690 Sentences With "equilateral" | Random Sentence Generator

Let's just say the three pointed shape is definitely not equilateral.

The dominant feature on the chart was the equilateral triangle pattern.

Starting January 2015 the dollar index developed an equilateral or symmetrical triangle.

Our examples above use equilateral triangles (regular triangles), squares (regular quadrilaterals) and regular hexagons.

For the equilateral-triangle tiling, we see six triangles coming together at each vertex.

Its detectors will be arranged in an equilateral triangle with sides 2.5m kilometres long.

However, the key message of the potential equilateral triangle pattern is one of indecision.

That's because the hexagon contains six equilateral triangles, each side of which equals the circle's radius.

An equilateral triangle has equal degrees of slope on both the upper and lower trend lines.

The ropes from which they hang form an equilateral triangle, sustained by the force in Foulkes' arms.

Even in the 1700s, there'd been some specific solutions found—like Euler's collinear configuration, and Lagrange's equilateral triangle.

With a bit of imagination, it's possible to plot an equilateral triangle pattern on the Australian market index.

"Down" quarks and all other quarks also come in these symmetric triplets, which are like sides of an equilateral triangle.

USA's equilateral funding encompasses a large swath of this country's arts that too often are left out of the conversation.

Using the equilateral triangle, an upside break has target near 5,960 and a downside break has a target near 5,560.

And connecting Alejandro Puente's "Untitled" (1967) — four equilateral triangles — compose a larger triangle, all in primary colors — with Kelly's "Blue Panel" (1977) was suggestive.

They projected this archipelago onto an icosahedron consisting of 20 equilateral triangles that could be rearranged to visualize geospatial information like air and sea routes.

With a planned launch date of 2034, eLISA would send three different spacecraft into orbit around the Sun, where they would form an equilateral triangle.

They're really all orbiting the sun, "with their orbits cleverly arranged so that they approximately form an equilateral triangle at all times," Boyle told Gizmodo.

According to the ancient Roman scholar and writer Marcus Terentius Varro, a structure made of hexagons is more compact than one made from squares or equilateral triangles.

For the other 2016 show, at the artist-run 4th Ward Project Space, I made a large equilateral triangle — the mountain — which extended from the floor to the ceiling.

This works out perfectly: The measure of each internal angle of an equilateral triangle is 60 degrees, and 6 × 60 = 360, which is exactly what we need around a single point.

The new metropolis would consist of a giant tetrahedron—a pyramid made of equilateral triangles—a shape that Fuller, the popularizer of the geodesic dome, admired for its stability and symmetry.

Unlike hexagons, however, regular pentagons cannot be built from equilateral triangles, nor can they tessellate a plane: When slid next to each other to tile a surface, gaps and overlaps inevitably arise.

Europe is offering the Einstein Telescope, a proposed interferometer with three arms arranged in an equilateral triangle buried underground and cooled to within ten degrees of absolute zero, to improve its sensitivity.

The monitors and your head have to be at the same height and form an equilateral triangle, so turn the speakers towards your ears to hear the sound as directly as possible.

LB: I used a circular shape that came from an Ellsworth Kelly, a plant-form shape that came from a Léger still life, an arch that came from a Georgia O'Keeffe, and an equilateral triangle.

Magna-Tiles, Clear Colors 100-Piece Set, available at Amazon, $119.95Magna-Tiles come in various sizes, colors, and shapes, like large and small squares (54 total pieces) and right, equilateral, isosceles triangles (46 total pieces).

RJH: In foreign and defense policy, Duterte is expected to adopt an equilateral balancing strategy, similar to the Ramos and Arroyo administrations, reaching out to both China and America without siding with any against the other.

What he came up with entailed three bright, inverted equilateral triangles joined at the center on a round black background, with shelter capacity circled near the base, followed by the words "Fallout Shelter" in large block capitals and directional arrows .

In 20183, at Benítez's sister's mission-style ranch home in Isla de Francia, a wealthy suburb of Asunción, the architects brought broken bricks from Benítez's nephew's foundry and embedded them in concrete, like a poor man's terrazzo, to form a pergola of interlocking equilateral triangles that resembles the lattice arch at the Teletón center flattened out and lifted seven feet off the ground.

Equilateral triangles are found in many other geometric constructs. The intersection of circles whose centers are a radius width apart is a pair of equilateral arches, each of which can be inscribed with an equilateral triangle. They form faces of regular and uniform polyhedra. Three of the five Platonic solids are composed of equilateral triangles.

Equilateral triangles on the sides of an arbitrary hexagon If an equilateral triangle is constructed externally on each side of any hexagon, then the midpoints of the segments connecting the centroids of opposite triangles form another equilateral triangle.

Equilateral dimension has also been considered for normed vector spaces with norms other than the Lp norms. The problem of determining the equilateral dimension for a given norm is closely related to the kissing number problem: the kissing number in a normed space is the maximum number of disjoint translates of a unit ball that can all touch a single central ball, whereas the equilateral dimension is the maximum number of disjoint translates that can all touch each other. For a normed vector space of dimension d, the equilateral dimension is at most 2d; that is, the L∞ norm has the highest equilateral dimension among all normed spaces.. asked whether every normed vector space of dimension d has equilateral dimension at least , but this remains unknown. There exist normed spaces in any dimension for which certain sets of four equilateral points cannot be extended to any larger equilateral set but these spaces may have larger equilateral sets that do not include these four points.

All regular polygons and isotoxal polygons are equilateral. An equilateral triangle is a regular triangle with 60° internal angles. :100px An equilateral quadrilateral is called a rhombus, an isotoxal polygon described by an angle α. It includes the square as a special case.

Venus Equilateral, Inc. is licensed by the Interplanetary Communications Commission to maintain interplanetary communications. Under the terms of the license, Venus Equilateral must relay at least one message every twenty-four hours. Venus Equilateral, Inc. also owns and operates an interplanetary spaceship called the Relay Girl that is based at the station.

In mathematics, the equilateral dimension of a metric space is the maximum number of points that are all at equal distances from each other. Equilateral dimension has also been called "metric dimension", but the term "metric dimension" also has many other inequivalent usages. The equilateral dimension of a d-dimensional Euclidean space is , and the equilateral dimension of a d-dimensional vector space with the Chebyshev distance (L∞ norm) is 2d. However, the equilateral dimension of a space with the Manhattan distance (L1 norm) is not known; Kusner's conjecture, named after Robert B. Kusner, states that it is exactly 2d.

Thus if the number of sides n is odd, a tangential polygon is equilateral if and only if it is regular.. Viviani's theorem generalizes to equilateral polygons:. The sum of the perpendicular distances from an interior point to the sides of an equilateral polygon is independent of the location of the interior point. The principal diagonals of a hexagon each divide the hexagon into quadrilaterals. In any convex equilateral hexagon with common side a, there existsInequalities proposed in “Crux Mathematicorum”, .

In particular, the regular tetrahedron has four equilateral triangles for faces and can be considered the three- dimensional analogue of the shape. The plane can be tiled using equilateral triangles giving the triangular tiling.

It is not usually considered a triambus, although it is equilateral.

So, like a circle, an equilateral triangle has a unique center.

Napoleon's theorem: If the triangles centered on L, M, and N are equilateral, then so is the green triangle. In geometry, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the lines connecting the centres of those equilateral triangles themselves form an equilateral triangle. The triangle thus formed is called the inner or outer Napoleon triangle. The difference in the area of these two triangles equals the area of the original triangle.

The evolution of the Sierpinski triangle The Sierpinski triangle may be constructed from an equilateral triangle by repeated removal of triangular subsets: # Start with an equilateral triangle. # Subdivide it into four smaller congruent equilateral triangles and remove the central triangle. # Repeat step 2 with each of the remaining smaller triangles infinitely. Each removed triangle (a trema) is topologically an open set.

For instance, subdividing an equilateral triangle into four equilateral triangles, removing the middle triangle, and recursing leads to the Sierpiński triangle. In three dimensions, a similar construction based on cubes is known as the Menger sponge.

Pisidium lilljeborgii has a less equilateral shape than Pisidium hibernicum 3-4.5mm.

A1 is formed by the apices of the isosceles triangles with apex angle 2π/3 erected over the sides of the triangle A0. The vertices of A1 are the centers of equilateral triangles erected over the sides of triangle A0. Thus the specialisation of the PDN theorem to a triangle can be formulated as follows: :If equilateral triangles are erected over the sides of any triangle, then the triangle formed by the centers of the three equilateral triangles is equilateral. The last statement is the assertion of the Napoleon's theorem.

A triangle that is itself equilateral has a unique isodynamic point, at its centroid; every non-equilateral triangle has two isodynamic points. Isodynamic points were first studied and named by .For the credit to Neuberg, see e.g. and .

For any d-dimensional Riemannian manifold the equilateral dimension is at least . For a d-dimensional sphere, the equilateral dimension is , the same as for a Euclidean space of one higher dimension into which the sphere can be embedded. At the same time as he posed Kusner's conjecture, Kusner asked whether there exist Riemannian metrics with bounded dimension as a manifold but arbitrarily high equilateral dimension.

There are numerous triangle inequalities that hold with equality if and only if the triangle is equilateral. An equilateral triangle is the most symmetrical triangle, having 3 lines of reflection and rotational symmetry of order 3 about its center.

Equilateral triangle Ptolemy's Theorem yields as a corollary a pretty theoremWilson, Jim. "Ptolemy's Theorem." link verified 2009-04-08 regarding an equilateral triangle inscribed in a circle. Given An equilateral triangle inscribed on a circle and a point on the circle. The distance from the point to the most distant vertex of the triangle is the sum of the distances from the point to the two nearer vertices.

Equilateral pentagon built with four equal circles disposed in a chain. An equilateral pentagon is a polygon with five sides of equal length. However, its five internal angles can take a range of sets of values, thus permitting it to form a family of pentagons. In contrast, the regular pentagon is unique up to similarity, because it is equilateral and it is equiangular (its five angles are equal).

An order-7 triangular tiling has equilateral triangles with 2π/7 radian internal angles.

Cortical shell hexangular, equilateral, five times as broad as the triangular, Triopyle-shaped medullary shell.

Cortical shell hexangular, equilateral, four times as broad as the circular, Triopyle-shaped medullary shell.

The suffix (triangular) -rotunda refers to the complex of three equilateral triangles and three regular pentagons surrounding another equilateral triangle, which bears structural resemblance to the pentagonal rotunda. The triangular hebesphenorotunda is the only Johnson solid with faces of 3, 4, 5 and 6 sides.

