 1846. They are particularly plentiful in the Neotropics. Ourapterygini are generally held to be the youngest tribe of their subfamily, and at least seasonally have characteristic apomorphic asymmetrical processes of the anellus.
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In Riemannian geometry, a Bryant surface is a 2-dimensional surface embedded in 3-dimensional hyperbolic space with constant mean curvature equal to 1... These surfaces take their name from the geometer Robert Bryant, who proved that every simply-connected minimal surface in 3-dimensional Euclidean space is isometric to a Bryant surface by a holomorphic parameterization analogous to the (Euclidean) Weierstrass–Enneper parameterization..
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Eogeometer is a prehistoric genus of Ennomine geometer moths in the tribe Boarmiini. The type and only species is Eogeometer vadens, the specimen of which measured about , and was estimated to be 44 million years old, dating back to Eocene epoch. Both the genus and species were described by Thilo C. Fischer, Artur Michalski and Axel Hausmann in 2019 as the first geometrid caterpillar in Baltic amber.
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In the former Soviet Union, it is commonly called Lobachevskian geometry, named after one of its discoverers, the Russian geometer Nikolai Lobachevsky. This page is mainly about the 2-dimensional (planar) hyperbolic geometry and the differences and similarities between Euclidean and hyperbolic geometry. Hyperbolic geometry can be extended to three and more dimensions; see hyperbolic space for more on the three and higher dimensional cases.
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In geometry, the Spieker center is a special point associated with a plane triangle. It is defined as the center of mass of the perimeter of the triangle. The Spieker center of a triangle ABC is the center of gravity of a homogeneous wire frame in the shape of triangle ABC. The point is named in honor of the 19th-century German geometer Theodor Spieker.
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According to art historian Kenneth Clark, "to medieval man, geometry was a divine activity. God was the great geometer, and this concept inspired the architect."Kenneth Clark; Civilisation; BBC 1969 Monumental cathedrals such as that of Chartres appear to evidence a complex understanding of mathematics. The Church has invested greatly in engineering and architecture and founded a number of architectural genres – including Byzantine, Romanesque, Gothic, High Renaissance, and Baroque.
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Crypsiphona ocultaria (erroneously as: Phalaena occultaria Guenée, 1857) the red-lined looper moth or red-lined geometer, is a moth of the family Geometridae. The species was first described by Edward Donovan in 1805 and it is found in Australia. It is one of the most common moths found in Australia. The "red-lined" part of the name refers to the red markings seen on the undersides of the wings.
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It is placed inside the water, in a meandering channel that runs through the park. Made of stainless steel and ceramic on a limestone base, it is conceived as a tribute to the Greek geometer Euclid. The work consists of four stainless steel railing circles supported by a vertical tube in the center of the diameter, in addition to several metal clamps set in the circles, which hold cylindrical ceramic pieces.
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The concept was named by Otto Stolz (in the 1880s) after the ancient Greek geometer and physicist Archimedes of Syracuse. The Archimedean property appears in Book V of Euclid's Elements as Definition 4: Because Archimedes credited it to Eudoxus of Cnidus it is also known as the "Theorem of Eudoxus" or the Eudoxus axiom. Archimedes used infinitesimals in heuristic arguments, although he denied that those were finished mathematical proofs.
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They are used as food plants by some Lepidoptera (butterfly and moth) caterpillars. These are mainly of noctuid moths - noted for feeding on many poisonous plants without harm - such as cabbage moth (Mamestra brassicae), dot moth (Melanchra persicariae) and mouse moth (Amphipyra tragopoginis). the engrailed (Ectropis crepuscularia), a geometer moth, also uses columbine as a larval food plant. The larvae of the Papaipema leucostigma also feed on columbine.
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A pancake number is the minimum number of flips required for a given number of pancakes. In this form, the problem was first discussed by American geometer Jacob E. Goodman. A variant of the problem is concerned with burnt pancakes, where each pancake has a burnt side and all pancakes must, in addition, end up with the burnt side on bottom. All sorting methods require pairs of elements to be compared.
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The Taroc guild leader sacrificed herself to imprison Animora, one of The First, who had been banished by Ingra, the leader of House Sinister. It was later revealed that a secret guild exists,(issue 33) called the Geometer guild; the members of which are allied with the Dark Magi guild and the Tantric guild. The Geometers believe themselves to be manipulators of all the other guilds; the guildmaster is named Archemus.
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Ecliptopera atricolorata, the dark-banded geometer moth, is a moth of the family Geometridae. It is found in North America, where it has been recorded from Alabama, Arkansas, Florida, Georgia, Indiana, Kentucky, Maryland, Mississippi, North Carolina, Ohio, Pennsylvania, South Carolina, Tennessee, Virginia and West Virginia.mothphotographersgroup The wingspan is 28–32 mm.American Insects There are brown and white markings on forewings, including a large squarish brown patch and a smaller oval.
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The essay is very revealing of Gergonne's philosophical ideas. He called for the abandonment of the words analysis and synthesis, claiming they lacked clear meanings. Surprisingly for a geometer, he suggested that algebra is more important than geometry at a time when algebra consisted almost entirely of the elementary algebra of the real field. He predicted that one day quasi- mechanical methods would be used to discover new results.
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General relativity is formulated completely in the language of tensors. Einstein had learned about them, with great difficulty, from the geometer Marcel Grossmann. Levi-Civita then initiated a correspondence with Einstein to correct mistakes Einstein had made in his use of tensor analysis. The correspondence lasted 1915–17, and was characterized by mutual respect: Tensors were also found to be useful in other fields such as continuum mechanics.
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Thomas James Willmore (16 April 1919 – 20 February 2005) was an English geometer. He is best known for his work on Riemannian 3-space and harmonic spaces. Willmore studied at King's College London. After his graduation in 1939, he was appointed as a lecturer, but the onset of World War II led him to working as a scientific officer at RAF Cardington, working mainly on barrage balloon defences.
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Many hyperbolic lines through point P not intersecting line a in the Beltrami Klein model A hyperbolic triheptagonal tiling in a Beltrami–Klein model projection In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit disk (or n-dimensional unit ball) and lines are represented by the chords, straight line segments with ideal endpoints on the boundary sphere. The Beltrami–Klein model is named after the Italian geometer Eugenio Beltrami and the German Felix Klein while "Cayley" in Cayley–Klein model refers to the English geometer Arthur Cayley. The Beltrami–Klein model is analogous to the gnomonic projection of spherical geometry, in that geodesics (great circles in spherical geometry) are mapped to straight lines. This model is not conformal, meaning that angles and circles are distorted, whereas the Poincaré disk model preserves these.
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But it is undoubtedly also true that a Greek geometer versed in the fourteen theorems of Euclid's "algebra" was far more adept in applying these theorems to practical mensuration than is an experienced geometer of today. Ancient geometric "algebra" was not an ideal tool, but it was far from ineffective. Euclid's statement (Proposition 4), "If a straight line be cut at random, the square on the whole is equal to the squares on the segments and twice the rectangle contained by the segments, is a verbose way of saying that (a + b)^2 = a^2 + 2ab + b^2," Many basic laws of addition and multiplication are included or proved geometrically in the Elements. For instance, proposition 1 of Book II states: :If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments.
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John Casey (12 May 1820, Kilbehenny, County Limerick, Ireland – 3 January 1891, Dublin) was a respected Irish geometer. He is most famous for Casey's theorem on a circle that is tangent to four other circles, an extension of Ptolemy's theorem. However, he contributed several novel proofs and perspectives on Euclidean geometry. He and Émile Lemoine are considered to be the co-founders of the modern geometry of the circle and the triangle.
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Eumacaria is a monotypic moth genus in the family Geometridae described by Packard in 1873. Its only species, Eumacaria madopata, the brown-bordered geometer moth, was first described by Achille Guenée in 1857. It is found in North America, where it has been recorded from British Columbia, northern Washington, southern Saskatchewan, from Maine to Florida, South Dakota, North Dakota, Nebraska, Wyoming, Idaho, Colorado and New Mexico. The habitat consists of orchards and shrublands.
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However, the Doctor was able to reconnect the geometer to the TARDIS, restoring its interior to normal. Brewster later convinced the Doctor to take him to 2008 supposedly to see his future. In fact, he wished to be reunited with a young woman named Connie Winter, whom he had met whilst travelling in the Doctor's TARDIS alone. Thomas decided to stay in 2008 with Connie rather than continue travelling with the Doctor and Nyssa.
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For that purpose, he engaged a geometer, Johann Heinrich Weiss of Strasbourg. The foundations for Meyer's map were baseline measurements by the scientist Johann Georg Tralles and landscape relief modelling by Joachim Eugen Müller, after which Weiss drew the map. The result of this work appeared between 1796 and 1802, and included 16 sheets and an overview map. The 16 sheets measure x , and depict Switzerland at a scale of approximately 1:120,000.
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He sees the scientist Dioscorides, the mythical Greek poets Orpheus and Linus, and Roman statesmen Marcus Tullius Cicero and Seneca. Dante sees the Alexandrian geometer Euclid and Ptolemy, the Alexandrian astronomer and geographer, as well as the physicians Hippocrates and Galen. He also encounters Avicenna, a Persian polymath, and Averroes, a medieval Andalusian polymath known for his commentaries on Aristotle's works. Dante and Virgil depart from the four other poets and continue their journey.
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Young (2008) Many members of this tribe are remarkably butterfly like. The tribe contains more partially diurnal species than usual for geometer moths, and many do not have the cryptic coloration typical for the family. There is a tendency to light yellowish hues and either little or a quite bold pattern, making some species rather conspicuous. It is known that at least some are noxious to predators, and such coloration might be aposematic.
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At Cambridge he fell under the influence of the geometer H. F. Baker. He gained a second MA in 1925. In 1926 he took up a teaching position at the University of Bristol, and began work on the interface between the Italian school of algebraic geometry, particularly problems posed by Francesco Severi, and the topological methods of Solomon Lefschetz. This made his reputation, but led to some initial scepticism on the part of Lefschetz.
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He studied projective differential geometry under Sun Guangyuan, a University of Chicago-trained geometer and logician who was also from Zhejiang. Sun is another mentor of Chern who is considered a founder of modern Chinese mathematics. In 1932, Chern published his first research article in the Tsinghua University Journal. In the summer of 1934, Chern graduated from Tsinghua with a master's degree, the first ever master's degree in mathematics issued in China.
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Leonardo applied one- point perspective as well as shallow focus to some of his works. Two-point perspective was demonstrated as early as 1525 by Albrecht Dürer, who studied perspective by reading Piero and Pacioli's works, in his Unterweisung der messung ("Instruction of the measurement"). Perspective features heavily in the research of the 17th-century architect, geometer, and optician Girard Desargues on perspective, optics and projective geometry, as well as the theorem named after him.
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Anastos, M. "The History of Byzantine Science." Dumbarton Oaks papers 16 (1962) In the field of engineering Isidore of Miletus, the Greek mathematician and architect of the Hagia Sophia, produced the first compilation of Archimedes works c. 530, and it is through this tradition, kept alive by the school of mathematics and engineering founded c. 850 during the "Byzantine Renaissance" by Leo the Geometer that such works are known today (see Archimedes Palimpsest).
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This therefore means that , where one of the points in the two tetrads overlap, hence meaning that other lines connecting the other three pairs must coincide to preserve cross ratio. Therefore, are collinear. Another proof for Pascal's theorem for a circle uses Menelaus' theorem repeatedly. Dandelin, the geometer who discovered the celebrated Dandelin spheres, came up with a beautiful proof using "3D lifting" technique that is analogous to the 3D proof of Desargues' theorem.