Equilateral square pyramids can also be chained together as a helix, with two vertex configurations, 3.4.3.4 and 3.3.4.3.3.4. This helix exists as finite ring of 30 pyramids in a 4-dimensional polytope. :800px And equilateral pentagonal pyramids can be chained with 3 vertex configurations, 3.3.

Venus Equilateral is a collection of science fiction short stories by American writer George O. Smith. The stories belong to Smith's Venus Equilateral series. The collection was first published in 1947 by Prime Press in an edition of 3,000 copies. "Mad Holiday" was written for this collection.

Hence triangle PBP ' is equilateral and \scriptstyle PP'\ =\ PB. Then \scriptstyle PA\ =\ P'C. Thus, triangle PCP ' has sides equal to PA, PB, and PC and the proof by construction is complete (see drawing).Jozsef Sandor: On the Geometry of Equilateral Triangles. Forum Geometricorum, Volume 5 (2005), pp.

It is possible to describe the five angles of any convex equilateral pentagon with only two angles α and β, provided α ≥ β and δ is the smallest of the other angles. Thus the general equilateral pentagon can be regarded as a bivariate function f(α, β) where the rest of the angles can be obtained by using trigonometric relations. The equilateral pentagon described in this manner will be unique up to a rotation in the plane.

A triangle ABC that has the sides a, b, c, semiperimeter s, area T, exradii ra, rb, rc (tangent to a, b, c respectively), and where R and r are the radii of the circumcircle and incircle respectively, is equilateral if and only if any one of the statements in the following nine categories is true. Thus these are properties that are unique to equilateral triangles, and knowing that any one of them is true directly implies that we have an equilateral triangle.

Although today the shape is generally in the form of an equilateral triangle, early instruments were often formed as non-equilateral isosceles triangles. In the early days the triangles did not have an opening and had jingling rings along the lower side. Early examples of triangles include ornamental work at the open end, often in a scroll pattern. Historically, the triangle has been manufactured from a solid iron and later steel rod and bent into a triangular shape roughly equilateral.

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.

Wrote Foreword. # The World in Focus; William MacQuitty, 1974. Wrote Foreword. # The Complete Venus Equilateral; George O. Smith, 1976.

If each vertex angle of the outer triangle is trisected, Morley's trisector theorem states that the purple triangle will be equilateral. In plane geometry, Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the first Morley triangle or simply the Morley triangle. The theorem was discovered in 1899 by Anglo-American mathematician Frank Morley. It has various generalizations; in particular, if all of the trisectors are intersected, one obtains four other equilateral triangles.

The tower was conceived as an equilateral triangular block with landscaped sky gardens at various levels. The architecture was designed by P&T; Group. Its unique design is composed of equilateral triangles and circles.Chinese article on CITIC Tower's unique geometrical appearance CITIC Tower was completed in 1997 under a fast track development programme.

The Gauss-Wantzel theorem showed in 1837 that constructing an equilateral n-gon is impossible for most values of n.

If the triangle is equilateral, the circumcenter and symmedian coincide and therefore the Brocard circle reduces to a single point.

Therefore, the same superlogarithmic dependence on d holds for the lower bound on the equilateral dimension of d-dimensional space.

A rectangle (equiangular quadrilateral) with integer side lengths may be tiled by unit squares, and an equiangular hexagon with integer side lengths may be tiled by unit equilateral triangles. Some but not all equilateral dodecagons may be tiled by a combination of unit squares and equilateral triangles; the rest may be tiled by these two shapes together with rhombi with 30 and 150 degree angles. A cyclic polygon is equiangular if and only if the alternate sides are equal (that is, sides 1, 3, 5, ... are equal and sides 2, 4, ... are equal). Thus if n is odd, a cyclic polygon is equiangular if and only if it is regular.De Villiers, Michael, "Equiangular cyclic and equilateral circumscribed polygons", Mathematical Gazette 95, March 2011, 102-107.

The Venus Equilateral series is a set of 13 science fiction short stories by American writer George O. Smith, concerning the Venus Equilateral Relay Station, an interplanetary communications hub located at the Lagrangian point of the Sun-Venus system. Most of the stories were first published in Astounding Science Fiction between 1942 and 1945.

Smith wrote mainly about outer space, with such works as Operation Interstellar (1950), Lost in Space (1959), and Troubled Star (1957). He is remembered chiefly for his Venus Equilateral series of short stories about a communications station in outer space. Most of the stories were collected in Venus Equilateral (1947), which was later expanded with the remaining three stories as The Complete Venus Equilateral (1976). His novel The Fourth "R" (1959) – re-published as The Brain Machine (1968) – was a digression from his focus on outer space, and an examination of a child prodigy.

In particular, the perimeter of a rectangle of width w and length \ell equals 2w + 2\ell. An equilateral polygon is a polygon which has all sides of the same length (for example, a rhombus is a 4-sided equilateral polygon). To calculate the perimeter of an equilateral polygon, one must multiply the common length of the sides by the number of sides. A regular polygon may be characterized by the number of its sides and by its circumradius, that is to say, the constant distance between its centre and each of its vertices.

3D model of a snub disphenoid In geometry, the snub disphenoid, Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron is a three-dimensional convex polyhedron with twelve equilateral triangles as its faces. It is not a regular polyhedron because some vertices have four faces and others have five. It is a dodecahedron, one of the eight deltahedra (convex polyhedra with equilateral triangle faces) and one of the 92 Johnson solids (non-uniform convex polyhedra with regular faces). It can be thought of as a square antiprism where both squares are replaced with two equilateral triangles.

The simplest kinetic approach for maintenance of the closest pair is to use variants of the Delaunay triangulations. Consider a hexagon and partition it into six equilateral triangles, and then create a Delaunay triangulation based on each equilateral triangle, as each one is a convex shape. The union of these six Delaunay triangulations, so called Equilateral Delaunay graph (EDG), is a supergraph for the nearest neighbor graph (NNG); the endpoints of the edge with minimum length in EDG gives the closest pair. It is straightforward to maintain Delaunay triangulations based on convex shapes.

The best known is the (convex, non-stellated) regular icosahedron—one of the Platonic solids—whose faces are 20 equilateral triangles.

In geometry, the triaugmented triangular prism, tetracaidecadeltahedron, or tetrakis triangular prism is one of the Johnson solids (J51). Each of its 14 faces is an equilateral triangle, making it a deltahedron. As the name suggests, it can be constructed by attaching equilateral square pyramids (J1) to each of the three equatorial faces of the triangular prism.

A regular hexagon has Schläfli symbol {6}. and can also be constructed as a truncated equilateral triangle, t{3}, which alternates two types of edges. A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle).

Progressions between an octahedron, pseudoicosahedron, and cuboctahedron The cuboctahedron is the unique convex polyhedron in which the long radius (center to vertex) is the same as the edge length; thus its long diameter (vertex to opposite vertex) is 2 edge lengths. This radial equilateral symmetry is a property of only a few polytopes, including the two-dimensional hexagon, the three- dimensional cuboctahedron, and the four-dimensional 24-cell and 8-cell (tesseract). Radially equilateral polytopes are those which can be constructed, with their long radii, from equilateral triangles which meet at the center of the polytope, each contributing two radii and an edge. Therefore, all the interior elements which meet at the center of these polytopes have equilateral triangle inward faces, as in the dissection of the cuboctahedron into 6 square pyramids and 8 tetrahedra.

Some rep-tiles are based on polyforms like polyiamonds and polyominoes, or shapes created by laying equilateral triangles and squares edge-to-edge.

Euler diagram of types of triangles, using the definition that isosceles triangles have at least 2 equal sides (i.e., equilateral triangles are isosceles).

In the figure above, ABC is the original triangle. AZB, BXC, and CYA are equilateral triangles constructed on its sides' exteriors, and points L, M, and N are the centroids of those triangles. The theorem for outer triangles states that triangle LMN (green) is equilateral. A quick way to see that the triangle LMN is equilateral is to observe that MN becomes CZ under a clockwise rotation of 30° around A and a homothety of ratio with the same center, and that LN also becomes CZ after a counterclockwise rotation of 30° around B and a homothety of ratio with the same center.

The building rests on an equilateral triangle footprint with each side measuring , the same length as a Canadian football field from goal post to goal post.U of T Q&A; Quote: Each side of the equilateral triangle is long - the length of a Canadian football field from goal post to goal post - and it can provide space for 4,000 persons at any one time. The building is oriented such that one side of the equilateral triangle faces west while the other two sides face northeast and southeast. From the southeast corner, the building appears as a turkey.

The triangle has no angle ≥ 120°. Construct the equilateral triangle BCD and let P be any point inside Δ and construct the equilateral triangle CPQ. Then CQD is a 60° rotation of CPB about C so d(P) = PA+PB+PC = AP+PQ+QD which is simply the length of the path APQD. Let P0 be the point where AD and CF intersect.

201 and 228–239. The equilateral triangle is the only acute triangle that is similar to its orthic triangle (with vertices at the feet of the altitudes) (the heptagonal triangle being the only obtuse one).Leon Bankoff and Jack Garfunkel, "The heptagonal triangle", Mathematics Magazine 46 (1), January 1973, 7–19. A regular tetrahedron is made of four equilateral triangles.

The shape of the molecule is predicted to be an equilateral triangle. Vibrations can occur in the molecule in two ways, firstly the molecule can expand and contract retaining the equilateral triangle shape (breathing), or one atom can move relative to the others distorting the triangle (bending). The bending vibration has a dipole moment and thus couples to infrared radiation.

The typical plot of a Venus Equilateral story consists of the station's engineers inventing new devices that allow them to solve the story problem.

A version of the isoperimetric inequality for triangles states that the triangle of greatest area among all those with a given perimeter is equilateral.

A hexagonal pyramid with equilateral triangles would be a completely flat figure, and a heptagonal or higher would have the triangles not meet at all.

Its symmetry group is the dihedral group of order 6 D3. Equilateral triangles are the only triangles whose Steiner inellipse is a circle (specifically, it is the incircle). The integer-sided equilateral triangle is the only triangle with integer sides and three rational angles as measured in degrees.Conway, J. H., and Guy, R. K., "The only rational triangle", in The Book of Numbers, 1996, Springer-Verlag, pp.

Among regular polygons, only the triangle and square can be dissected into smaller equally sized copies of themselves. However, a regular hexagon can be dissected into six equilateral triangles, each of which can be dissected into a regular hexagon and three more equilateral triangles. This is the basis for an infinite tiling of the hexagon with hexagons. The hexagon is therefore an irrep-∞ or irrep-infinity irreptile.