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Franz Aurenhammer (born September 25, 1957) is an Austrian computational geometer known for his research in computational geometry on Voronoi diagrams, straight skeletons, and related structures. He is a professor in the Institute for Theoretical Computer Science of Graz University of Technology.Curriculum vitae, retrieved 2018-08-12. Aurenhammer earned a diploma in technical mathematics from Graz University of Technology in 1982, and completed his doctorate there in 1984 and his habilitation in 1989.
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A prominent follower of al-Majriti was the philosopher and geometer Abu al-Hakam al-Kirmani who was followed, in turn, by Abu Bakr Ibn al-Sayigh, usually known in the Arab world as Ibn Bajjah, "Avempace". The al-Andalus philosopher Averroes (1126–1198) was the founder of the Averroism school of philosophy, and his works and commentaries influenced medieval thought in Western Europe. Another influential al-Andalus philosopher was Ibn Tufail.
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Owned by the king, it was under royal patronage, which was typically jealous, enthusiastic, and participatory. The kings bought, begged, borrowed and stole the precious books whenever and wherever they could. Books were of the highest value, affordable only to wealthy patrons. Collecting them was a royal obligation. Pergamon was known for its parchment industry, whence “parchment” is derived from “Pergamon.” Apollonius brings to mind Philonides of Laodicea, a geometer whom he introduced to Eudemus in Ephesus.
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Erannis is a geometer moth genus of the subfamily Ennominae erected by Jacob Hübner in 1825. It is placed by some entomologists in the tribe Erannini as the type genus, but others merge this group into the tribe Boarmiini or Bistonini. The adults of these smallish moths typically live in the crowns of their host trees. The genus is most diverse in the Holarctic; few of the 12 or so known species occur in adjacent regions.
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The Nacophorini are one of the smaller tribes of geometer moths in the subfamily Ennominae. They are the most diverse Ennominae of Australia and are widespread in the Americas. If the African genera tentatively placed herein indeed belong here, the distribution of the Nacophorini is distinctly Gondwanan, with their probable origin either of Australia, South America or even Antarctica (which was not ice-covered until a few million years ago). In Eurasia, they are rare by comparison.
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The Circolo Matematico di Palermo (Mathematical Circle of Palermo) is an Italian mathematical society, founded in Palermo by Sicilian geometer Giovanni B. Guccia in 1884.The Mathematical Circle of Palermo, The MacTutor History of Mathematics archive, retrieved 2011-06-19. It began accepting foreign members in 1888, and by the time of Guccia's death in 1914 it had become the foremost international mathematical society, with approximately one thousand members.. However, subsequently to that time it declined in influence.
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Louis Beethoven Prout (1864–1943) was an English entomologist and musicologist. Prout specialised in the insect order of Lepidoptera, especially the Geometridae, or geometer moths, on which he was a foremost authority. His notebooks and publications formed the basis of the Geometridae card indexes in the Natural History Museum, the then British Museum (Natural History). He was the secretary of the North London Natural History Society and worked in association with the Natural History Museum at Tring.
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In 1730 he was made professor of hydrography at Havre, and succeeded Pierre Louis Maupertuis as associate geometer of the Academy of Sciences. He also invented a heliometer, afterwards perfected by Joseph von Fraunhofer. He was afterwards promoted in the Academy to the place of Maupertuis, and went to reside in Paris. In 1735 Bouguer sailed with Charles Marie de La Condamine on a scientific mission to Peru, to measure a degree of the meridian arc near the equator.
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He entered National Taiwan University in 1984, originally for international business, but after a year he switched to mathematics. He earned his BS in Mathematics at National Taiwan University in 1988 and his MS from the same institution in 1992. He received a PhD in Mathematics in 1998 from Harvard University with a thesis entitled "Generalized harmonic maps and representations of discrete groups." His thesis adviser at Harvard was Chinese Fields Medalist and differential geometer Shing-Tung Yau.
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Larentiinae is a subfamily of moths containing roughly 5,800 speciesÕunap et al. (2008) that occur mostly in the temperate regions of the world. They are generally considered a subfamily of the geometer moth family (Geometridae) and are divided into a few large or good-sized tribes, and numerous very small or even monotypic ones which might not always be valid. Well-known members are the "pug moths" of the Eupitheciini and the "carpets", mainly of the Cidariini and Xanthorhoini.
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In measure theory, an area of mathematics, Egorov's theorem establishes a condition for the uniform convergence of a pointwise convergent sequence of measurable functions. It is also named Severini–Egoroff theorem or Severini–Egorov theorem, after Carlo Severini, an Italian mathematician, and Dmitri Egorov, a Russian physicist and geometer, who published independent proofs respectively in 1910 and 1911. Egorov's theorem can be used along with compactly supported continuous functions to prove Lusin's theorem for integrable functions.
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Theodorus Moretus, also known as Theodor or Theodore MoretusHis original family name was 'Moerentorf',which was latinized as 'Moretus' (1602–1667) was a Flemish Jesuit priest who was also a mathematician, geometer, theologian and philosopher. He spent most of his working life in Prague and Breslau (now Wroclaw) where he taught philosophy, theology and mathematics. He published a number of treatises on these three subjects and also on physics and music theory.Leon Voet, The Golden Compasses.
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In 1669, Blondel was admitted to the Académie des Sciences as a geometer (cartographer).Vuillemin 2008, p. 158. Tagell 1996 states Blondel was admitted as a mathematician. That year, in the course of a trip to London in the company of Jean-Baptiste du Hamel, secretary of the Académie, he witnessed an unsuccessful blood transfusion effected by the Royal Society in hopes of curing a madman, with the thought that the human passions were transmitted in the blood.
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Socrates adds a big bifurcation to this speech, saying that there are only two kinds of lives to be lived: a divinely happy one, lived by righteous philosophers or a godless, miserable one, such as most people live (176-177). Socrates admits this was a digression that threatens to drown his original project, which was to define knowledge. Theodorus, the old geometer, tells Socrates that he finds this sort of thing easier to follow than his earlier arguments.
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After academy graduation, he worked at N.Y. Zhukovsky Central Aero-hydrodynamic Institute (TsAGI) as a design engineer. The desire to complete university education and specialize in geometry professionally led A.V. Pogorelov to Moscow State University. By recommendation of I.G. Petrovsky (Dean of the Mechanics and Mathematics Department) and a well-known geometer V.F. Kagan, Aleksei Vasil'evich met A.D. Aleksandrov – the founder of the theory of non-smooth convex surfaces. There were many new questions concerning this theory.
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In 2016 Duchin was named as a Fellow of the American Mathematical Society "for contributions to geometric group theory and Teichmüller theory, and for service to the mathematical community".2017 Class of the Fellows of the AMS, accessed December 11, 2016. She was also a Mathematical Association of America Distinguished Lecturer for that year, speaking on the mathematics of voting systems.Math and the Vote: A Geometer Examines Elections, Mathematical Association of America, accessed December 11, 2016.
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"Cubic equation and intersection of conic sections" the first page of two-chaptered manuscript kept in Tehran University. Tusi's commentaries on Khayyam's treatment of parallels made its way to Europe. John Wallis, professor of geometry at Oxford, translated Tusi's commentary into Latin. Jesuit geometer Girolamo Saccheri, whose work (euclides ab omni naevo vindicatus, 1733) is generally considered as the first step in the eventual development of non-Euclidean geometry, was familiar with the work of Wallis.
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Huic lux prima mori > Dedit Octobris seniori; Vivat ut in coelis Exoret quisque fidelis. MCXXXV. > A good philosopher, a worthy Astrologer of Lorraine, A pious and humble man, > the prior monk of this fold, Here lies in a casket, a geometer skilled in > the abacus, Doctor Walcher. The people weeps, the cleric grieves everywhere. > To him, our elder, the first day of October brought death; That he should > live in heaven may every faithful soul pray. 1135.
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In 1890, Bianchi and Dini supervised the dissertation of the noted analyst and geometer Guido Fubini. In 1898, Bianchi worked out the Bianchi classification of nine possible isometry classes of three-dimensional Lie groups of isometries of a (sufficiently symmetric) Riemannian manifold. As Bianchi knew, this is essentially the same thing as classifying, up to isomorphism, the three-dimensional real Lie algebras. This complements the earlier work of Lie himself, who had earlier classified the complex Lie algebras.
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Brahms was born on October 24, 1692, in Sanderahm, Sande, in what is now the Friesland district of Lower Saxony, Germany.. He was elected as dike judge in 1718, after the disastrous Christmas flood of 1717, which had caused many deaths, and he retained the position until 1752., p. 12. For his work in dike engineering, he was honored as a "princely geometer" of the Principality of Anhalt-Zerbst (), to which Sande at that time belonged..
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Also, Odontoptila is already used for a geometer moth genus: ICZN (1999), uBio (2005) – from the Paleocene-Eocene boundary of Morocco – is the smallest pseudotooth bird discovered to date and was just a bit larger than a white- chinned petrel (Procellaria aequinoctialis).Scarlett (1972), Olson (1985: pp. 199–200), Bourdon (2005, 2006), Mayr (2008, 2009: pp. 57,59), Mayr et al. (2008) The Pelagornithidae had extremely thin-walled bones widely pneumatized with the air sac extensions of the lungs.
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Gnophos is a genus in the geometer moth family (Geometridae). A mostly Old World lineage, it is abundant in the Palearctic, with some North American species as well; in Europe six species are recorded. This genus has about 120 known species altogether in several recognized subgenera, with new ones still being discovered occasionally.Pitkin & Jenkins (2004a), FE (2009), and see references in Savela (2009) This is the type genus of the tribe Gnophini in subfamily Ennominae, which some authors include in the Boarmiini.
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Proclus (410-485), author of Commentary on the First Book of Euclid, was one of the last important players in Hellenistic geometry. He was a competent geometer, but more importantly, he was a superb commentator on the works that preceded him. Much of that work did not survive to modern times, and is known to us only through his commentary. The Roman Republic and Empire that succeeded and absorbed the Greek city- states produced excellent engineers, but no mathematicians of note.
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The "fair cup" or Pythagorean cup, which dates from about the 6th century BC, is a hydraulic technology whose invention is credited to the Greek mathematician and geometer Pythagoras. It was used as a learning tool. The cup consists of a line carved into the interior of the cup, and a small vertical pipe in the center of the cup that leads to the bottom. The height of this pipe is the same as the line carved into the interior of the cup.
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This family is sometimes massively expanded, with the closely related Bistonini, Bupalini, Erannini, Gnophini, Melanolophini, Phaseliini and Theriini all merged into it. The eggs of all these geometer moths have the chorion cells characteristically arranged in longitudinal rows. The eggs of the Boarmiini in the narrow sense usually have a typical slender and narrow shape, with a soft chorion consisting of heavy-walled but unridged polygonal cells. However, in Cleora for example, the eggs approach the wide-walled shape found in many Bistonini.
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Over one- hundred newly described insects bear the species epithet slossoni (or slossonae) in her honor, often because she collected the first specimen. Her collection of some 35,000 insects was donated to the American Museum of Natural History. Some examples of insects named for her include: Coelioxys slossoni, a leaf-cutter bee, Rhopalotria slossoni, a weevil associated with cycads, especially Zamia pumila, and Zethus slossonae, a wasp. Another previously unknown species that Slosson described was Eubaphe meridiana, a species of geometer moth.
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Other relationships include the algorithmic analysis of artworks by X-ray fluorescence spectroscopy, the finding that traditional batiks from different regions of Java have distinct fractal dimensions, and stimuli to mathematics research, especially Filippo Brunelleschi's theory of perspective, which eventually led to Girard Desargues's projective geometry. A persistent view, based ultimately on the Pythagorean notion of harmony in music, holds that everything was arranged by Number, that God is the geometer of the world, and that therefore the world's geometry is sacred.