Regular triangular coordinates are in a grid of equilateral triangles and are of the form (x,y,z) such that x,y,z are equal to or greater than 0. Regular tetrahedral coordinates are in a Euclidean 3-space 'grid' of equilateral tetrahedra and are of the form (w,x,y,z) such that w,x,y,z are equal to or greater than 0.

From this it can be seen that a triangle with a vertex at the center of the regular hexagon and sharing one side with the hexagon is equilateral, and that the regular hexagon can be partitioned into six equilateral triangles. Like squares and equilateral triangles, regular hexagons fit together without any gaps to tile the plane (three hexagons meeting at every vertex), and so are useful for constructing tessellations. The cells of a beehive honeycomb are hexagonal for this reason and because the shape makes efficient use of space and building materials. The Voronoi diagram of a regular triangular lattice is the honeycomb tessellation of hexagons.

This is the product of three equilateral triangles and is a uniform polytope. The 6-cube, can be constructed as a triple product {4} × {4} × {4}.

The crossed octagrammic cupola is a star-cupola made from an octagram, {8/5} and parallel hexadecagram, {16/5}, connected by 8 equilateral triangles and squares.

In geometry, the octagrammic cupola is a star-cupola made from an octagram, {8/3} and parallel hexadecagram, {16/3}, connected by 8 equilateral triangles and squares.

Neurosurgeon-turned-space-pirate Allison "Hellion" Murdoch attacks Venus Equilateral. Channing is able to use a super-electron-gun to short out the attacking ships' electrical systems.

The largest strictly-convex deltahedron is the regular icosahedron This is a truncated tetrahedron with hexagons subdivided into triangles. This figure is not a strictly-convex deltahedron since coplanar faces are not allowed within the definition. In geometry, a deltahedron (plural deltahedra) is a polyhedron whose faces are all equilateral triangles. The name is taken from the Greek upper case delta (Δ), which has the shape of an equilateral triangle.

The three tiered glass-cupola is formed out of rectangular glass and narrow steel supports. The second tier of the cupola is formed out of rectangles and equilateral triangles that are further subdivided into eight or twelve smaller equilateral triangles. All these glass pieces are joined together by steel struts. The third tier of the cupola is formed with similar designs, although the triangular glass panes are isosceles triangles.

These two equilateral triangles represent a synchronous and an inverse system. If the phasors V were a perfectly synchronous system, the vertex of the outer triangle not on the base line would be at the same position as the corresponding vertex of the equilateral triangle representing the synchronous system. Any amount of inverse component would mean a deviation from this position. The deviation is exactly 3 times the inverse phase component.

Beta Psi's badge was a equilateral triangle of enameled black, surrounded by a gold border, with the point toward the bottom. This was superimposed by the Greek letters Β and Ψ. The ψ was somewhat larger, encompassing most of the triangle and rendered in polished gold. The Β was superimposed on this, set with 12 pearls. The pledge pin is a gilded shield in which is set a black equilateral triangle.

For any point within an equilateral triangle, the sum of the perpendiculars to the three sides is equal to the altitude of the triangle. This is Viviani's theorem.

The crossed heptagrammic cupola is a star-cupola made from a heptagram, {7/5} and parallel tetradecagram, {14/5}, connected by 7 mutually intersecting equilateral triangles and squares.

The setting for most of the stories in the series is Venus Equilateral, a space station three miles long and one mile in diameter that serves as a communications relay between Venus, Earth, and Mars whenever interference from the Sun prevents line-of-sight communication between them. Venus Equilateral was formed out of a nickel-iron asteroid that was moved into Venus' point. At the time the stories take place, the asteroid has been completely reworked, resulting in a burnished steel cylinder with a large docking port at one end and a bank of communications dishes at the other. Venus Equilateral spins on its axis to provide its roughly 3000 inhabitants with centrifugal pseudo-gravity.

In geometry, the heptagrammic cupola is a star-cupola made from a heptagram, {7/3} and parallel tetradecagram, {14/3}, connected by 7 mutually intersecting equilateral triangles and squares.

The Koch snowflake can be constructed by starting with an equilateral triangle, then recursively altering each line segment as follows: # divide the line segment into three segments of equal length. # draw an equilateral triangle that has the middle segment from step 1 as its base and points outward. # remove the line segment that is the base of the triangle from step 2. The first iteration of this process produces the outline of a hexagram.

Equilateral pentagon built with four equal circles disposed in a chain. In geometry an equilateral pentagon is a polygon with five sides of equal length. Its five internal angles, in turn, can take a range of sets of values, thus permitting it to form a family of pentagons. The requirement is that all angles must add up to 540 degrees and must be between 0 and 360 degrees but not equal to 180 degrees.

In contrast, the regular pentagon is unique, because it is equilateral and moreover it is equiangular (its five angles are equal; the measure is 108 degrees). Four intersecting equal circles arranged in a closed chain are sufficient to determine a convex equilateral pentagon. Each circle's center is one of four vertices of the pentagon. The remaining vertex is determined by one of the intersection points of the first and the last circle of the chain.

The question published by Lemoine poses the following construction problem: :Given one vertex of each of the equilateral triangles placed on the sides of a triangle, construct the original triangle.

However, in Section 189(e) of An Elementary Treatise on Quaternions,Clarendon Press, Oxford, 1867, pp. 133--135 also in 1867, Tait treats the problem (in effect, echoing Davies' remarks in the Gentleman's Diary in 1831 with regard to Question 1265, but now in the setting of quaternions): : If perpendiculars be erected outwards at the middle points of the sides of a triangle, each being proportional to the corresponding side, the mean point of their extremities coincides with that of the original triangle. Find the ratio of each perpendicular to half the corresponding side of the old triangle that the new triangle may be equilateral. Tait concludes that the mean points of equilateral triangles erected outwardly on the sides of any triangle form an equilateral triangle.

Three interconnected Sonobe units will form an open-bottomed triangular pyramid with an equilateral triangle for the open bottom, and isosceles right triangles as the other three faces. It will have a right-angle apex (equivalent to the corner of a cube) and three tab/pocket flaps protruding from the base. This particularly suits polyhedra that have equilateral triangular faces: Sonobe modules can replace each notional edge of the original deltahedron by the central diagonal fold of one unit and each equilateral triangle with a right-angle pyramid consisting of one half each of three units, without dangling flaps. The pyramids can be made to point inwards; assembly is more difficult but some cases of encroaching can be obviously prevented.

Consider the largest square that can be placed in an arbitrary triangle. It may be that such a square could be positioned in the triangle in more than one way. If the largest such square can be positioned in three different ways, then the triangle is either an equilateral triangle or the Calabi triangle.Calabi's triangle at Mathworld Thus, the Calabi triangle may be defined as a triangle that is not equilateral and has three placements for its largest square.

The construction includes 9 equilateral triangles. Bars are disposed in four levels. Physical models are possible selecting correctly the size of the pieces in order bars and bolts don't obstruct anything else.

One way to identify Cetonia aurata is to look at its scutellum; on the noble chafer the scutellum is an equilateral triangle, but on the rose chafer it is an isosceles triangle.

1 quad. = 90° = rad = turn = 100 grad. In German the symbol ∟ has been used to denote a quadrant. ;Sextant (n = 6): The sextant (angle of the equilateral triangle) is of a turn.

Truss members are made up of all equivalent equilateral triangles. The minimum composition is two regular tetrahedrons along with an octahedron. They fill up three dimensional space in a variety of configurations.

In geometry, the snub heptaheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{7,7}, constructed from two regular heptagons and three equilateral triangles around every vertex.

In geometry, the snub pentapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{5,5}, constructed from two regular pentagons and three equilateral triangles around every vertex.

Since the sum of a positive number and its reciprocal is at least 2 by AM–GM inequality, we are finished. Equality holds only for the equilateral triangle, where P is its centroid.

Coxeter and Greitzer state the Napoleon Theorem thus: If equilateral triangles are erected externally on the sides of any triangle, their centers form an equilateral triangle. They observe that Napoleon Bonaparte was a bit of a mathematician with a great interest in geometry. However, they doubt whether Napoleon knew enough geometry to discover the theorem attributed to him. The earliest recorded appearance of the result embodied in Napoleon's theorem is in an article in The Ladies' Diary appeared in 1825.

The fibula is approximately an equilateral triangle in cross-section, with the inner face slightly concave and outer face convex. The flatter surface of the fibula is wide, and opposite ridge protrudes from this.

Analogously, the angles formed by the second isodynamic point satisfy the equationsAS'B = ACB - \pi/3, AS'C = ABC - \pi/3, and BS'C = BAC - \pi/3. The pedal triangle of an isodynamic point, the triangle formed by dropping perpendiculars from S to each of the three sides of triangle ABC, is equilateral,; . as is the triangle formed by reflecting S across each side of the triangle.. Among all the equilateral triangles inscribed in triangle ABC, the pedal triangle of the first isodynamic point is the one with minimum area..

By the Gauss–Lucas theorem, the root of the double derivative must be the average of the two foci, which is the center point of the ellipse and the centroid of the triangle. In the special case that the triangle is equilateral (as happens, for instance, for the polynomial ) the inscribed ellipse degenerates to a circle, and the derivative of has a double root at the center of the circle. Conversely, if the derivative has a double root, then the triangle must be equilateral .

In geometry, three or more than three straight lines (or segment of a line) make a polygon and an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, it doesn’t need to be equiangular (doesn’t need to have all angles equal), but if it does then it is a regular polygon. If the number of sides is at least five, an equilateral polygon doesn’t need to be a convex polygon: it could be concave or even self- intersecting.

In geometry, the snub apeiroapeirogonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of s{∞,∞}. It has 3 equilateral triangles and 2 apeirogons around every vertex, with vertex figure 3.3.∞.3.∞.

External images For terms see Morphology of Diptera Wing length 6·5-10·25 mm. Legs yellow coxae and trochanters black. Femora and tibiae 3 completely pale. Yellow marks on tergite 2 linear (not equilateral triangles).

Tergites are blackish, absolutely without reddish- brown markings. Male ocelli are in an equilateral triangle. Male genitalia figured by Van Veen (2004).Van Veen, M. (2004) Hoverflies of Northwest Europe: identification keys to the Syrphidae. 256pp.

It is the length of the space diagonal of a unit cube. The vesica piscis has a major axis to minor axis ratio equal to 1:, this can be shown by constructing two equilateral triangles within it.

In three variables, compositional data in three variables can be plotted via ternary plots. The use of a barycentric plot on three variables graphically depicts the ratios of the three variables as positions in an equilateral triangle.

The dark greyish-brown forewings are oblong. The greyish-brown costa is gently curved, with seven pairs of very narrow white transverse lines. The apex is sub-rectangular. The middle dorsum has an equilateral triangular white spot.

It represents the triad of mother, father and child, but, inverted, it also happens to be the logo for Ballantine beer. Plant's symbol of a feather within a circle was his own design, being based on the sign of the supposed Mu civilisation. A fifth, smaller symbol chosen by guest vocalist Sandy Denny represents her contribution to "The Battle of Evermore"; the figure, composed of three equilateral triangles, appears on the inner sleeve of the LP, serving as an asterisk. Sandy Denny's symbol of three downward- pointing equilateral triangles.

All the equilateral pentagons plotted within the area delimited by the condition α ≥ β ≥ δ. Three regions for each of three types of pentagons are shown: stellated, concave and convex The equilateral pentagon as a function of two variables can be plotted in the two-dimensional plane. Each pair of values (α, β) maps to a single point of the plane and also maps to a single pentagon. The periodicity of the values of α and β and the condition α ≥ β ≥ δ permit the size of the mapping to be limited.

A cyclic polygon (one inscribed in a circle) has the largest area of any polygon with a given number of sides of the same lengths. A version of the isoperimetric inequality for triangles states that the triangle of greatest area among all those with a given perimeter is equilateral. The triangle of largest area of all those inscribed in a given circle is equilateral; and the triangle of smallest area of all those circumscribed around a given circle is equilateral.Dorrie, Heinrich (1965), 100 Great Problems of Elementary Mathematics, Dover Publ.

During the 1896 Philippine Revolution, the Filipino leaders had no permanent political symbol, but, two different emblems were easily adopted. Both consisted of an equilateral triangle, but differed on what symbols were placed inside the triangle. Many documents of the Katipunan bore a letter K which stood for Kalayaan (Liberty), while some had the rising mythological sun in the center. General Emilio Aguinaldo, officially the first President of the Philippines, adopted the mythological sun and the three stars in each angle of the equilateral triangle as his emblem.

On the outermost level, with just over one Earth gravity, are living quarters for the station's crew. The next level in consists of offices, recreation centers, stores, churches, the cafeteria, and Joe's: the station's only bar. The innermost level, surrounding the station's zero-gravity axis, houses automatic machinery, the hydroponic farms, storerooms, the servogyroscopes and their beam finders, and the air plant (which consists of genetically engineered Martian sawgrass that efficiently renews the station's air supply via photosynthesis). The Venus Equilateral Relay Station is owned and operated by Venus Equilateral, Inc.

134 geodesic stations were set up on the peninsula's mountains, as well as on Aegina, Hydra and Nafplion. Thus, equilateral triangles whose sides measured about were drawn. The angles were measured with Gambey's theodolites.”Notice…”, Peytier et al.

The base of the noseleaf is narrow when viewed from the side. The lancet is short, wide, and rounded with convex margins. Its shape is similar to an equilateral triangle. The sella tapers and curves downward at the tip.

These figures, sometimes called deltohedra, must not be confused with deltahedra, whose faces are equilateral triangles. In texts describing the crystal habits of minerals, the word trapezohedron is often used for the polyhedron properly known as a deltoidal icositetrahedron.

Rotating-frame depiction of the horseshoe exchange orbits of Janus and Epimetheus Animation of Epimetheus orbit - Rotating reference frame Objects in a horseshoe orbit librate around 180° from the primary. Their orbits encompass both equilateral Lagrangian points, i.e. and .

The permanent structure is a three-sided tower. The tower contains 6 occupiable pods with open space in between. One of the pods displays the Olympic rings. It is 128m tall, with 7 occupiable floors, each an equilateral triangle.

It is the only radially equilateral convex polyhedron. Its dual polyhedron is the rhombic dodecahedron. The cuboctahedron was probably known to Plato: Heron's Definitiones quotes Archimedes as saying that Plato knew of a solid made of 8 triangles and 6 squares.

Two possible ways in which an equilateral triangle could distort due to a Jahn–Teller effect. A somewhat special role is played by tetrahedral systems like CH4+ and P4+. Here threefold degenerate electronic states and vibrational modes come into play.

The panicle is equilateral, linear, open, is long and carry 3–4 fertile spikelets. The main panicle branches are indistinct and almost racemose. Spikelets are ovate, solitary and are long. They also have fertile spikelets that have filiformed and pubescent pedicels.

The pledge pin was a diamond divided in half horizontally into two equilateral triangles. The top half being dark colored, the bottom light colored.photo, The 1931 Badger, p. 385 The membership badge was a black enamel shield surrounded by jewels.

In Ireland, Brigid's crosses (pictured on the right) were made at Imbolc. A Brigid's cross usually consists of rushes woven into a four-armed equilateral cross, although three-armed crosses have also been recorded.Evans, Emyr Estyn. Irish Folk Ways, 1957. p.

In an obituary to Moran, published by The San Diego Union-Tribune, fellow botanist Tom Oberbauer noted that Moran "had a dry sense of humor". The entire paper was republished under the heading "Reprinted Classic Madroño Articles" in Madroño, volume 60, p. 359 in 2013, the California Botanical Society's centennial year. For all its brevity, the paper is not the shortest ever published as, for example, John H. Conway and Alexander Soifer's 2003 paper "Can n2+ 1 unit equilateral triangles cover an equilateral triangle of side > n, say n + ε?" is shorter, having just two words, albeit with two figures.

Let A'BC be the equilateral triangle having base BC and vertex A' on the negative side of BC and let AB'C and ABC' be similarly constructed equilateral triangles based on the other two sides of triangle ABC. Then the lines AA', BB' and CC' are concurrent and the point of concurrence is the 1st isogonal center. Its trilinear coordinates are :csc(A + π/3) : csc(B + π/3) : csc(C + π/3). Expressing these coordinates in terms of a, b and c, one can verify that they indeed satisfy the defining properties of the coordinates of a triangle center.

The light enters through the hypotenuse face and is reflected back through it, being refracted twice at the same surface. The total refraction, and the total dispersion, is the same as would occur if an equilateral prism were used in transmission mode.

The Emirates Office Tower is located in the financial centre of Dubai. The Emirates Towers complex designed by NORR represents modern business age architecture. Two equilateral triangles are one of their kind in Dubai. The tower consists of three large core walls.

The two-dimensional polytopes are called polygons. Regular polygons are equilateral and cyclic. A p-gonal regular polygon is represented by Schläfli symbol {p}. Usually only convex polygons are considered regular, but star polygons, like the pentagram, can also be considered regular.

3D model a pentagonal cupola In geometry, the pentagonal cupola is one of the Johnson solids (J5). It can be obtained as a slice of the rhombicosidodecahedron. The pentagonal cupola consists of 5 equilateral triangles, 5 squares, 1 pentagon, and 1 decagon.

A generic epoxide. An epoxide is a cyclic ether with a three-atom ring. This ring approximates an equilateral triangle, which makes it strained, and hence highly reactive, more so than other ethers. They are produced on a large scale for many applications.

Let DEF be the triangle formed by the intersections of the adjacent angle trisectors of triangle ABC. Triangle DEF is called the Morley triangle of triangle ABC. Morley's trisector theorem states that the Morley triangle of any triangle is always an equilateral triangle.

The horned triangle, created by erecting a series of smaller triangles on one corner of an equilateral triangle, is another example of a teragon. It is also an example of a rep-tile, or shape that can be completely dissected into smaller copies of itself.

36 pink and glossy, forming an approximate rounded equilateral triangle with the stem at the center. They typically ripen in August and September. When dry these pods exhibit explosive dehiscence, throwing the seeds out forcefully. The seeds are glossy dark brown, about 2 mm across.

For example, a square or equilateral-triangle core would also have two equal-speed polarization solutions for the fundamental mode; such general shapes also arise in photonic-crystal fibers. Again, any random imperfections that break the symmetry would lead to PMD in such a waveguide.

Above each clock face is an equilateral pediment. On the top of the tower is elaborate wrought iron work supporting a weathervane. The inscription on the tower reads as follows. The clock tower was designated as a Grade II listed building on 14 June 1984.

Members of this family have inequivalve, oblong valves that are nearly equilateral. The right valve is more convex than the left, and there are usually no teeth. The ligament connecting the two valves is in an internal groove, and the hinge has a free ossicle.

Erick De Jesus was the designer of the flag. The rectangular flag consists of a purple equilateral triangular field, the color of the Moca tree flower. In this field appear five-point stars, silver-plated, surrounding a greater gold star, also with five points.

It is a chiral pattern, meaning that it is impossible to superpose it on top of its mirror image using only translations and rotations. A uniform tiling is a tiling in which each tile is a regular polygon and in which every vertex can be mapped to every other vertex by a symmetry of the tiling. Usually, uniform tilings additionally are required to have tiles that meet edge-to-edge, but if this requirement is relaxed then there are eight additional uniform tilings. Four are formed from infinite strips of squares or equilateral triangles, and three are formed from equilateral triangles and regular hexagons.

Construction of equilateral triangle with compass and straightedge An equilateral triangle is easily constructed using a straightedge and compass, because 3 is a Fermat prime. Draw a straight line, and place the point of the compass on one end of the line, and swing an arc from that point to the other point of the line segment. Repeat with the other side of the line. Finally, connect the point where the two arcs intersect with each end of the line segment An alternative method is to draw a circle with radius r, place the point of the compass on the circle and draw another circle with the same radius.

The elongated square gyrobicupola (J37), a Johnson solid 24 equilateral triangle example is not a Johnson solid because it is not convex. This 24-square example is not a Johnson solid because it is not strictly convex (has 180° dihedral angles.) In geometry, a Johnson solid is a strictly convex polyhedron such that each face of which is a regular polygon. There is no requirement that each face must be the same polygon, or that the same polygons join around each vertex. An example of a Johnson solid is the square-based pyramid with equilateral sides (J1); it has 1 square face and 4 triangular faces.

3D model of an augmented sphenocorona In geometry, the augmented sphenocorona is one of the Johnson solids (J87), and is obtained by adding a square pyramid to one of the square faces of the sphenocorona. It is the only Johnson solid arising from "cut and paste" manipulations where the components are not all prisms, antiprisms or sections of Platonic or Archimedean solids. . Johnson uses the prefix spheno- to refer to a wedge-like complex formed by two adjacent lunes, a lune being a square with equilateral triangles attached on opposite sides. Likewise, the suffix -corona refers to a crownlike complex of 8 equilateral triangles.