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A line segment therefore cannot be scaled up indefinitely. A geometer measuring the geometrical properties of the space he or she inhabits can detect, via measurements, that there is a certain distance scale that is a property of the space. On scales much smaller than this one, the space is approximately flat, geometry is approximately Euclidean, and figures can be scaled up and down while remaining approximately similar. A great deal of Euclidean geometry carries over directly to elliptic geometry.
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Carl Friedrich Gauss, on reading the Appendix, wrote to a friend saying "I regard this young geometer Bolyai as a genius of the first order." To Bolyai, however, Gauss wrote: "To praise it would amount to praising myself. For the entire content of the work...coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years." In 1848 Bolyai learned that Nikolai Ivanovich Lobachevsky had published a similar piece of work in 1829.
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Caterpillars are the staple food for nestlings, with some – e.g. those of geometer moths (Geometridae) – preferred over others.Bachynski & Kadlec (2003), Foster (2007) The predators of yellow and mangrove warblers are those - snakes, foxes, birds of prey, and many others - typical of such smallish tree-nesting passerines. The odds of an adult American yellow warbler to survive from one year to the next are on average 50%; in the southern populations, by contrast, about two-thirds of the adults survive each year.
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A spiric section is sometimes defined as the curve of intersection of a torus and a plane parallel to its rotational symmetry axis. However, this definition does not include all of the curves given by the previous definition unless imaginary planes are allowed. Spiric sections were first described by the ancient Greek geometer Perseus in roughly 150 BC, and are assumed to be the first toric sections to be described. The name spiric is due to the ancient notation spira of a torus.
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Edward Kingsley Wakeford (E. K. Wakeford; 15 June 1894 – 26 July 1916) was an English geometer. Born at Plymouth, England, the son of Edward W. Wakeford of Gibraltar, E. K. was educated at Borden Grammar School and Clifton College then entered Trinity College, Cambridge with a mathematics scholarship in 1912. As a scholar of mathematics, he extended the work of the English mathematician James Joseph Sylvester (1814–1897) on canonical binary forms for odd degrees, solving the forms for even degrees.
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Old town Bydgoszcz in 1876 Buildings Jackman and Frederic in Bydgoszcz 1903 On a detailed plan of the city, prepared by the Prussian geometer Gretha in 1774, plots along the street are partially occupied by current buildings. In the western part, the street ran along the municipal cemetery to the bridge connecting Mill Island in Bydgoszcz. On the eastern side, the watered castle moat is still standing. Between the castle and the Brda river stands the cane sugar refinery building (now PZU building).
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Ludwig Danzer (15 November 1927 – 3 December 2011) was a German geometer working in discrete geometry. He was a student of Hanfried Lenz, starting his career in 1960 with a thesis about "Lagerungsprobleme". Danzer's name is popularized in the concepts of a Danzer set, a set of points that touches all large convex sets, and the Danzer cube, an example of a non-shellable triangulation of the cube. It is an example of a power complex, studied by Danzer in the 1980s.
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Richard M. Pollack (January 25, 1935 – September 18, 2018)"Ricky Pollack", sent by Joseph S. B. Mitchell on behalf of the Computational Geometry steering committee to the compgeom-announce mailing list, September 19, 2018 was an American geometer who spent most of his career at the Courant Institute of Mathematical Sciences at New York University, where he was Professor Emeritus till his death. In 1986 he and Jacob E. Goodman were the founding co-editors- in-chief of the journal Discrete & Computational Geometry (Springer-Verlag).
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In 1900 Grossmann graduated from the Federal Polytechnic School (ETH) and became an assistant to the geometer Wilhelm Fiedler. He continued to do research on non- Euclidean geometry and taught in high schools for the next seven years. In 1902, he earned his doctorate from the University of Zurich with the thesis Ueber die metrischen Eigenschaften kollinearer Gebilde (translated On the Metrical Properties of Collinear Structures) with Fiedler as advisor. In 1907, he was appointed full professor of descriptive geometry at the Federal Polytechnic School.
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Brückner's photo of the final stellation of the icosahedron, a stellated polyhedron first studied by Brückner Photo of polyhedra models by Brückner. Johannes Max Brückner (5 August 1860 – 1 November 1934) was a German geometer, known for his collection of polyhedral models. Brückner was born on August 5, 1860 in Hartau, in the Kingdom of Saxony, a town that is now part of Zittau, Germany. He completed a Ph.D. at Leipzig University in 1886, supervised by Felix Klein and Wilhelm Scheibner, with a dissertation concerning conformal maps.
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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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Karl Wilhelm von Feuerbach (30 May 1800 - 12 March 1834) was a German geometer and the son of legal scholar Paul Johann Anselm Ritter von Feuerbach, and the brother of philosopher Ludwig Feuerbach. After receiving his doctorate at age 22, he became a professor of mathematics at the Gymnasium at Erlangen. In 1822 he wrote a small book on mathematics noted mainly for a theorem on the nine- point circle, which is now known as Feuerbach's theorem. In 1827 he introduced homogeneous coordinates, independently of Möbius.
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In 1986, geometer Sheldon Katz proved that the number of curves, such as circles, that are defined by polynomials of degree two and lie entirely in the quintic is 609,250. By the year 1991, most of the classical problems of enumerative geometry had been solved and interest in enumerative geometry had begun to diminish. According to mathematician Mark Gross, "As the old problems had been solved, people went back to check Schubert's numbers with modern techniques, but that was getting pretty stale."Yau and Nadis 2010, p.
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Littlewood was born on 9 June 1885 in Rochester, Kent, the eldest son of Edward Thornton Littlewood and Sylvia Maud (née Ackland). In 1892, his father accepted the headmastership of a school in Wynberg, Cape Town, in South Africa, taking his family there.: "He later accepted the headmastership of a newly founded school at Wynberg near Cape Town, taking his family there in 1892." Littlewood returned to England in 1900 to attend St Paul's School in London, studying under Francis Sowerby Macaulay, an influential algebraic geometer.
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Under Abbot David (1216–1234) there was a new phase of building, notably the construction in around 1220 of a chapel dedicated to the Blessed Virgin Mary, abutting the northern side of the choir. This building, which still stands, was to become known as the "Elder Lady Chapel". The architect, referred to in a letter as 'L', is thought to have been Adam Lock, master mason of Wells Cathedral. The stonework of the eastern window of this chapel is by William the Geometer, of about 1280.
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Gerard of Brussels (, ) was an early thirteenth-century geometer and philosopher known primarily for his Latin book Liber de motu (On Motion), which was a pioneering study in kinematics, probably written between 1187 and 1260. It has been described as "the first Latin treatise that was to take the fundamental approach to kinematics that was to characterize modern kinematics."Marshall Clagett, "The Reduction of Curvilnear Velocities to Uniform Rectilinear Velocities," A Source Book in Medieval Science, ed. Edward Grant (Harvard University Press, 1974), 234.
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There is a copperplate from A. Kaltschmied from 1735, according to a geometer Mikovíny, providing historical evidence of the widespread linden trees in the area of contemporary "Palisades". On the plan from 1768 there is a dominant tree marked in the garden of baron Jesenák, it is mentioned also by M. Korabinský in his publication on Bratislava from 1781. The tree raised attention of the Slovak revival generation. The tree represented a symbol to so called Ľudovít Štúr - movements - the linden is considered to be a symbol of Slavs.
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In 1900, he became professor for infinitesimal calculus at Modena. There, he became dean from 1913 to 1919, then moved back to the University of Bologna, where he retired in 1936. He was an Invited Speaker of the ICM in 1924 in Toronto and in 1928 in Bologna. Bortolotti must also be considered a differential geometer and a relativist too. In fact, in the year 1929, he commented on the geometric basis for Einstein’s absolute parallelism theory in a paper entitled "Stars of congruences and absolute parallelism: Geometric basis for a recent theory of Einstein".
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René Descartes (1596–1650) originated the modern conception of matter. He was primarily a geometer. Instead of, like Aristotle, deducing the existence of matter from the physical reality of change, Descartes arbitrarily postulated matter to be an abstract, mathematical substance that occupies space: For Descartes, matter has only the property of extension, so its only activity aside from locomotion is to exclude other bodies:though even this property seems to be non-essential (René Descartes, Principles of Philosophy II [1644], "On the Principles of Material Things", no. 4.) this is the mechanical philosophy.
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Kurt Schiffler (6 April 1896 - 25 February 1986) was a German engineer, entrepreneur, inventor and amateur geometer. Schiffler's father was an elementary school teacher and his grandfather was a toy manufacturer. Schiffler was born in Gotha, Thuringia, where he grew up as well. He had just completed the local gymnasium (high-school) in 1914, when he was drafted as a soldier in World War I. After the war Schiffler studied first at the Freiberg University of Mining and Technology and later at the University of Stuttgart, which awarded him an engineering degree.
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An illustration of Desargues' theorem, a result in Euclidean and projective geometry Geometry (from the ; geo- "earth", -metron "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.
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However, Gistl misread the name of the spider genus Theraphosa (established by Charles Athanase Walckenaer in 1805) as Tephrosia, and thus came to believe that Tephrosia was in need of a new name. He chose Coenobita, which to his misfortune had been given to a genus of hermit crabs by Pierre André Latreille in 1829 already.Pitkin & Jenkins (2004b) The other preoccupied synonym, Boarmia, had earlier been given to closely related moths. That group is now included in Hypomecis, which thus has become the type genus of the tribe Boarmiini in the geometer moth subfamily Ennominae.
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Gradually, and partly through the movement of academies of the arts, the Italian techniques became part of the training of artists across Europe, and later other parts of the world. The culmination of these Renaissance traditions finds its ultimate synthesis in the research of the architect, geometer, and optician Girard Desargues on perspective, optics and projective geometry. The Vitruvian Man by Leonardo da Vinci(c. 1490)The Secret Language of the Renaissance - Richard Stemp depicts a man in two superimposed positions with his arms and legs apart and inscribed in a circle and square.
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A polygon with Heesch number 5, the highest finite such number known, found by Casey Mann In geometry, the Heesch number of a shape is the maximum number of layers of copies of the same shape that can surround it. Heesch's problem is the problem of determining the set of numbers that can be Heesch numbers. Both are named for geometer Heinrich Heesch,, as cited by and . who found a tile with Heesch number 1 (the union of a square, equilateral triangle, and 30-60-90 right triangle) and proposed the more general problem.
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In 1912 Cartan became Professor there, based on the reference he received from Poincaré. He remained in Sorbonne until his retirement in 1940 and spent the last years of his life teaching mathematics at the École Normale Supérieure for girls. As a student of Cartan, the geometer Shiing-Shen Chern wrote: > Usually the day after [meeting with Cartan] I would get a letter from him. > He would say, “After you left, I thought more about your questions...”—he > had some results, and some more questions, and so on.
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A detailed portrait of the Mughal Emperor Jahangir holding a globe probably made by Muhammad Saleh Thattvi, (painting by: Abul Hasan, Nadir al-Zaman (dated 1617 AD) Muhammad Saleh Thattvi (1074 AH/1663–64 AD), Mughal metallurgist, astronomer, geometer and craftsman, was born and raised in Thatta, Sindh province in Pakistan, during the reign of the Mughal Emperor Shah Jahan and the governorship of the Mughal Nawab Mirza Ghazi Beg of Sindh. During those years young metallurgists were recruited, patronized and delivered to the Mughal court at Agra.
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The Kitab al- Istikmal deals with irrational numbers, conic sections, quadrature of the parabolic segment, volumes and areas of various geometric objects, and the drawing of the tangent to a circle, among other mathematical problems. In the work appears an attempt to classify mathematics into Aristotelian categories. The classification includes a chapter for arithmetic, two chapters for geometry and two others for stereometry. Al-Mu'taman is the author of the first known formulation of Ceva's theorem, which was only known in Europe in 1678 in De lineis rectis by the Italian geometer Giovanni Ceva.
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Aside from being personally associated with Aghaboe Abbey and Salzburg Cathedral, a number of parishes around the world are dedicated to him, mostly being founded by small populations of far-flung Irish Catholics, like himself. There is a church still bearing his name dedicated to him in Broad Channel, Queens, New York, which recently merged with another parish in 2008. A parish in Morris Plains, New Jersey, is also dedicated to him. Fittingly for this Irish geometer who predicted antipodes, several churches in the Southern Hemisphere are dedicated to him.
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With Cavalieri, Fermat, Vincentio, Kepler, Torricelli and Valerio, Lalouvere can be considered one of the forerunners of modern integral calculus. In his main work of 1651, Quadratura Circuli, he calculates volumes and centers of gravity by inverting the rule of Paul Guldin. As a geometer Lalouvère is also the first to have studied the properties of the helix. In 1658, he was engaged in a resounding controversy with Blaise Pascal who accused him of plagiarizing Gilles de Roberval's solution of the roulette problem, an accusation which seems now unfounded.
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The dodecahedral conjecture in geometry is intimately related to sphere packing. László Fejes Tóth, a 20th-century Hungarian geometer, considered the Voronoi decomposition of any given packing of unit spheres. He conjectured in 1943 that the minimal volume of any cell in the resulting Voronoi decomposition was at least as large as the volume of a regular dodecahedron circumscribed to a unit sphere.. Thomas Callister Hales and Sean McLaughlin proved the conjecture in 1998,. following the same strategy that led Hales to his proof of the Kepler conjecture.
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Geometrinae is the nominate subfamily of the geometer moth family (Geometridae). It is strongly split, containing a considerable number of tribes of which most are presently very small or monotypic. These small moths are often a light bluish green, leading to the common name of emerald moths, though a few species called thus are also found in the tribe Campaeini of the Ennominae. In 2018, a phylogeny and classification based on a molecular phylogenetic analysis was published in the Zoological Journal of the Linnean Society in which 13 tribes were accepted.
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Rekelj & Česanek (2009), and see references in Haaramo (2010) Like most of their closest relatives, they are mid-sized moths (a few cm/around 1 inch wingspan) which may be active all day, but avoid direct sunlight. Unlike many of the Callimorphina, they are inconspicuous and coloured a somewhat translucent grey-brown and without bold markings. They have the typical slender body shape of other species of their subtribe, and they resemble, at a casual glance, certain larentiine geometer moths (Geometridae), e.g. the Operophterini, rather than the more typical Callimorphina.
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In 1828, when the "pneumatic paradox," as it was called, was attracting the attention of scholars, he first suggested a true theory, which was afterwards experimentally proved by his nephew, Jos. H. Abbot, and an article thereon published in the American Journal of Science and Arts. In 1837-1838, he detected the fallacy of the instrument called the geometer, to which the attention of Congress was then called. The instrument supposedly applied an alleged discovery in magnetism by which, in addition to the direction of the north pole, latitude could be ascertained.
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Tachytes generally predates on Orthoptera (grasshoppers and katydids, especially those of the families Acrididae, Tettigoniidae, Tetrigidae, and Tridactylidae), though Tachytes bidens reportedly predates on geometer moths. Like other hunting wasps, the female captures a prey item, stings to paralyze it, and seals it in a burrow along with an egg that consumes the prey during development. The sting often paralyzes the prey completely, though in a few species, it only appears to prevent them from attempting to escape. Their burrows can be very long, up to one meter in Tachytes praedator.
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Bacon studied for her master's degree at the University of Chicago, completing her thesis in 1903 and graduating in September 1904, after six summers of study. She achieved her PhD from Johns Hopkins University in 1911, one of only four women to receive a PhD from the university that year, the first year that women were granted PhDs without special approval from the trustees. At Johns Hopkins, Bacon was a student of the geometer Frank Morley, who was her dissertation adviser. Her thesis was published in American Journal of Mathematics in 1913.
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Prof Arthur Geoffrey Walker FRS FRSE (17 July 1909 in Watford, Hertfordshire, England – 31 March 2001) was a leading mathematician who made important contributions to physics and physical cosmology. Although he was an accomplished geometer, he is best remembered today for two important contributions to general relativity. Together with H. P. Robertson, they devised the well-known Robertson-Walker unit for the Friedmann–Lemaître–Robertson–Walker cosmological models, which are exact solutions of the Einstein field equation. Together with Enrico Fermi, he introduced the notion of Fermi–Walker differentiation.
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Tolpygo was born during WWI in Kyiv, Ukraine, then part of the Russian Empire. His father, Boris Nikolaevich Tolpygo (1889 – 1958) was a jurist who received the Order of St. Stanislaus for his services to the Russian army during World War I. Tolpygo's mother, Tatiana B. Bukreeva (1889 – 1992), was the daughter of Boris Yakovlevich Bukreev, a mathematician and geometer at Kyiv University (University of St. Volodymyr, Kyiv)."Bukreev" History.mcs.st-and.ac.uk. accessed 3 April 2012 In 1923, Tolpygo's father was arrested by the Cheka, for alleged "counter-revolutionary" activities.
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And so on indefinitely. The theorem has been compared to Clifford's circle theorems since they both are an infinite chain of theorems. In 1941 Richmond argued that Cox's chain was superior: :Cox's interest lay in the discovery of applications of Grassmann's Ausdehnungslehre and he uses the chain to that end. Any present-day geometer (to whom many of Cox's properties of circles in a plane must appear not a little artificial) would agree that his figure of points and planes in space is simpler and more fundamental than that of circles in a plane which he derives from it.
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The material is located in the surviving false “Prefaces” of the books of his Conics. These are letters delivered to influential friends of Apollonius asking them to review the book enclosed with the letter. The Preface to Book I, addressed to one Eudemus, reminds him that Conics was initially requested by a house guest at Alexandria, the geometer, Naucrates, otherwise unknown to history. Naucrates had the first draft of all eight books in his hands by the end of the visit. Apollonius refers to them as being “without a thorough purgation” (ou diakatharantes in Greek, ea non perpurgaremus in Latin).
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The first great work of architectural theory of this period belongs to Leon Battista Alberti, De re aedificatoria, which placed Vitruvius at the core of the most profound theoretical tradition of the modern ages. From Alberti, good architecture is validated through the Vitruvian triad, which defines its purpose. This triplet conserved all its validity until the 19th century. A major transition into the 17th century and ultimately to the Age of Enlightenment was secured through the advanced mathematical and optical research of the celebrated architect and geometer Girard Desargues, with an emphasis on his studies on conics, perspective and projective geometry.
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Al-Urdi (full name: Moayad Al-Din Al-Urdi Al-Amiri Al-Dimashqi) () (d. 1266) was a medieval Syrian astronomer and geometer. Born circa 1200, presumably (from the nisba al‐ʿUrḍī) in the village of ʿUrḍ in the Syrian desert between Palmyra and Resafa, he came to Damascus at some point before 1239, where he worked as an engineer and teacher of geometry, and built instruments for al- Malik al-Mansur of Hims. In 1259 he moved to Maragha in northeastern Iran, after being asked by Nasir al-Din al-Tusi to help establish the Maragha observatory under the patronage of Hulagu.
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The eldest of three sons, Samelson was born on 3 March 1916, in Strassburg, Germany (now Strasbourg, France). His brother Klaus later became a mathematician and early computer science pioneer in Germany. His parents—one of Protestant and one of Jewish background—were both pediatricians. He spent most of his youth in Breslau, Germany (now Wroclaw, Poland), and began his advanced mathematical education there, at the University of Breslau. His family helped him leave Nazi Germany in 1936 for Zurich, Switzerland, where he studied with the geometer Heinz Hopf and received his doctorate in 1940 from the Swiss Federal Institute of Technology.
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The geometer moths are moths belonging to the family Geometridae of the insect order Lepidoptera, the moths and butterflies. Their scientific name derives from the Ancient Greek geo or "the earth", and metron "measure" in reference to the way their larvae, or "inchworms", appear to "measure the earth" as they move along in a looping fashion. A very large family, it has around 23,000 species of moths described, and over 1400 species from six subfamilies indigenous to North America alone. A well-known member is the peppered moth, Biston betularia, which has been subject of numerous studies in population genetics.
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Borda's reflecting circle, on display at Toulon naval museum Mendoça's reflecting circle on display at the Musée national de la Marine. The reflecting circle was invented by the German geometer and astronomer Tobias Mayer in 1752, with details published in 1767. His development preceded the sextant and was motivated by the need to create a superior surveying instrument. The reflecting circle is a complete circular instrument graduated to 720° (To measure distances between heavenly bodies, there is no need to read an angle greater than 180°, since the minimum distance will always be less than 180°.).
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At the same time, however, a new class of scholarship arose, one which, while never questioning the literal truth of the ark story, began to speculate on the practical workings of Noah's vessel from within a purely naturalistic framework. In the 15th century, Alfonso Tostada gave a detailed account of the logistics of the Ark, down to arrangements for the disposal of dung and the circulation of fresh air. The 16th-century geometer Johannes Buteo calculated the ship's internal dimensions, allowing room for Noah's grinding mills and smokeless ovens, a model widely adopted by other commentators.
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KSV (, ) Sanctus Virgilius (also known as Virgiel) is the largest student fraternity/sorority in Delft, named after the Irish born astronomer, geometer and bishop Saint Virgil. There are about 2000 student members (mostly students at TU Delft) who gather together on a daily or weekly basis at an old monastery named Alcuin in the city centre of Delft. A wide variety of sports and cultural events are organized by members of Virgiel, including football, field hockey, rugby and climbing. Virgiel was created in 1898 as the result of emancipation of the Catholic youth in the Netherlands.
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The oldest map on which Gries appears (compiled in 1564 by the geometer Tilemann Stella), for instance, is to be found at the Swedish Imperial Archive in Stockholm. Over the centuries, the power structure would change often, with only Gries's local lords, the Counts (later Imperial Counts) of Leyen remaining the same, each holding the fief under his respective overlord. Until the French Revolution, the local ruling structure thus did not change again. Gries still belonged to the lordship of the House of Leyen, who as of 1773 resided in Blieskastel, whence they continued to expand their hereditary domain.
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This minor planet was named after the Greek mythological figure, Menelaus, husband of Helen of Troy, brother of Agamemnon, and king and leader of the Spartan contingent of the Greek army during the Trojan War. The discoverer followed the convention to name bodies located in the camp to the east of Jupiter after famous Greek heroes. The Dictionary of Minor Planet Names also mentions that the lunar crater Menelaus was named after the Greek hero. However, based on the official International Astronomical Union–WGPSN nomenclature, it is named after Greek geometer and astronomer Menelaus of Alexandria (70–140).
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Pierre René Jean Baptiste Henri Brocard (12 May 1845 - 16 January 1922) was a French meteorologist and mathematician, in particular a geometer. His best- known achievement is the invention and discovery of the properties of the Brocard points, the Brocard circle, and the Brocard triangle, all bearing his name. Contemporary mathematician Nathan Court wrote that he, along with Émile Lemoine and Joseph Neuberg, was one of the three co-founders of modern triangle geometry. He is listed as an Emeritus at the International Academy of Science, was awarded the Ordre des Palmes Académiques, and was an officer of the Légion d'honneur.
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The shaft is wide at the point where it flares into the trochleae. It was thus more than twice as large as "Odontoptila inexpectata"Only published in a thesis, and hence a nomen nudum; also a junior homonym of the geometer moth genus Odontoptila and unavailable for the bird. Formerly "Odontopteryx n. sp. 1": ICZN (1999), Bourdon (2005) from the Late Paleocene/Early Eocene of the Ouled Abdoul Basin (Morocco), and - like Osteodontornis orri - thus belonged to the large pseudotooth birds, with a wingspan of more than 5, perhaps as much as 6 m (16–20 ft).