Stora Hammars I stone The name "Borromean rings" comes from their use in the coat of arms of the aristocratic Borromeo family in Northern Italy. The link itself is much older and has appeared in the form of the , three linked equilateral triangles with parallel sides, on Norse image stones dating back to the 7th century. A stone pillar in the 6th-century Marundeeswarar Temple in India shows the Borromean rings in another form, three linked equilateral triangles rotated from each other to form a regular enneagram. The Ōmiwa Shrine in Japan is also decorated with a motif of the Borromean rings, in their conventional circular form.

Two-dimensional examples are helpful in order to get some understanding about the origin of the competition between local rules and geometry in the large. Consider first an arrangement of identical discs (a model for a hypothetical two-dimensional metal) on a plane; we suppose that the interaction between discs is isotropic and locally tends to arrange the disks in the densest way as possible. The best arrangement for three disks is trivially an equilateral triangle with the disk centers located at the triangle vertices. The study of the long range structure can therefore be reduced to that of plane tilings with equilateral triangles.

Use of the matter duplicator allows the staff of Venus Equilateral to invent a method of instantaneous communication. Since line-of-sight is no longer necessary for communication, Venus Equilateral itself is obsolete, and the staff prepare to abandon the relay station. Meanwhile, Kingman sneaks aboard the station, rigs a power transmitter to lower the station's temperature to absolute zero, and kidnaps Walt Franks and Christine Baler, leaving them to freeze to death. Not knowing of the new instantaneous communication, Kingman assumes that the station has stopped relaying messages because of his sabotage, and he sues to gain VE's communications franchise for Terran Electric.

The foot is whitish, translucid, and may be extruded to a length more than equalling that of the shell, the body being brought up to it with a jerk, as in allied species. Full-grown examples are slightly more equilateral and more angulate than young ones.

It has twelve columns in the interior. Design elements of the gavit's west portal were heavily influenced by Islamic architecture. It has a decorative archway mounted by an equilateral pointed arch, surrounded by a rectangular frame containing geometric patterns (see also Neghutsi Vank and Orbelian's Caravanserai).

The hind wing is well developed, and either highly reduced or absent; with normal transverse folds, or lacking transverse folds. Radial cell of hind wing well developed; elongate. Inner posterior angle formed at base of radial cell right or obtuse. Radial cell is not forming equilateral triangle.

However it is often chosen so that both the incoming and outgoing light rays hit the surface at around the Brewster angle; beyond the Brewster angle reflection losses increase greatly. Most frequently, dispersive prisms are equilateral (apex angle of 60 degrees) where this is approximately the case.

The coat of arms features an equilateral triangle which represents equality. Inside the triangle are five volcanoes, which represent the five members of the federation. The triangle also contains symbols of liberty and peace which is represented by a red Phrygian cap, white rays and a rainbow].

Runestone The Kingittorsuaq runestone (old spelling: Kingigtorssuaq runestone) dating from the Middle Ages was found in 1824 on the highest point of the island, in a group of three cairns forming an equilateral triangle. The stone is now located at the National Museum of Denmark in Copenhagen.

The Warren truss design consists of alternating equilateral triangles along the sides of the bridge; the bridge has two sets of overlapping Warren trusses on each side, making it double intersectional. The bridge was added to the National Register of Historic Places on May 20, 1999.

The heptagonal triangle's orthic triangle, with vertices at the feet of the altitudes, is similar to the heptagonal triangle, with similarity ratio 1:2. The heptagonal triangle is the only obtuse triangle that is similar to its orthic triangle (the equilateral triangle being the only acute one).

A variety of polygonal shapes. Some simple shapes can be put into broad categories . For instance, polygons are classified according to their number of edges as triangles, quadrilaterals, pentagons, etc. Each of these is divided into smaller categories; triangles can be equilateral, isosceles, obtuse, acute, scalene, etc.

The Morley triangle, resulting from the trisection of each interior angle. This is an example of a finite subdivision rule. Morley's trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the Morley triangle.

The four regular hendecagrams {11/2}, {11/3}, {11/4}, and {11/5} In geometry, a hendecagrammic prism is a star polyhedron made from two identical regular hendecagrams connected by squares. The related hendecagrammic antiprisms are made from two identical regular hendecagrams connected by equilateral triangles.

The other alkali metals also form dimers: dilithium Li2, Na2, K2, and Cs2. The rubidium trimer has also been observed on the surface of helium nanodroplets. The trimer, Rb3 has the shape of an equilateral triangle, bond length of 5.52 A˚ and a binding energy of 929 cm−1.

The clock tower is about high. The sandstone plinth stands on a square base. On the sides of the plinth are rectangular panels, the south panel having an inscription and the date. On top of each side of the plinth is an equilateral pediment with a ball flower finial.

At that time Fliegerstaffel 3 changed to the AMIR badge. The original badge was a red equilateral triangle with white outer edges. In this badge was the head of a white Bulldog with black spot over the right eye and black collar. Underneath “3ème ESCADRILLE” was written in black.

3, p. 171 (topological equivalence of trihexagonal and two-triangle tilings). It consists of equilateral triangles and regular hexagons, arranged so that each hexagon is surrounded by triangles and vice versa. The name derives from the fact that it combines a regular hexagonal tiling and a regular triangular tiling.

It was covered with mirrored groin vault. Walls are encased with two rows of thoroughly drafted stone plates over which oversails brick placement of cushions. The upper chamber is a straight 12 edged dimension of oversailed proportions. Rectangular niches on the walls are framed by more narrow equilateral niches.

When arranged according to the circle of fifths, it looks like this: ::Image:Fifths.png Looking above at the marked chords from "Have You Met Miss Jones?", B, G and D are spaced a major third apart. On the circle of fifths it appears as an equilateral triangle: ::Image:Thirds cycle.

The patch is a royal blue equilateral triangle, bordered in gold, standing on its vertex. A white unicorn, its features outlined in blue, stands in the center. A golden lightning bolt overlaps the unicorn and forms the shape of a large seven. The large and powerful unicorn signifies strength.

The patch is a light blue circle bordered in red, superimposed on a black and white equilateral triangle. A large black unicorn with a white mane, red horn and green eye is within the circle. A green Arabic numeral "18" highlighted in red sits to the unicorn?s left.

The first four iterations of the Koch snowflake The first seven iterations in animation Zooming into the Koch curve The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry" by the Swedish mathematician Helge von Koch. The Koch snowflake can be built up iteratively, in a sequence of stages. The first stage is an equilateral triangle, and each successive stage is formed from adding outward bends to each side of the previous stage, making smaller equilateral triangles.

Then \epsilon, \gamma, and the two remaining angles of the green triangle can be found from four equations stating that the sum of the angles of the pentagon is 540°, the sum of the angles of the green triangle is 180°, the angle \gamma is the sum of its three components, and the angle \epsilon is the sum of its two components. A cyclic pentagon is equiangular if and only if it has equal sides and thus is regular. Likewise, a tangential pentagon is equilateral if and only if it has equal angles and thus is regular.De Villiers, Michael, "Equiangular cyclic and equilateral circumscribed polygons", Mathematical Gazette 95, March 2011, 102-107.

Because of this, all the apothems in a polygon will be congruent. For a regular pyramid, which is a pyramid whose base is a regular polygon, the apothem is the slant height of a lateral face; that is, the shortest distance from apex to base on a given face. For a truncated regular pyramid (a regular pyramid with some of its peak removed by a plane parallel to the base), the apothem is the height of a trapezoidal lateral face. For an equilateral triangle, the apothem is equivalent to the line segment from the midpoint of a side to any of the triangle's centers, since an equilateral triangle's centers coincide as a consequence of the definition.

A lens-shaped Δ-biangle rotating in an equilateral triangle Δ curves (delta curves), the simplest of which is the circle, are curves which can be rotated in the equilateral triangle, have many similar properties to curves of constant width. Delta curves of height h all share the same perimeter, . The generalization of the definition of bodies of constant width to convex bodies in R³ and their boundaries leads to the concept of surface of constant width (in the case of a Reuleaux triangle, this does not lead to a Reuleaux tetrahedron, but to Meissner bodies). There is also the concept of space curves of constant width, whose widths are defined by tangent planes.

Sierpiński triangle Generated using a random algorithm conjunctions of lexicographically ordered arguments. The columns interpreted as binary numbers give 1, 3, 5, 15, 17, 51... The Sierpiński triangle (sometimes spelled Sierpinski), also called the Sierpiński gasket or Sierpiński sieve, is a fractal attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. Originally constructed as a curve, this is one of the basic examples of self- similar sets—that is, it is a mathematically generated pattern that is reproducible at any magnification or reduction. It is named after the Polish mathematician Wacław Sierpiński, but appeared as a decorative pattern many centuries before the work of Sierpiński.

On May 11, 1969, near Chapeau, a farmer by the name of Leo-Paul Chaput was awakened at 2 am, and witnessed a brilliant white light emanating from a flat-bottomed domed craft, resembling a French WWI military helmet. The next morning, a wide circular imprint was found in the ground, with a ring of scorched grass wide, containing three indentations forming an equilateral triangle, with sides long, each dent wide and deep, suggesting a "landing tripod". A second smaller circle was also found, with a ring of scorched grass, but the triangle of indentations was smaller and not equilateral. A third scorched marking, although a semicircle, contained a pile of rocks.

The dimensionless quantities often represent the degree of deviation from an ideal shape, such as a circle, sphere or equilateral polyhedron.L. Wojnar & K.J. Kurzydłowski, et al., Practical Guide to Image Analysis, ASM International, 2000, p 157-160, . Shape factors are often normalized, that is, the value ranges from zero to one.

As a sublunary daemonical power (as Hera, Poseidon, Demeter), it dwells in the elements, and these daemonical natures, midway between gods and men, are related to them as the isosceles triangle is to the equilateral and the scalene.Stobaeus, Ecl. Phys. i. 62; Plutarch, de Orac. defect.; Cicero, de Natura Deorum, i.

Coffins in Egyptian culture date back to the Old Kingdom. During this era, coffins were relatively simple; they were equilateral makings with minor details. These included three openings, one that the Ka was intended to pass through and two that represented eyes. However, as time passed coffins and their structures evolved.

Lauritsala Church Lauritsala Church () is an Evangelical Lutheran church in the Lauritsala district of Lappeenranta, Finland. The church was opened in December 1969. The modernist concrete design was created by architect Toivo Korhonen and architect student Jaakko Laapotti. The basis of the design is an equilateral triangle symbolising the Holy Trinity.