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The main title of Snellius's book therefore means "the Dutch helmsman". and by Adriaan Metius, the geometer and astronomer from Holland, for Primum Mobile (1631). (Latin). "Sciography", a variant of "sciagraphy", is the branch of the science of perspective dealing with the projection of shadows, or the art or practice of determining time by observing the shadow of the sun, moon or stars on a dial: Following Wright's proposals, Richard Norwood measured a degree on a great circle of the earth at , publishing the information in 1637. Wright was praised by Charles Saltonstall in The Navigator (1642).
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Freemasonry unambiguously states that it is not a religion, nor a substitute for religion.For example, this is stated in exactly these words on the web site of the United Grand Lodge of England There is no separate "Masonic" God.Also from United Grand Lodge of England Nor is there a separate proper name for a deity in any branch of Freemasonry.United Grand Lodge of England In keeping with the geometrical and architectural theme of Freemasonry, the Supreme Being is referred to in Masonic ritual by the attributes of Great Architect of the Universe (sometimes abbreviated as G.A.O.T.U.), Grand Geometer or something similar.
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Within Pfeffelbach's current limits, two now vanished villages can be mentioned, Herzweiler and Stauderhof. Herzweiler lay near the municipal limit with Reichweiler and was likely forsaken as long ago as the 15th century, but references to it still crop up in rural cadastral toponyms, such as Herzerberg. The Stauderhof – the name took a definite article – was named in geometer Johannes Hoffmann's writings ("Der Stauderhof war damals eine Räuberhöhle, und die Bewohner schreckten auch vor Morden nicht zurück" – "The Stauderhof was then a den of robbers, and its dwellers did not shy away from murder, either."), but otherwise crops up nowhere else.
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Marc Levine at the MFO, 2005 Fabien Morel (born 22 January 1965, in Reims) is a French algebraic geometer and key developer of A¹ homotopy theory with Vladimir Voevodsky. Among his accomplishments is the proof of the Friedlander conjecture, and the proof of the complex case of the Milnor conjecture stated in Milnor's 1983 paper 'On the homology of Lie groups made discrete'. This result was presented at the Second Abel Conference, held in January–February 2012. In 2006 he was an invited speaker with talk A1-algebraic topology at the International Congress of Mathematicians in Madrid.
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The distinctive pedagogical aim of the work, as stated in its preface, was to elucidate for graduate students the often obscure relationship between classical differential geometry—geometrically intuitive but imprecise—and its modern counterpart, replete with precise but unintuitive algebraic definitions. On several occasions, most prominently in Volume 2, Spivak "translates" the classical language that Gauss or Riemann would be familiar with to the abstract language that a modern differential geometer might use. The Leroy P. Steele Prize was awarded to Spivak in 1985 for his authorship of the work. Spivak has also authored several well-known undergraduate textbooks.
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Jean-Victor Poncelet (1788−1867) author of the first text on projective geometry, Traité des propriétés projectives des figures, was a synthetic geometer who systematically developed the theory of poles and polars with respect to a conic. Poncelet maintained that the principle of duality was a consequence of the theory of poles and polars. Julius Plücker (1801−1868) is credited with extending the concept of duality to three and higher dimensional projective spaces. Poncelet and Gergonne started out as earnest but friendly rivals presenting their different points of view and techniques in papers appearing in Annales de Gergonne.
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The 9.43 hectares of Romanée Saint-Vivant were bought in 1791 by Nicolas-Joseph Marey, son-in-law of the geometer Gaspard Monge. The Marey-Monge family sold off part of their holdings to the Latour family in 1898, leased the remaining 5.28 hectares to Domaine de la Romanée-Conti in 1966, and finally sold to the domaine in 1988. This last deal was financed by the sale and leaseback of the domaine's holdings in Échezeaux and some in Grands Échezeaux. As one of Napoleon's generals, Louis Liger-Belair was well placed to acquire good vineyards.
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In 1934, Chern received a scholarship to study in the United States at Princeton and Harvard, but at the time he wanted to study geometry and Europe was the center for the maths and sciences. He studied with the well-known Austrian geometer Wilhelm Blaschke. Co-funded by Tsinghua and the Chinese Foundation of Culture and Education, Chern went to continue his study in mathematics in Germany with a scholarship. Chern studied at the University of Hamburg and worked under Blaschke's guidance first on the geometry of webs then on the Cartan-Kähler theory and invariant theory.
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Depiction of Vienna in the Nuremberg Chronicle, 1493 Vienna in 1683 Evidence has been found of continuous habitation in the Vienna area since 500 BC, when Celts settled the site on the Danube. In 15 BC the Romans fortified the frontier city they called Vindobona to guard the empire against Germanic tribes to the north. Close ties with other Celtic peoples continued through the ages. The Irish monk Saint Colman (or Koloman, Irish Colmán, derived from colm "dove") is buried in Melk Abbey and Saint Fergil (Virgil the Geometer) served as Bishop of Salzburg for forty years.
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In 1926, 1930 and 1937 he gave a series of lectures as titular professor at the Faculty of Sciences in Sorbonne. He also gave many lectures at the Free University of Brussels (1926) and the University of Rome (1927). Țițeica wrote about 400 articles, of which 96 are scientific projects, most addressing problems of differential geometry. Carrying on the researches of the American geometer of German origin Ernest Wilczynski, Țițeica discovered a new category of surfaces and a new category of curves which now carry his name; his contributions represent the beginning of a new chapter in mathematics, namely the affine differential geometry.
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Prout married Julia West in 1861, and they had five children, Florence (1862–1921), Louis Beethoven (1864–1944), Edith Julia (1867–1913), Alice (1869–1870) and Alice Ellen (1871–1957). Louis Beethoven was a writer on musical theory, having trained under his father at the Royal Academy, and becoming professor at the Guildhall School. Louis Beethoven Prout's principal works are an Analysis of Bach's 48 Fugues (Weekes); Harmonic Analysis (Augener); Sidelights on Harmony (Augener); and Time, Rhythm and Expression (Augener). Like his sister Alice Ellen, he was also an entomologist, being a foremost authority on the Geometridae, or geometer moths.
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Fatio was in communication with some of the most famous scientists of his time. Newton, Huygens and Halley on Fatio's manuscript There was a strong personal relationship between Isaac Newton and Fatio in the years 1690 to 1693. Newton's statements on Fatio's theory differed widely. For example, after describing the necessary conditions for a mechanical explanation of gravity, he wrote in an (unpublished) note in his own printed copy of the Principia in 1692:The unique hypothesis by which gravity can be explained is however of this kind, and was first devised by the most ingenious geometer Mr. N. Fatio.
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On the first detailed plan of Bromberg, realized in 1774 by Prussian geometer Greth, most of the buildings on Przyrzecze street are located on the southern part, near Długa street. In the northern part, houses were only present in the eastern frontage, as backsides of tenements located on parallel Jezuicka Street. Like today, the northern area of Przyrzecze street gently slid down to the river, offering a public access to water collection. On a plan of the city from 1876, the development of the street is similar as today, with townhouses on the eastern side, and industrial buildings on the west side.
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The circles of Apollonius are any of several sets of circles associated with Apollonius of Perga, a renowned Greek geometer. Most of these circles are found in planar Euclidean geometry, but analogs have been defined on other surfaces; for example, counterparts on the surface of a sphere can be defined through stereographic projection. The main uses of this term are fivefold: # Apollonius showed that a circle can be defined as the set of points in a plane that have a specified ratio of distances to two fixed points, known as foci. This Apollonian circle is the basis of the Apollonius pursuit problem.
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Triangle , its medial triangle, the Spieker circle (the incircle of the medial triangle), and the Spieker center (the center of the Spieker circle) In geometry, the incircle of the medial triangle of a triangle is the Spieker circle, named after 19th-century German geometer Theodor Spieker. Its center, the Spieker center, in addition to being the incenter of the medial triangle, is the center of mass of the uniform-density boundary of triangle. The Spieker center is also the point where all three cleavers of the triangle (perimeter bisectors with an endpoint at a side's midpoint) intersect each other.
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Like his friend and colleague Gregorio Ricci-Curbastro, Bianchi studied at the Scuola Normale Superiore in Pisa under Enrico Betti, a leading differential geometer who is today best remembered for his seminal contributions to topology, and Ulisse Dini, a leading expert on function theory. Bianchi was also greatly influenced by the geometrical ideas of Bernhard Riemann and by the work on transformation groups of Sophus Lie and Felix Klein. Bianchi became a professor at the Scuola Normale Superiore in Pisa in 1896, where he spent the remainder of his career. At Pisa, his colleagues included the talented Ricci.
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According to Heath, “The Methods of Apollonius” were not his and were not personal. Whatever influence he had on later theorists was that of geometry, not of his own innovation of technique. Heath says, > “As a preliminary to the consideration in detail of the methods employed in > the Conics, it may be stated generally that they follow steadily the > accepted principles of geometrical investigation which found their > definitive expression in the Elements of Euclid.” With regard to moderns speaking of golden age geometers, the term "method" means specifically the visual, reconstructive way in which the geometer unknowingly produces the same result as an algebraic method used today.
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Unlike the family Geometridae, in which they had been placed by the geometer expert L.B.Prout, hedylids lack tympanic organs at the base of the abdomen, but have them on the wings (see under Behaviour). Unlike other butterflies, however (except the unique case of the remarkable Australian skipper butterfly Euschemon rafflesia, whose males possess these structures), the single-spined frenulum and retinaculum are not lost or reduced in males, except in three Macrosoma species where there is no functional wing coupling system. The retinaculum is always lost in females, and the frenulum may be vestigial. The family have been fully catalogued and illustrated in an identification guide.
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Ferro-cement experimental architecture based on principles of Catenatic Geometry: Mojave Desert, California,Structural-spatial configurations of the Ars-Vivant desert tortoise nurseries--Edwards Air Force Base, California, USA. 2004Williams uses the geometry of Natural Structure, Catenatic Geometry principles, and Symbolic analysis as fundamental components of his architectural, environmental design, and cosmology work.Komori, V. The Broad Perspective. Radio interview with Robert Williams: Geometer, Cosmologist, Architect: “The Geometric reminder of our interconnectedness and place in our Universe.” 9/11/2009. In 1967, he became a charter member "New Beginnings," E.A.T. News (6/1/67). Vol. 1, No. 2, p. 3 of Experiments in Art and Technology(E.
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Between Eßweiler and Oberweiler im Tal, the Sprengelburg (or Springeburg – a castle) was built about 1300. It was not standing very long before it was destroyed. The castle lords at the time were the Knights of Mülenstein (or Mühlenstein), vassals of the Waldgraves,Daniel Hinkelmann: Die Ritter Mülenstein von Grumbach (1318–1451) und ihr Schloß Springeburg (nach Erkenntnissen bis April 1978). Westrich Kalender 1979 although little else is known about the castle’s history. Only in a 1595 description of the Eßweiler Tal written by state scrivener and geometer Johannes Hofmann on Count Palatine Johann’s behalf can anything be read about the Sprengelburg and its eventual destruction by merchants from Strasbourg.
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Osinga earned a master's degree in 1991 and a Ph.D. in 1996 from the University of Groningen. Her doctoral dissertation, jointly supervised by dynamical systems theorist Hendrik Broer and computational geometer Gert Vegter, was on the computation of invariant manifolds. After postdoctoral studies at The Geometry Center and the California Institute of Technology, and a short-term lecturership at the University of Exeter, she became a lecturer at the University of Bristol in 2001, and was promoted to reader and professor there in 2005 and 2011, respectively. She moved to Auckland in 2011, becoming the first female mathematics professor at Auckland and the second in New Zealand..