The scanner produces a 'map' of the area that is represented as voxels. Each voxel represents the activity of a specific volume in three-dimensional space. The exact size of a voxel varies depending on the technology. fMRI voxels typically represent a volume of 27 mm3 in an equilateral cuboid.

Channing is on board the Ariadne when a meteor strike leaves it crippled and off course. He is able to turn the ship into a signalling device, and Franks on Venus Equilateral, anticipating him, is able to work out a means of receiving his signal and tracking down the ship.

The different hatch marks simply signal that the length measurements may be considered to be independent of each other. So, for example, while the triangles in the accompanying figure cannot be shown to be isosceles triangles or equilateral triangles, it is nevertheless possible that they could be either of those.

The Color Harmony Manual is made up of charts of colored chips representing a color space. The overall shape of a chart is an equilateral triangle made up of 28 samples. Each chart is made up of samples of approximately the same hue. Each chart has one sample with the greatest purity.

The Meritorious Public Service Medal is a bronze disc in height and in width. On the obverse is an equilateral triangle symbolic of the civilian. Superimposed on the triangle is the eagle from the Great Seal of the United States. At the base of the medal is a wreath denoting nonmilitary service.

SQT measurements are scaled proportionately by relative impact and visually represented on triaxial graphs. Evaluation of sediment integrity and interrelationships between components can be determined by the size and morphology of the triangle. The magnitude of the triangle is indicative of the relative impact of contamination. Equilateral triangles imply agreement among components.

Boronia rhomboidea was first formally described in 1905 by William Jackson Hooker from a specimen collected by Ronald Campbell Gunn on the "side of the Western Mountains". The description was published in Icones Plantarum. The specific epithet (rhomboidea) is derived from Latin word rhombus meaning "an equilateral parallelogram with unequal pairs of angles".

This polyhedron is in the family of elongated bipyramids, of which the first three can be Johnson solids: J14, J15 and J16. The hexagonal form can be constructed by all regular faces, but is not a Johnson solid because 6 equilateral triangles would form six co-planar faces (in a regular hexagon).

Bôcher notes that when P is the orthocenter, one obtains the nine-point circle, and when P is on the circumcircle of ABC, then the conic is an equilateral hyperbola. In 1912 Maud Minthorn showed that the nine- point conic is the locus of the center of a conic through four given points.

They are almost shaped as an equilateral triangle with straight front and rear edges. More to behind the triangles are lower and wider. From the fifth pair onwards the front edges become longer and strongly concave, off-setting the point to the rear. The last pair, immediately before the knob, is strongly rounded.

In 1972-3, Brother Patrick, a monk of Prinknash, contributed the design and manufacture of a number of items at Clifton Cathedral, Bristol. These included the votive candelabra hanging in the Lady Chapel, made from twenty stainless steel equilateral triangles (a regular icosahedron), and the decorative screens to the Blessed Sacrament Chapel.

These 12 order-5 vertices can be truncated such that all edges are equal length. The original 30 rhombic faces become non-regular hexagons, and the truncated vertices become regular pentagons. The hexagon faces can be equilateral but not regular with D2 symmetry. The angles at the two vertices with vertex configuration 6.6.

The alternated octagonal tiling, a hyperbolic tiling of squares and equilateral triangles, overlaid on Escher's image Escher seems to have believed that the white curves of his woodcut, which bisect the fish, represent hyperbolic lines in the Poincaré disk model of the hyperbolic plane, in which the whole hyperbolic plane is modeled as a disk in the Euclidean plane, and hyperbolic lines are modeled as circular arcs perpendicular to the disk boundary. Indeed, Escher wrote that the fish move "perpendicularly to the boundary". However, as Coxeter demonstrated, there is no hyperbolic arrangement of lines whose faces are alternately squares and equilateral triangles, as the figure depicts. Rather, the white curves are hypercycles that meet the boundary circle at angles of approximately 80°.

In The Legend of Zelda, the Triforce of Wisdom was split into eight pieces; the pieces are inconsistently rendered, as equilateral triangles on the main display, but as 45–45–90 (isosceles right) triangles in the status screen, and the overall Triforce of Wisdom is also shown as a 45–45–90 triangle, shorter than a (60–60–60) equilateral triangle. In The Wind Waker, the Triforce of Courage was split into eight irregularly shaped shards and the Triforce of Wisdom into two. In some games, each of the three Triforce parts manifests itself as a symbol on the hand of its bearer. When two or more Triforce bearers come into close proximity, the Triforce symbols on their hands will glow.

Among the tiles you may see are > equilateral crosses with four arms bent at 90°, known historically as > swastikas. The word swastika comes from the Sanskrit svastika - "su" meaning > "good," "asti" meaning "to be," and "ka" as a suffix. Thus, swastika, > literally means "to be good." The origins of this symbol are quite ancient.

Dually, it can be tiled with 56 equilateral triangles, with 24 vertices, each of degree 7, as a quotient of the order-7 triangular tiling. Klein's quartic arises in many fields of mathematics, including representation theory, homology theory, octonion multiplication, Fermat's last theorem, and Stark's theorem on imaginary quadratic number fields of class number 1.

The great icosahedron is one of the four regular star Kepler-Poinsot polyhedra. Its Schläfli symbol is {3, }. Like the convex form, it also has 20 equilateral triangle faces, but its vertex figure is a pentagram rather than a pentagon, leading to geometrically intersecting faces. The intersections of the triangles do not represent new edges.

A submerge-arc furnace's shell or casing is fabricated from steel. The lower part is lined with hard blocks of strongly calcined carbon, and the upper part with firebrick. The floor and lower section of the furnace are water-cooled. Three electrodes are placed at the angles of an equilateral triangle with rounded corners.

The sum of the angles of a triangle is equal to a straight angle (180 degrees).Euclid, book I, proposition 32 This causes an equilateral triangle to have three interior angles of 60 degrees. Also, it causes every triangle to have at least two acute angles and up to one obtuse or right angle.

In 1983, coins were introduced for , 1, 2, 5, 10 and 20 cents, with the cent the same size and composition as the earlier 5 mil coins. The other coins were struck in nickel-brass. The cent was only struck in 1983. In 1991, cupronickel, Reuleaux heptagonal (curved-equilateral-heptagonal) 50-cent coins were introduced.

The Azrieli Center Triangular Tower has a height of . Construction of this tower, like the circular tower, began in 1996 and was completed in 1999. It has 46 floors and its main occupant is Bezeq, Israel's largest telecommunications company; Bezeq occupies 13 floors of the tower. The tower's cross-section is an equilateral triangle.

When the engineering staff of Terran Electric use a Martian power transmitter to create a faster- than-light communicator, Kingman uses it to manipulate Venus Equilateral's stock price in an effort to gain a controlling interest in the company. When Venus Equilateral independently reproduces the FTL communicator, Channing discovers Kingman's plot, and manipulates him back.

The structure is composed by triangles ranging from scalene to equilateral. Three triangles serve as legs to connect two large triangles at the top, so that it looks like an open airplane. Each of the triangles is filled with 16 smaller triangles and all have lines like air vents that light up in the night.

Wright designed the house around a "diamond module" with 60- and 120-degree angles. The red cement floors had a diamond pattern in the same shape. The skylights were equilateral triangles, each corner 60 degrees. The pool, nestled into the wide corner of the L-shaped house, was a parallelogram with a notch out of one corner.

The middle star represents Honduras, located in the center of the Central American Union. The coat of arms was established in 1945. It is an equilateral triangle, at the base is a volcano between three castles, over which is a rainbow and the sun shining. The triangle is placed on an area that symbolizes being bathed by both seas.

These clams have two short siphons, each with a horny sheath. The shell is shaped like a rounded-cornered equilateral triangle and there is a slight gape at the posterior. Each valve bears two cardinal teeth with four lateral teeth on the right valve and two on the left. The foot is white and wedge-shaped.

Some rep-tiles, like the square and equilateral triangle, are symmetrical and remain identical when reflected in a mirror. Others, like the sphinx, are asymmetrical and exist in two distinct forms related by mirror- reflection. Dissection of the sphinx and some other asymmetric rep-tiles requires use of both the original shape and its mirror-image.

The grid point with high resolution creates difficulty for both structured and unstructured. For example, in case of boundary layer, structured scheme produces elongated grid in the direction of flow. On the other hand unstructured grids require a higher cell density in the boundary layer because the cell needs to be as equilateral as possible to avoid errors.

The opaque forest problem was originally introduced by Mazurkiewicz in 1916. Since then, not much progress has been made with respect to the original problem. There does not exist any verified general solution to the problem. In fact, the optimal solution for even simple fixed inputs such as the unit square or equilateral triangle are unknown.

The Koch curve can be expressed by the following rewrite system (Lindenmayer system): :Alphabet : F :Constants : +, − :Axiom : F :Production rules: : F → F+F--F+F Here, F means "draw forward", - means "turn right 60°", and + means "turn left 60°". To create the Koch snowflake, one would use F--F--F (an equilateral triangle) as the axiom.

The third method is best for moonless and clear nights, as it uses two faint "clouds" in the Southern Sky. These are marked in astronomy books as the Large and Small Magellanic Clouds. These "clouds" are actually dwarf galaxies near the Milky Way. Make an equilateral triangle, the third point of which is the south celestial pole.

The design of the probationary membership pin is an upward-pointing equilateral triangle of black enamel surrounded by a border of red enamel, with a thin gold border separating the red and black enamel and another thin gold border around the outside of the pin surrounding the red enamel."Probationary Membership Pin". sinfoniastore.org; retrieved May 3, 2009.

A uniform antiprism has, apart from the base faces, 2n equilateral triangles as faces. Uniform antiprisms form an infinite class of vertex- transitive polyhedra, as do uniform prisms. For we have the regular tetrahedron as a digonal antiprism (degenerate antiprism), and for the regular octahedron as a triangular antiprism (non-degenerate antiprism). Dual polyhedra of antiprisms are trapezohedra.

Potato-filled Bourekas come in a certain box shape. Pizza filled Bourekas resemble a co-centric tower, while spinach filled bourekas resemble a pastry knot. There are also the so-called "Turkish Bourekas" which form rounded equilateral triangles, and are filled with various fillings, whose type can usually be determined by the addition on their outside.

Alternatively, a Reuleaux triangle may be constructed from an equilateral triangle T by drawing three arcs of circles, each centered at one vertex of T and connecting the other two vertices. Or, equivalently, it may be constructed as the intersection of three disks centered at the vertices of T, with radius equal to the side length of T.