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Inner section of Kepler's Platonic solid model of planetary spacing in the Solar System from Mysterium Cosmographicum (1596) Sacred geometry ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions.dartmouth.edu: Paul Calter, Polygons, Tilings, & Sacred Geometry It is associated with the belief that a god is the geometer of the world. The geometry used in the design and construction of religious structures such as churches, temples, mosques, religious monuments, altars, and tabernacles has sometimes been considered sacred. The concept applies also to sacred spaces such as temenoi, sacred groves, village greens, pagodas and holy wells, and the creation of religious art.
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"Plato's Dream" (original French title "Songe de Platon") is a 1756 short story written in the 18th century by the French philosopher and satirist Voltaire. Along with his 1752 novella Micromégas, "Plato's Dream" is among the first modern works in the genre of science fiction. "Plato's Dream" is a pointed philosophical criticism of religious doctrine, told as a dream contained within the framework of a famous (and religiously-tolerated) personality of antiquity. His story recounts a dream attributed to Greek philosopher Plato, in which Demiurgos, a god-like entity referred to as the "eternal geometer", charges a number of "lesser superbeings" with the task of creating their own worlds.
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The ICCM awards the Chern Prize and the Morningside Medal, among other prizes, to Chinese mathematicians who have made significant contributions to pure or applied mathematics. The Morningside Medal was established with the First Congress in 1998 and is awarded to mathematicians younger than 45; winners are traditionally announced on the first day of the ICCM. The Chern Prize was first awarded at the Second Congress in 2001 in honor of differential geometer Shiing-Shen Chern; thus it predates the Chern Prize awarded by the International Mathematical Union by nine years. Winners of both prizes are selected by a committee of prominent Chinese mathematicians.
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The quadratrix of Dinostratus (also called the quadratrix of Hippias) was well known to the ancient Greek geometers, and is mentioned by Proclus, who ascribes the invention of the curve to a contemporary of Socrates, probably Hippias of Elis. Dinostratus, a Greek geometer and disciple of Plato, discussed the curve, and showed how it effected a mechanical solution of squaring the circle. Pappus, in his Collections, treats its history, and gives two methods by which it can be generated. # Let a helix be drawn on a right circular cylinder; a screw surface is then obtained by drawing lines from every point of this spiral perpendicular to its axis.
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Other animals move in terrestrial habitats without the aid of legs. Earthworms crawl by a peristalsis, the same rhythmic contractions that propel food through the digestive tract. Leech moving on a flat surface Leeches and geometer moth caterpillars move by looping or inching (measuring off a length with each movement), using their paired circular and longitudinal muscles (as for peristalsis) along with the ability to attach to a surface at both anterior and posterior ends. One end is attached and the other end is projected forward peristaltically until it touches down, as far as it can reach; then the first end is released, pulled forward, and reattached; and the cycle repeats.
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They rest with their wings stretched out parallel to the surface, and the hindwings hidden under the forewings unlike most related Ennominae. Though they are among the larger Geometridae, they are nonetheless not very conspicuous; the outer third of the forewings is usually conspicuously lighter than the middle third, and at the apical end of the forewing cell there is usually a white or black spot, altogether very much reminiscent of the Ennomini's pattern. At least some Azelinini lack the sensillae at the end of the adults' antennae found in most geometer moths. The foreleg tarsi are relatively short, as in many of their relatives.
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Sir Christopher Wren PRS FRS (; – ) was one of the most highly acclaimed English architects in history, as well as an anatomist, astronomer, geometer, and mathematician-physicist. He was accorded responsibility for rebuilding 52 churches in the City of London after the Great Fire in 1666, including what is regarded as his masterpiece, St Paul's Cathedral, on Ludgate Hill, completed in 1710. The principal creative responsibility for a number of the churches is now more commonly attributed to others in his office, especially Nicholas Hawksmoor. Other notable buildings by Wren include the Royal Hospital Chelsea, Royal Naval College, Greenwich, and the south front of Hampton Court Palace.
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Others are plants such as dead-nettles, white butterbur, bitter-cress, wall barley, yellow and blue anemone and the endangered multicolored viola. In addition a total of nine species of orchids have been registered although in later years only six has been noted - these are the broad-leaved helleborine, green-flowered helleborine, early-purple orchid, western marsh orchid, early marsh-orchid, eggleaf twayblade and the greater butterfly-orchid. The border zone between Tåstrup Bog and Lillering Forest contains woodland geranium and mountain melick. The area contains several rare species of geometer moths associated with buckthorns that grow at the woodland edge or in Tåstrup Bog.
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Even though he was mentored by Democritus, Protagoras did not share his enthusiasm for the pursuit of mathematics. "For perceptible lines are not the kind of things the geometer talks about, since no perceptible thing is straight or curved in that way, nor is a circle tangent to a ruler at a point, but the way Protagoras used to say in refuting the geometers" (Aristotle, Metaphysics 997b34-998a4). Protagoras was skeptical about the application of theoretical mathematics to the natural world; he did not believe they were really worth studying at all. According to Philodemus, Protagoras said that "The subject matter is unknowable and the terminology distasteful".
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Miljanić was born in 1930 in Bitola, a town his geometer father Akim Miljanić had found employment in and moved the family to two years earlier in 1928. Previously, in 1922, Akim had come to Belgrade from Montenegro's Banjani area in order to study at the newly opened Geodesy School. The family also consisted of mother Zorka and sisters Mira and Nada. In 1941, with Nazi Germany invading, conquering, and dismembering Kingdom of Yugoslavia into territories administered by newly-established local collaborationist regimes or neighbouring Axis powers states, the Miljanićs were forced into fleeing Bitola by the occupying Bulgarian force that had been given Vardar Banovina.
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By 1854, Bernhard Riemann, a student of Gauss, had applied methods of calculus in a ground- breaking study of the intrinsic (self-contained) geometry of all smooth surfaces, and thereby found a different non-Euclidean geometry. This work of Riemann later became fundamental for Einstein's theory of relativity. William Blake's "Newton" is a demonstration of his opposition to the 'single-vision' of scientific materialism; here, Isaac Newton is shown as 'divine geometer' (1795) It remained to be proved mathematically that the non-Euclidean geometry was just as self-consistent as Euclidean geometry, and this was first accomplished by Beltrami in 1868. With this, non-Euclidean geometry was established on an equal mathematical footing with Euclidean geometry.
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All the work related to the Parallel Postulate revealed that it was quite difficult for a geometer to separate his logical reasoning from his intuitive understanding of physical space, and, moreover, revealed the critical importance of doing so. Careful examination had uncovered some logical inadequacies in Euclid's reasoning, and some unstated geometric principles to which Euclid sometimes appealed. This critique paralleled the crisis occurring in calculus and analysis regarding the meaning of infinite processes such as convergence and continuity. In geometry, there was a clear need for a new set of axioms, which would be complete, and which in no way relied on pictures we draw or on our intuition of space.
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The "horn" between the antenna sockets which is present in many geometer moths is usually exceptionally well developed in the Nacophorini. Some have a crest of thorns on their thorax, and a few have a spine at the tip of their foreleg tibia. The hindleg tibia is usually swollen in males, which also often have a "penciltip" of hairs tucked into a groove. Together with a comb of setae on the third abdominal segment, these structures probably serve to distribute pheromones, and while the abdominal comb is found in many Ennominae, the full set of structures is rarely found outside of the Nacophorini, which usually possess at least a swollen tibia or tibial "pencil", and often both.
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Wnile the female genitalia are rather nondescript, there are a number of features of the male genitalia that are usually not exclusive to Nacophorini, but in combination are quite characteristic. Like in most Boarmiini, the valval costa typically has a batch of bristles on its underside near the tip, whereas the harpe or "clasper" of Nacophorini lacks the complex modifications found in Boarmiini. The aedagus has a pointed tip in almost all members of this tribe, displaying little of the variation found in related geometer moths. The anellus usually has extensions at the side, which extend from the edge of the juxta and can be lobes or spines, small or large, covered in bristles or nude.
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Tensor calculus has many applications in physics, engineering and computer science including elasticity, continuum mechanics, electromagnetism (see mathematical descriptions of the electromagnetic field), general relativity (see mathematics of general relativity), quantum field theory, and machine learning. Working with a main proponent of the exterior calculus Elie Cartan, the influential geometer Shiing-Shen Chern summarizes the role of tensor calculus: > In our subject of differential geometry, where you talk about manifolds, one > difficulty is that the geometry is described by coordinates, but the > coordinates do not have meaning. They are allowed to undergo transformation. > And in order to handle this kind of situation, an important tool is the so- > called tensor analysis, or Ricci calculus, which was new to mathematicians.
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The diet consists of insects and other small arthropods. One study of red-capped robin faeces conducted near Kambalda, Western Australia, revealed 96% of their diet was made up of beetles, while ants made up the remainder. Other prey recorded include spiders, and insects such as grasshoppers, including the Australian plague locust (Chortoicetes terminifera), adult and larval butterflies and moths, including geometer moths, dragonflies and damselflies, mantises, antlions, true bugs, including chinch bugs of the family Lygaeidae and shield bugs, various types of beetles, earwigs, and flies such as blow-flies and horse-flies. The red-capped robin mostly pounces on prey on the ground, although it can swoop and catch creatures while airborne.
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He then built off Napoleon by proving that if an equilateral triangle was constructed with equilateral triangles incident on each vertex, the midpoints of the connecting lines between the non-incident vertices of the outer three equilateral triangles create an equilateral triangle. Other similar work was done by the French Geometer Thébault in his proof that given a parallelogram and squares that lie on each side of the parallelogram, the centers of the squares create a square. Mauldon then analyzed coplanar sets of triangles, determining if they were similarity systems based on the criterion, if all but one of the triangles were directly similar, then all of the triangles are directly similar.
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Similarly, the structures of parabolic arches are purely in compression. Paraboloids arise in several physical situations as well. The best-known instance is the parabolic reflector, which is a mirror or similar reflective device that concentrates light or other forms of electromagnetic radiation to a common focal point, or conversely, collimates light from a point source at the focus into a parallel beam. The principle of the parabolic reflector may have been discovered in the 3rd century BC by the geometer Archimedes, who, according to a dubious legend, constructed parabolic mirrors to defend Syracuse against the Roman fleet, by concentrating the sun's rays to set fire to the decks of the Roman ships.
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In 1954, she joined the first cohort of mathematics students in the Faculty of Philosophy in Novi Sad, now part of the University of Novi Sad. She finished her studies there in 1958 and became a high school mathematics teacher in Zrenjanin. She returned to Novi Sad (newly founded as a university) in 1960, as an assistant to geometer Mileva Prvanović and in the same year was responsible for the university's first mathematics publication, of her lecture notes on straightedge and compass constructions. She traveled to Rome in 1961 to work with Lucio Lombardo-Radice then, returning to Novi Sad in 1963, defended her Ph.D., the first mathematical doctorate at Novi Sad.
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Diagram of Gossard perspector Harry Clinton Gossard (1884–1954) was an American educator and geometer. He is credited with the discovery of a then unknown triangle center in 1916 to which John Conway assigned the name Gossard perspector in 1998. After receiving his Ph.D. from Johns Hopkins University in 1912, Gossard taught at University of Oklahoma (1912–1916), the U. S. Naval Academy (1916–18), University of Oklahoma (1918–19), University of Wyoming (1921–25), and Nebraska Wesleyan University (1926–31). During the period 1931 to 1939, Gossard was president of New Mexico Normal University (now Highlands University), and during 1939 to 1950, he was dean of Eastern New Mexico College (now Eastern New Mexico University).
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Newton, by William Blake; here, Newton is depicted critically as a "divine geometer". This copy of the work is currently held by the Tate Collection. Newton and Robert Boyle's approach to the mechanical philosophy was promoted by rationalist pamphleteers as a viable alternative to the pantheists and enthusiasts, and was accepted hesitantly by orthodox preachers as well as dissident preachers like the latitudinarians. The clarity and simplicity of science was seen as a way to combat the emotional and metaphysical superlatives of both superstitious enthusiasm and the threat of atheism, and at the same time, the second wave of English deists used Newton's discoveries to demonstrate the possibility of a "Natural Religion".
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There are several different vineyard owners in Romanée-Saint-Vivant today, although Domaine de la Romanée-Conti is the largest. The entire vineyard of Romanée Saint-Vivant was bought in 1791 by Nicolas-Joseph Marey, son-in-law of the geometer Gaspard Monge, when it was up for sale after the French Revolution after much land had been sequestered. After keeping it as a monopole for over 100 years, the Marey-Monge family sold off the southwestern part of the vineyard (lieu-dit Le Clos des Quatre Journeaux) to the Latour family in 1898, which in turn later resold around half of it. At a later stage, another portion in the northern part of the vineyard was sold to Charles Noellat.
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Tunstall Pedoe was the son of the academic mathematician and geometer, Daniel Pedoe, and Mary Tunstall. His twin brother, Hugh, was also a cardiologist, but who worked in teaching. The brothers and their elder sister, Naomi, were born when their father was an assistant lecturer at Southampton University. For much of the children's childhood, their father worked abroad, in Khartoum and Singapore, although the family spent Christmasses together. The twins were educated at Haberdashers’ Aske’s School, at the time located in Hampstead, and Dulwich College. They attended King’s College, Cambridge, together. Dan studied at St Bartholomew’s Hospital in London and earned a PhD at Wolfson College, Oxford, studying the measurement of blood flow in the heart. He also spent a year in post-graduate study in California.
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Ludwig Burmester Ludwig Ernst Hans Burmester (5 May 1840 – 20 April 1927) was a German kinematician and geometer. His doctoral thesis Über die Elemente einer Theorie der Isophoten (About the elements of a theory of isophotes) concerned lines on a surface defined by light direction. After a period as a teacher in Łódź he became professor of synthetic geometry at Dresden where his growing interest in kinematics culminated in his Lehrbuch der Kinematik, Erster Band, Die ebene BewegungL. Burmester, Lehrbuch der Kinematik, Felix Verlag, Liepzig, 1888 (Textbook of Kinematics, First Volume, Planar Motion) of 1888, developing the approach to the theory of linkages introduced by Franz Reuleaux, whereby a planar mechanism was understood as a collection of Euclidean planes in relative motion with one degree of freedom.
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French mathematician Alain Connes has been working for a number of years to reconcile general relativity with quantum mechanics using noncommutative geometry. Fractality also arises in this approach to quantum gravity. An article by Alexander Hellemans in the August 2006 issue of Scientific AmericanHellemans, Alexander -- The Geometer of Particle Physics -- Scientific American - August, 2006 quotes Connes as saying that the next important step toward this goal is to "try to understand how space with fractional dimensions couples with gravitation." The work of Connes with physicist Carlo Rovelli suggests that time is an emergent property or arises naturally, in this formulation, whereas in causal dynamical triangulation, choosing those configurations where adjacent building blocks share the same direction in time is an essential part of the 'recipe.
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Aged 22, John von Collas was a member of the Royal Society and started a journey to Asia. Initially on his way through he arrived in Königsberg in autumn 1701 and decided to stay in East Prussia. He became a Royal Prussian Engineer, counsellor, director of the Geometer and respected scholar. He was mentioned as a member of the Prussian Academy of Sciences in 1704. Dönhoffstädt Palace Finckenstein Palace Collas became the landlord of several estates in East Prussia like Dommelkeim (1703–1753), Naujeninken (1703–1731), Brandwehten (1703–1731), Perkuhnen (1717–1731), Sauerwalde (1720–1731), Laugallen (1718–1731), Kraupischkehmen, (1718–1731), Weißenstein/ Gutenfeld (1721–1753) and owned houses in Wehlau (1721–1753) and Borchersdorf (1724–1753), in total he possessed about 2,720 Hectare.
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The geometer Shiing-Shen Chern was one of the leaders in differential geometry of the 20th century and was awarded the 1984 Wolf Prize in mathematics. The physicist Chien-Shiung Wu, nicknamed the "First Lady of Physics" contributed to the Manhattan Project and radically altered modern physical theory and changed the accepted view of the structure of the universe. The biochemist Chi-Huey Wong is well known for his pioneering research in glycoscience research and developing the first enzymatic method for the large-scale synthesis of oligosaccharides and the first programmable automated synthesis of oligosaccharides. The physical chemist Ching W. Tang, was the inventor of the organic light-emitting diode (OLED) and hetero-junction organic photovoltaic cell (OPV) and is widely considered the "Father of Organic Electronics".
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Jacques Alexandre César Charles (November 12, 1746 – April 7, 1823) was a French inventor, scientist, mathematician, and balloonist. Charles wrote almost nothing about mathematics, and most of what has been credited to him was due to mistaking him with another Jacques Charles, also a member of the Paris Academy of Sciences, entering on May 12, 1785. He was sometimes called Charles the Geometer. (See J. B. Gough, Charles the Obscure, Isis 70, #254, pgs 576-579) Charles and the Robert brothers launched the world's first unmanned hydrogen-filled gas balloon in August 1783; then in December 1783, Charles and his co-pilot Nicolas-Louis Robert ascended to a height of about 1,800 feet (550 m) in a manned gas balloon.
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The argument was that scientific pursuits were a type of "good work" and therefore a sign of election. "This-worldly asceticism which inspired Puritans to greater economic activity also motivated them to diligent and painstaking scientific enquiry." In 1975, Charles Webster builds on the argument in The Great Instauration: Science, Medicine and Reform, 1626-1660, claiming that the prevailing factor in English society in the mid-1600s was Puritanism and its relationship with the growth of the English scientific movement was extremely close. A longing to discern the universe's composition and reveal the force of the "Great Geometer" provided a sense of wonder at the universe's immensity and intricacy. Exploring "God’s great mechanism" was the perfect "good work" for the Puritan.
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After the First Partition of Poland, Kingdom of Prussia seized Poland and Bydgoszcz, drawing up an exact inventory of the city. On a detailed map realized by geometer Greth in 1774, properties on the Market Square are, by and large, the same as those currently standing, apart from a few plots not built at the time, at the corners with Teofil Magdziński street and with Farna Street. In the last quarter of the 18th century, there was no more parcels left: on the corner with John II Casimir street was constructed a large building, dedicated to host the Netze District authorities and the Court of Appeal. The entire western frontage, formerly owned by the Jesuits, was taken over by the Prussian state.
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Three of the quadrants include negative coordinates meaning directions opposite the reference axes of zero. Apollonius has no negative numbers, does not explicitly have a number for zero, and does not develop the coordinate system independently of the conic sections. He works essentially only in Quadrant 1, all positive coordinates. Carl Boyer, a modern historian of mathematics, therefore says: > ”However, Greek geometric algebra did not provide for negative magnitudes; > moreover, the coordinate system was in every case superimposed a posteriori > upon a given curve in order to study its properties .... Apollonius, the > greatest geometer of antiquity, failed to develop analytic geometry....’’ No one denies, however, that Apollonius occupies some sort of intermediate niche between the grid system of conventional measurement and the fully developed Cartesian Coordinate System of Analytic Geometry.
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Oronce Finé, Quadratura circuli, 1544 J. P. de Faurè, Dissertation, découverte, et demonstrations de la quadrature mathematique du cercle, 1747 The problem of squaring the circle has been mentioned by poets such as Dante and Alexander Pope, with varied metaphorical meanings. Its literary use dates back at least to 414 BC, when the play The Birds by Aristophanes was first performed. In it, the character Meton of Athens mentions squaring the circle, possibly to indicate the paradoxical nature of his utopian city. Dante's Paradise canto XXXIII lines 133–135 contain the verses: As the geometer his mind applies To square the circle, nor for all his wit Finds the right formula, howe'er he tries For Dante, squaring the circle represents a task beyond human comprehension, which he compares to his own inability to comprehend Paradise.
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It shows that by 1640 he was familiar with the 'New Algebra' of François Viète. In this book he provides a critique of the solutions given by the geometer Marino Ghetaldi of Ragusa in his De Resolutione et Compositione Matematica to the problems posed by Apollonius of Perga.Ronald Calinger : Vita mathematica: historical research and integration with teaching His published mathematical work is summarised in a treatise of nineteen pages, Exercitatio geometrica, de maximis et minimis (1666) in which he studies the maxima of functions of the form x^m(a - x)^n and tangents to curves with equation y^m = kx^n, using methods that are an early form of induction. This treatise was much admired by his contemporaries and has recently been republished as an appendix to Mercator's 'Logarithmo-Technia' (1688).
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Later he worked as a professor at the University of Königsberg (außerordentlicher Professor from 1895 to 1897), the University of Kiel (ordentlicher Professor, 1897 to 1905), University of Hannover (1905 to 1908), the Karlsruhe Institute of Technology (1908 to 1913), and the University of Heidelberg (1913 to 1919). Stäckel worked on both mathematics and the history of mathematics. He edited the letters exchanged between Carl Friedrich Gauss and Wolfgang Bolyai, made contributions to editions of the collected works of Euler and Gauss (for whose works he wrote Gauss als Geometer), and edited the Geometrischen Untersuchungen by Wolfgang and Johann Bolyai (published in 1913). Additionally he translated works of Jacob Bernoulli, Johann Bernoulli, Augustin Louis Cauchy, Leonhard Euler, Joseph-Louis Lagrange, Adrien-Marie Legendre, Carl Gustav Jacobi from French and Latin into German for the series Ostwalds Klassiker der exakten Wissenschaften.
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Text from a manuscript of his Trattato d'Abbaco in Paolo's own handwriting Paolo Dagomari da Prato (1282-1374), known in Latin as Paulus Geometrus (Paolo il Geometra, "Paul the Geometer"), was a noted Florentine mathematician and astronomer, such a maestro dell'abbaco (master/teacher of the abacus) that he gained the epithet Paolo dell'Abbaco. Franco Sacchetti called him Paolo Arismetra e Astrologo (arithmetician and astronomer) and Giorgio Vasari Paulo Strolago or Paolo Astrologo (astronomer). He reputedly had 6,000-10,000 pupils over the course of his life, being praised by contemporaries like Giovanni Gherardi da Prato,Il Dagomari a moltissimi, anzi a infiniti nella nostra Firenze fu in aritmetica diligentissimo maestro, rinovellatore di buone e utilissime regole, e principiò a scorgere la nostra città alle utili e leggiadre regole dell'algoritmo inaudito e morto per moltissimi secoli (Paradiso degli Alberti, Vol. II, p.
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Given the many prehistoric archaeological finds in the broader Nerzweiler area, it can be assumed that the area right around what is now Nerzweiler was likewise inhabited by people during the Bronze Age and the Iron Age, and perhaps even as early as the New Stone Age. There were people here during Roman times, too. In state scrivener and geometer Johannes Hofmann's 1595 description of the Eßweiler Tal, he wrote: “Likewise one also finds a walled sign near Hintzweiler and Nerzweiler in the fields down below at the Gutleuthaus (literally “good people’s house”, but actually a house for lepers) on the road. There, too, such stones, coins and quite solid pieces of limestone, like one fashioned into a table, have been found in the earth.” Obviously, he was writing about finds from Roman times, such as many that were found throughout the dale.