3D model of regular octahedron. In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. A regular octahedron is the dual polyhedron of a cube.

Bravais used an equilateral glass prism which he spun around its vertical axis. When illuminated by parallel white light, this produced an artificial Parhelic circle and many of the embedded parhelia. Similarly, A. Wegener used hexagonal rotating crystals to produce artificial subparhelia.“Die Nebensonnen unter dem Horizont,” Meteorol. Z. 34–52(8/ 9), 295–298, A. Wegner, 1917.

The tesseract, like all hypercubes, tessellates Euclidean space. The self-dual tesseractic honeycomb consisting of 4 tesseracts around each face has Schläfli symbol {4,3,3,4}. Hence, the tesseract has a dihedral angle of 90°. The tesseract's radial equilateral symmetry makes its tessellation the unique regular body-centered cubic lattice of equal-sized spheres, in any number of dimensions.

Einthoven's triangle is an imaginary formation of three limb leads in a triangle used in electrocardiography, formed by the two shoulders and the pubis. The shape forms an inverted equilateral triangle with the heart at the center that produces zero potential when the voltages are summed. It is named after Willem Einthoven, who theorized its existence.

The badge of the squadron is "On an equilateral triangle, a Petrel's head erased". In the First World War, airmen would often stick bottle labels to their aircraft and so the Bass red triangle - the first registered UK trademark - was incorporated as the main part of the badge with the head of a petrel – a small seabird.

The ovate shell is oblong, transverse, equilateral, inequivalve, and inflated. The beaks are small, that of the left slightly notched. The valves are white, delicate, and diaphanous, rounded upon the anterior side, truncated obliquely upon the posterior sid. The side is bounded outwardly by an obtuse angle, which extends from the beak to the lower and posterior edges.

This triangle connects the constellations of Boötes, Virgo, and Leo. It is visible rising in the south eastern sky of the northern hemisphere between March and May. George Lovi of Sky & Telescope magazine had a slightly different Spring triangle, including the tail of Leo, Denebola, instead of Regulus. Denebola is dimmer, but the triangle is more nearly equilateral.

For any point P in the plane of an equilateral triangle ABC, the distances of P from the vertices, PA, PB, and PC, are such that, unless P is on the triangle's circumcircle, they obey the basic triangle inequality and thus can themselves form the sides of a triangle: :PA+PB > PC, \quad PB+PC > PA, \quad PC+PA > PB. However, when P is on the circumcircle the sum of the distances from P to the nearest two vertices exactly equals the distance to the farthest vertex. A triangle is equilateral if and only if, for every point P in the plane, with distances PD, PE, and PF to the triangle's sides and distances PA, PB, and PC to its vertices, ::4(PD^2+PE^2+PF^2) \geq PA^2+PB^2+PC^2.

Many alternative axioms can be formulated which are logically equivalent to the parallel postulate (in the context of the other axioms). For example, Playfair's axiom states: :In a plane, through a point not on a given straight line, at most one line can be drawn that never meets the given line. The "at most" clause is all that is needed since it can be proved from the remaining axioms that at least one parallel line exists. A proof from Euclid's Elements that, given a line segment, one may construct an equilateral triangle that includes the segment as one of its sides: an equilateral triangle ΑΒΓ is made by drawing circles Δ and Ε centered on the points Α and Β, and taking one intersection of the circles as the third vertex of the triangle.

Fig 2. Geometry of the first isogonic center. Fig. 2 shows the equilateral triangles ARB, AQC and CPB attached to the sides of the arbitrary triangle ABC. Here is a proof using properties of concyclic points to show that the three lines RC, BQ and AP in Fig 2 all intersect at the point F and cut one another at angles of 60°.

The board is in the shape of an equilateral triangle with truncated corners. It contains 157 triangular in an alternating color pattern; 75 cells are light-colored, 82 are dark-colored. Each player has 18 pieces in his or her own color: 16 regular pieces and 2 captains. Because the board is triangular, the two armies are set up asymmetrically (see illustration).

Given a point P in the interior of an equilateral triangle, the ratio of the sum of its distances from the vertices to the sum of its distances from the sides is greater than or equal to 2, equality holding when P is the centroid. In no other triangle is there a point for which this ratio is as small as 2.

The apices of the triangle are north-west and south-east making it nearly equilateral. At the foot on the northern side lies the village of Tathavade (p. 1,001) with people nearly all cultivators mostly Ramoshis and Marathas. The defences consist of three walls, the top wall going all round the hill and forming what may be called the citadel.

Sleeping Venus (c. 1510), Gemäldegalerie Alte Meister, Dresden, Germany. For his home town of Castelfranco, Giorgione painted the Castelfranco Madonna, an altarpiece in sacra conversazione form—Madonna enthroned, with saints on either side forming an equilateral triangle. This gave the landscape background an importance which marks an innovation in Venetian art, and was quickly followed by his master Giovanni Bellini and others.

In geometry, an apeirogonal antiprism or infinite antiprismConway (2008), p. 263 is the arithmetic limit of the family of antiprisms; it can be considered an infinite polyhedron or a tiling of the plane. If the sides are equilateral triangles, it is a uniform tiling. In general, it can have two sets of alternating congruent isosceles triangles, surrounded by two half-planes.

Its name comes from a topological construction from the snub dodecahedron with the kis operator applied to the pentagonal faces. In this construction, all the vertices are computed to be the same distance from the center. The 80 of the triangles are equilateral, and 60 triangles from the pentagons are isosceles. It is a (2,1) geodesic polyhedron, made of all triangles.

The small pectoral fins are falcate (sickle-shaped) with relatively pointed tips. The first dorsal fin is broad, forming nearly an equilateral triangle in adults, with a blunt apex; it originates over the pectoral fin rear tips. The second dorsal fin is small and originates over the midpoint of the anal fin base. No ridge exists between the dorsal fins.

In 1767, Leonhard Euler found three families of periodic solutions in which the three masses are collinear at each instant. See Euler's three-body problem. In 1772, Lagrange found a family of solutions in which the three masses form an equilateral triangle at each instant. Together with Euler's collinear solutions, these solutions form the central configurations for the three-body problem.

All triangles are affine-regular. In other words, all triangles can be generated by applying affine transformations to an equilateral triangle. A quadrilateral is affine-regular if and only if it is a parallelogram, which includes rectangles and rhombuses as well as squares. In fact, affine-regular polygons may be considered a natural generalization of parallelograms.. See in particular p. 249.

The 5-cell is a solution to the problem: Make 10 equilateral triangles, all of the same size, using 10 matchsticks, where each side of every triangle is exactly one matchstick. No solution exists in three dimensions. The convex hull of the 5-cell and its dual (assuming that they are congruent) is the disphenoidal 30-cell, dual of the bitruncated 5-cell.

The second method uses Canopus (the second-brightest star in the sky) and Achernar. Make a large equilateral triangle using these stars for two of the corners. The third imaginary corner will be the south celestial pole. If Canopus has not yet risen, the second- magnitude Alpha Pavonis can also be used to form the triangle with Achernar and the pole.

A simple composition with cloud and rooftop that creates asymmetry. Related to the rule of odds is the observation that triangles are an aesthetically pleasing implied shape within an image. In a canonically attractive face, the mouth and eyes fall within the corners of the area of an equilateral triangle. Paul Cézanne successfully used triangles in his compositions of still lifes.

The tower is the first green tower in Israel, and also the first to feature a double curtain wall system.Exclusive: The Incredible Hulk - The First Glimpse of the International Tower. Calcalist.co.il. Retrieved 2016-10-16. The design of the tower consists of 5 equilateral triangular prisms, set on top of each other at different heights, creating 3 large balconies for the building's occupants.

Although the triangle is nearly equilateral, some asymmetry exists. Due to the eccentricity of Jupiter's orbit, the side - slightly differs from the two other sides. When Jupiter is in aphelion, the mean velocity of the objects moving along this side is somewhat smaller than that of the objects moving along the other two sides. When Jupiter is in perihelion, the reverse is true.

On painted porcelain, China The triakis triangular tiling is a tiling of the Euclidean plane. It is an equilateral triangular tiling with each triangle divided into three obtuse triangles (angles 30-30-120) from the center point. It is labeled by face configuration V3.12.12 because each isosceles triangle face has two types of vertices: one with 3 triangles, and two with 12 triangles.

3D model of a square pyramid In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it is a right square pyramid, and has C4v symmetry. If all edges are equal, it is an equilateral square pyramid,Franz Hocevar, Solid Geometry, 1903, p. 44 the Johnson solid J1.

It is surrounded by a triangular iron-railed viewing platform. Three of the cupola walls containing the door and windows are parallel to the tower walls. The door leads out onto the viewing platform. The platform is in the form of an equilateral triangle, with edges parallel to the south cupola wall and the windowed (north west and north east) cupola walls.

The receiver station has three of these arrays, arranged in an equilateral triangle. The transmitter antenna array has 36 re-configurable masts and is 440 m wide. Radar signals were detected by some amateur radio operators in the 9.2–19.745 MHz frequency band. Pulse repetition rate is 50 pulses per second, bandwidth about 14 kHz, frequency modulation on pulse (FMOP) is used.

The skeleton of the icosidodecahedron forms a 60-edge symmetric graph. There are 60 one-sided hexominoes, the polyominoes made from six squares. In geometry, it is the number of seconds in a minute, and the number of minutes in a degree. In normal space, the three interior angles of an equilateral triangle each measure 60 degrees, adding up to 180 degrees.

In these more recently discovered flexagons, each square or equilateral triangular face of a conventional flexagon is further divided into two right triangles, permitting additional flexing modes. The division of the square faces of tetraflexagons into right isosceles triangles yields the octaflexagons, and the division of the triangular faces of the hexaflexagons into 30-60-90 right triangles yields the dodecaflexagons.

The fifty pence (50p) () coin was a subdivision of the Irish pound. It was introduced in Ireland on 17 February 1970. It replaced the ten shilling coin when decimalised, and due to this conversion was introduced a year before Decimal Day in 1971. It is a seven sided coin, an equilateral curve heptagon of constant breadth (3 centimetres) and mass 13.5 grams.

Pleasure Beach Bridge is a riveted Warren through-truss, consisting of longitudinal members joined only by angled cross-members, forming alternately inverted equilateral triangle-shaped spaces along the length. The bridge is supported by timber pilings. The swing span is made of two separate Warren through-trusses that pivots on concrete pier. The operator's house is located on the mainland approach.