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17, Edinburgh, Edinburgh University, 1995 In Annals of the Four Masters and Annals of Ulster, he is referenced as the Abbot of Aghaboe, in County Laois, where he was known as "the Geometer" because of his knowledge of geography. Around 745, he left Ireland, intending to visit the Holy Land; but, like many of his countrymen, who seemed to have adopted this practice as a work of piety, he settled down in France, where he was received with great favour by Pippin the Younger, who was then Mayor of the Palace under Childeric III of Franconia. He was an adviser to Pippin. He probably used a copy of the "Collectio canonum Hibernensis" (an Irish collection of canon law) to advise him to receive royal unction in 751, to assist his recognition as king Pippin III after the deposition of Childeric.
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Archimedes lived in the 3rd century BC and wrote his proofs as letters in Doric Greek addressed to contemporaries, including scholars at the Great Library of Alexandria. These letters were first compiled into a comprehensive text by Isidorus of Miletus, the architect of the Hagia Sophia patriarchal church, sometime around 530 AD in the then Byzantine Greek capital city of Constantinople. A copy of Isidorus' edition of Archimedes was made around 950 AD by an anonymous scribe, again in the Byzantine Empire, in a period during which the study of Archimedes flourished in Constantinople in a school founded by the mathematician, engineer, and former Greek Orthodox archbishop of Thessaloniki, Leo the Geometer, a cousin to the patriarch. This medieval Byzantine manuscript then traveled from Constantinople to Jerusalem, likely sometime after the Crusader sack of Byzantine Constantinople in 1204.
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While attending a geometry workshop in 1997, she saw fragile paper models of hyperbolic planes, designed by geometer William Thurston. She decided to make more durable models, and did so by crocheting them. Due to her success in this she was invited, together with her husband David Henderson, a math professor also at Cornell, to give a presentation at a Cornell workshop.. Crocheted mathematical models later appeared in three geometry textbooks they wrote together, of which the most popular is Experiencing Geometry: Euclidean and non-Euclidean with History. An article about Taimiņa's innovation in New Scientist was spotted by the Institute For Figuring, a small non-profit organisation based in Los Angeles, and she was invited to speak about hyperbolic space and its connections with nature to a general audience which included artists and movie producers.
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During this service, he is pestered by a variety of unwelcome visitors including a young versifier out to hire himself to the new city as its official poet, an oracle-monger with prophecies for sale, a famous geometer, Meton, offering a set of town-plans, an imperial inspector from Athens with an eye for a quick profit, and a statute-seller trying to peddle a set of laws originally written for a remote, barely-heard-of town called Olophyx. Pisthetaerus chases off all these intruders and then retires indoors to finish the religious service. The birds of the Chorus step forward for another parabasis. They promulgate laws forbidding crimes against their kind (such as catching, caging, stuffing, or eating them) and they end by advising the festival judges to award them first place or risk getting defecated on.
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Before the ship could come to any further harm, Brewster was helped by an elderly Adric (who was unintentionally saved from his apparent death in Earthshock by Block Transfer Computations subconsciously sent to him by the Doctor while trying to recover the stolen TARDIS, that caused Adric to be sent into a pocket dimension based on an Aztec jungle), who got him back to London a few months after his departure. Afterwards, the Doctor invited him to join him on his travels. Soon after he joined, they returned to the location of one of his previous travels, where it was revealed that Brewster had sold several vital components of the TARDIS to the marooned crew of the Gamma. Among the components Brewster sold was the TARDIS' conceptual geometer, the removal of which greatly destabilised the structure of the TARDIS and eventually caused the collapse of the ship's internal dimensions.
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Adding further to the uncertainty is the fact that the Alsophilinae, usually treated as a small subfamily in their own right, might be a specialized lineage of Boarmiini; though their caterpillars are quite different, their pupae have a peculiar T-shaped cremaster which very much resembles that of the Boarmiini.Holloway (1994), Young (2008) Boarmiini in the narrow sense are typically slender geometer moths that rest with the wings spread out flatly and do not tuck the hindwings under the forewings while at rest. Typically, they are cryptically colored and rather dark, with brownish-grey hues predominating; in many, there are two or three weak wavy bands extending across the wings and forming a rough semicircle when the moths are at rest. Though they all look quite similar in habitus, there are few unequivocal characters that can be easily used to recognize adult members of this tribe.
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The Manuscript Found in Saragossa collects intertwining stories, all of them set in whole or in part in Spain, with a large and colorful cast of Romani, thieves, inquisitors, a cabbalist, a geometer, the cabbalist's beautiful sister, two Moorish princesses (Emina and Zubeida) and others that the brave, perhaps foolhardy, Walloon Guard Alphonse van Worden meets, imagines or reads about in the Sierra Morena mountains of 18th-century Spain while en route to Madrid. Recounted to the narrator over the course of sixty- six days, the novel's stories quickly overshadow van Worden's frame story. The bulk of the stories revolve around the Gypsy chief Avadoro, whose story becomes a frame story itself. Eventually the narrative focus moves again toward van Worden's frame story and a conspiracy involving an underground — or perhaps entirely hallucinated — Muslim society, revealing the connections and correspondences between the hundred or so stories told over the novel's sixty- six days.
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While Oenopides's innovations as an astronomer mainly concern practical issues, as a geometer he seems to have been rather a theorist and methodologist, who set himself the task to make geometry comply with higher standards of theoretical purity. Thus he introduced the distinction between 'theorems' and 'problems': though both are involved with the solution of an exercise, a theorem is meant to be a theoretical building block to be used as the fundament of further theory, while a problem is only an isolated exercise without further follow-up or importance. Oenopides apparently also was the author of the rule that geometrical constructions should use no other means than compass and straightedge. In this context his name adheres to two specific elementary constructions of plane geometry: first, to draw from a given point a straight line perpendicular to a given straight line; and second, on a given straight line and at a given point on it, to construct a rectilineal angle equal to a given rectilineal angle.
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The Piero della Francesca Trail is an excursion which traces the works created by Piero della Francesca in Arezzo, Monterchi, San Sepolcro (his birthplace) and Urbino. To his contemporaries, Piero was admired as a mathematician and geometer as well as a painter, and today his paintings are celebrated for their serene humanism and use of geometric forms. Summer's Lease has made famous the Piero Della Francesca Trail, which sees Molly set out from the Chianti District near Siena and travel to view the following paintings of Piero Della Francesca: #The Legend of the True Cross, Basilica di San Francesco d'Assisi, Arezzo #The Pregnant Madonna, Museo della Madonna del Parto, Monterchi #The Resurrection, Museo Civico, San Sepolcro #The Flagellation, Galleria Nazionale delle Marche, Palazzo Ducale, Urbino Molly and her elusive landlord Buck Kettering share a love of the art work of Piero Della Francesca. The Piero Della Francesca Trail ultimately leads Molly to Buck, who for reasons of his own does not want to be found.
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Immediately after finishing his studies at the École Polytechnique, he was appointed répétiteur (teaching assistant) there, a position which he had occupied as an amateur while still a pupil in the school; for his schoolmates had made a custom of visiting him in his room after an unusually difficult lecture to hear him repeat and explain it. He was made deputy professor (professeur suppléant) in 1802, and, in 1806 full professor succeeding Jean Baptiste Joseph Fourier, whom Napoleon had sent to Grenoble. In 1808 he became astronomer to the Bureau des Longitudes; and when the was instituted in 1809 he was appointed a professor of rational mechanics (professeur de mécanique rationelle). He went on to become a member of the Institute in 1812, examiner at the military school (École Militaire) at Saint-Cyr in 1815, graduation examiner at the École Polytechnique in 1816, councillor of the university in 1820, and geometer to the Bureau des Longitudes succeeding Pierre-Simon Laplace in 1827. In 1817, he married Nancy de Bardi and with her, he had four children.
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Mosaic of the Last Judgment at the Golden Gate (annotated) While Matthias of Arras was schooled as a geometer, thus putting an emphasis on rigid systems of proportions and clear, mathematical compositions in his design, Parler was trained as a sculptor and woodcarver. He treated architecture as a sculpture, almost as if playing with structural forms in stone. Aside from his bold vaults, the peculiarities of his work can also be seen in the design of pillars (with classic, bell-shaped columns which were almost forgotten by High Gothic), the ingenious dome vault of new St Wenceslaus chapel, the undulating clerestory walls, the original window tracery (no two of his windows are the same, the ornamentation is always different) and the blind tracery panels of the buttresses. Architectural sculpture was given a considerable role while Parler was in charge of construction, as can be seen in the corbels, the passageway lintels, and, particularly, in the busts on the triforium, which depict faces of the royal family, saints, Prague bishops, and the two master builders, including Parler himself.
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The origin of the class of such problems has been attributed to the Indian mathematician Mahāvīra in chapter VI, §131, 132 of his Ganita-sara-sangraha (“Compendium of the Essence of Mathematics”), circa 850CE, which dealt with serial division of fruit and flowers with specified remainders.CHRONOLOGY OF RECREATIONAL MATHEMATICS by David Singmaster That would make progenitor problems over 1000 years old before their resurgence in the modern era. Problems involving division which invoke the Chinese remainder theorem appeared in Chinese literature as early as the first century CE. Sun Tzu asked: Find a number which leaves the remainders 2,3,2 when divided by 3,5,7 respectively. Diophantus of Alexandria first studied problems requiring integer solutions in the 3rd century CE. The Euclidean algorithm for greatest common divisor which underlies the solution of such problems was discovered by the Greek geometer Euclid and published in his Elements in 300CE. Singmaster traces a series of less plausibly related problems through the middle ages, with a few references as far back as the Babylonian empire circa 1700BC.
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A typical page from the Archimedes Palimpsest. The text of the prayer book is seen from top to bottom, the original Archimedes manuscript is seen as fainter text below it running from left to right Discovery reported in the New York Times on July 16, 1907 The Archimedes Palimpsest is a parchment codex palimpsest, originally a Byzantine Greek copy of a compilation of Archimedes and other authors, containing two unknown works of Archimedes (the "Stomachion" and the "Method of Mechanical Theorems") and the only surviving original Greek edition of his work "On Floating Bodies." The first version of the compilation is believed to have been produced by Isidorus of Miletus, the architect of the geometrically complex Hagia Sophia cathedral in Constantinople, sometime around 530 AD. The copy found in the palimpsest was created from this original, also in Constantinople, during the Macedonian Renaissance (c. 950 AD), a time when math in the capital was being revived by the former Greek Orthodox bishop of Thessaloniki Leo the Geometer, a cousin of the Patriarch.
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In 1547, the Zweibrücker Oberamtsbannbuch mentioned the ditch in the southwest of Dittweiler's municipal area, a fortification that by that time had fallen into disrepair. In 1556, Prince-Elector Ottheinrich introduced the Reformation for all his subjects. This was, of course, obligatory. Dittweiler then appeared in the 1564 description of the Oberamt of Zweibrücken by the geometer Tilemann Stella, which described, among other things, a boundary stone with a cross on it that marked the limit between Duntzweiller and Ditweiller (a transcription and translation of this section of the book is to be found at the Dunzweiler article). In 1600, Master Forester Philipp Vellmann toured the villages in the Amt of Kübelberg on Prince-Elector Friedrich IV's behalf, and on the tour described Dittweiler's environs with its dales, woods and ponds, also meanwhile noting the mill, which was now called “Arnold Mühl”. In a 1610 description in the Altenkirchen parish “competence book”, it says that Dittweiler did indeed belong to Electoral Palatinate, but that the tithe was owed to the Zweibrücken monastery of Wörschweiler, and thereby to Count Palatine Johannes of Zweibrücken, and that one third of this tithe was to go to the likewise Zweibrücken-held Church of Ohmbach.
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