Honduran law describes the coat of arms as follows:La Gaceta, num. 9495, Decreto No. 16 The Arms to be used are an equilateral triangle. In its base there is a volcano between two castles, over them a rainbow, and below it, behind the volcano, raises a sun spreading light. The triangle is settled on a terrain bathed by both seas.

The 1 and 5 cents were struck in Nickel-brass, with the other denominations struck in cupro-nickel. In 1996, high inflation caused the introduction of 1, 5 and 10 dollars coins. The 1 and 5 dollars are struck in copper-plated steel, whilst the 10 dollars is struck in nickel-plated steel and has an equilateral- curved heptagonal shape.

Let f be a triangle center function. If two sides of a triangle are equal (say a = b) then so two components of the associated triangle center are always equal. Therefore all triangle centers of an isosceles triangle must lie on its line of symmetry. For an equilateral triangle all three components are equal so all centers coincide with the centroid.

Four 'sphinx' hexiamonds can be put together to form another sphinx. In geometry, the sphinx tiling is a tessellation of the plane using the "sphinx", a pentagonal hexiamond formed by gluing six equilateral triangles together. The resultant shape is named for its reminiscence to the Great Sphinx at Giza. A sphinx can be dissected into any square number of copies of itself,.

Kalfus and his family have lived in Paris, Dublin, Belgrade, and Moscow. He believes his time in other countries keeps his observations fresh and provides him with valuable insights.Dwight Garner, "The Salon Interview: Ken Kalfus", Salon/com, 23 Jul 1998, accessed 25 May 2009 Kalfus began his career by publishing short stories and now writes novels. His most recent novel was Equilateral (2013).

Valves of these animals are fragile, either equivalved or nearly so, small to medium-sized, and are described as subcircular to obscurely ovate in shape. Like other scallops, the valves have pronounced "ears" on the anterior and posterior sides of the hinge joint. Valves are also very nearly equilateral. All species have a byssal notch which will vary with depth of species.

Currently there are more than 67,000 members of Delta Phi Epsilon. The current international president of Delta Phi Epsilon is Stacy Segal (Psi-University of Georgia). Delta Phi Epsilon's flower is the Lovely Purple Iris, and its international mascot is the Unicorn. The sisterhood badge is an equilateral triangle in gold surrounded by 21 pearls, the jewel of the sorority.

The medal is irregular in shape, taking the form of a downward pointing equilateral triangle, enameled in red. At each point of the triangle is a gold star. Superimposed in the center of the triangle is the "Philippines sun" in gold with eight pointed rays. A green laurel wreath passes around and behind the triangle and is visible between each of the points.

175px The is a fictional artifact from Nintendo's The Legend of Zelda series of video games. Referred to as "The Golden Power" in ancient Hylian literature, it represents the essence of the Golden Goddesses who created the realm of Hyrule that was left behind when they departed the realm for the heavens. It is said to grant godlike power to the one who holds all three pieces and is a main focus of the plot of many games in the series, including The Legend of Zelda, The Adventure of Link, A Link to the Past, Ocarina of Time, Oracle of Ages, Oracle of Seasons, The Wind Waker, Skyward Sword, and A Link Between Worlds. The Triforce consists of three equilateral triangles, which are joined (with an empty triangle in the middle) to form a large equilateral triangle.

The fact that the chromatic number of the plane must be at least four follows from the existence of a seven-vertex unit distance graph with chromatic number four, named the Moser spindle after its discovery in 1961 by the brothers William and Leo Moser. This graph consists of two unit equilateral triangles joined at a common vertex, x. Each of these triangles is joined along another edge to another equilateral triangle; the vertices y and z of these joined triangles are at unit distance from each other. If the plane could be three- colored, the coloring within the triangles would force y and z to both have the same color as x, but then, since y and z are at unit distance from each other, we would not have a proper coloring of the unit distance graph of the plane.

139–157, Societas Scientiarum Naturalium Helveticae, Lausanne, 1953, . Summarized at: Dartmouth College. This property is also true for another triangle center, the nine-point center, although it had not been defined in Euler's time. In equilateral triangles, these four points coincide, but in any other triangle they are all distinct from each other, and the Euler line is determined by any two of them.

The Medal "Defender of a Free Russia" is a 34mm in diameter circular medal made of silvered red brass. Its obverse bears a straight equilateral cross, on the cross center in relief, St George on horseback slaying the dragon. On the lower arm of the cross, the relief inscription "August 21, 1991" (). Between the cross arms, multiple branches of oak and laurel protruding towards the outer circumference.

The Outer Circle Official Seal of Filamer Christian University represents the programs and services that Filamer offers. The Inner Circle symbolizes the development of the individual's well-rounded personality. The Equilateral Triangle inside the circle stands for the three balanced components of human potentialities: the spiritual, the intellectual, and the physical with the spiritual aspect as the base. The Cross represents the victorious Christ as the center.

Cornish flag of St. Piran This flag is an exact negative of the flag of Cornwall, sometimes known as Saint Piran's Flag. The connections between Cornwall and Brittany are well documented but the historical links between the two flags, if any exist, are unknown. The United Baltic Duchy flag is similar in appearance; however the latter is a Nordic Cross rather than an equilateral cross.

The interpunct () was regularly used in classical Latin to separate words. In addition to the most common round form, inscriptions sometimes use a small equilateral triangle for the interpunct, pointing either up or down. It may also appear as a mid-line comma, similar to the Greek practice of the time. The interpunct fell out of use , and Latin was then written for several centuries.

The set of all Lorentz transformations form a group called the Lorentz group (this may be generalised to the Poincaré group). Discrete groups describe discrete symmetries. For example, the symmetries of an equilateral triangle are characterized by the symmetric group \, S_3. A type of physical theory based on local symmetries is called a gauge theory and the symmetries natural to such a theory are called gauge symmetries.

Rep-2 rep-tiles are also rep-2n and the rep-4,8,16+ triangles yield further rep-tiles. These are found by discarding half of the sub-copies and permutating the remainder until they are mirror-symmetrical within a right triangle. In other words, two copies will tile a right triangle. One of these new rep-tiles is reminiscent of the fish formed from three equilateral triangles.

The original article by Alain Chenciner and Richard Montgomery. Annals of Mathematics, 152 (2000), 881–901. One such orbit is a circular orbit, with equal masses at the corners of an equilateral triangle; another is the figure-8 orbit, first discovered numerically in 1993 by Cristopher Moore Moore's numerical discovery of the figure-8 choreography using variational methods. and subsequently proved to exist by Chenciner and Montgomery.

Inside, the decoration is stark and mostly modern, especially in the main altar area. An equilateral cross with an image of Christ is suspended over the altar area and there are small modern crosses and other elements on the side walls. However, the most important decorative element is an 18th-century narrative mural. This mural was uncovered during the renovation work in the mid 20th century.

1867, in memory of the Cory family. The nave, long by wide, is divided from the south aisle by an arcade of four equilateral pointed arches raised on massive octagonal piers that date from the fourteenth century. In 1883 the arches were raised by two feet. The nave is divided from the north aisle by a similar arcade of four arches, built in 1883.

The Kingittorsuaq Runestone was found in 1824 in a group of three cairns that formed an equilateral triangle on top of the mountain on Kingittorsuaq Island in the south-central part of the Upernavik Archipelago. The stone is now located at the National Museum of Denmark in Copenhagen. The stone has been dated to the Middle Ages. The Catholic Encyclopedia states the date as April 25, 1135.

The Public Service Commendation Medal is a bronze disc 35 mm height and 32 mm in width. Superimposed on the disc is an equilateral triangle which symbolizes civilians. Displayed on the triangle is the coat of arms of the United States, symbolizing service to the federal government. The reverse of the medal bears the inscription FOR COMMENDABLE PUBLIC SERVICE TO THE UNITED STATES ARMY.

The triangular prism is first in a dimensional series of semiregular polytopes. Each progressive uniform polytope is constructed vertex figure of the previous polytope. Thorold Gosset identified this series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes (equilateral triangles and squares in the case of the triangular prism). In Coxeter's notation the triangular prism is given the symbol −121.

A Makoto court consists of three metal beams arranged in an equilateral triangle on the floor. At each corner of the triangle there is a six-foot-tall column, equipped with a speaker. Each column has twelve targets which have pressure sensors. There are optional floor targets that can add four more targets to each column for a total of 48 targets in the arena.

The building is set on a grid of 30-and 60-degree equilateral parallelograms with the master bedroom as a hexagon at the head, with the children's bedrooms coming off of it. It was originally designed with two, instead of three, children's bedrooms because Wright misunderstood how many children the Kinneys had. Therefore, his apprentice, John H. "Jack" Howe, later enlarged the building.Storrer, William Allin.

3D model of a pentagonal pyramid In geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point (the vertex). Like any pyramid, it is self-dual. The regular pentagonal pyramid has a base that is a regular pentagon and lateral faces that are equilateral triangles. It is one of the Johnson solids (J2).

The national flag of The Bahamas The Bahamian flag was adopted in 1973. Its colours symbolise the strength of the Bahamian people; its design reflects aspects of the natural environment (sun and sea) and economic and social development. The flag is a black equilateral triangle against the mast, superimposed on a horizontal background made up of three equal stripes of aquamarine, gold and aquamarine.

For the VOA, the main target areas for the station's shortwave broadcasts were Latin America, the Caribbean with special emphasis on Cuba, and Africa. Three complexes, one for management, distribution, and monitoring, and the other two for actual transmitting, formed an approximately equilateral triangle around Greenville. At one time, these formed the largest international broadcasting site in the world. Two of the three sites have been decommissioned.

In geometry, the elongated dodecahedron,Coxeter (1973) p.257 extended rhombic dodecahedron, rhombo-hexagonal dodecahedronWilliamson (1979) p169 or hexarhombic dodecahedronFedorov's five parallelohedra in R³ is a convex dodecahedron with 8 rhombic and 4 hexagonal faces. The hexagons can be made equilateral, or regular depending on the shape of the rhombi. It can be seen as constructed from a rhombic dodecahedron elongated by a square prism.

A regular tetrahedron is a tetrahedron in which all four faces are equilateral triangles. It is one of the five regular Platonic solids, which have been known since antiquity. In a regular tetrahedron, all faces are the same size and shape (congruent) and all edges are the same length. a thin volume of empty space is left, where the five edge angles do not quite meet.

Not every subset D ⊆ T is a viable domain. In order to support the bisymmetry test D must be symmetric about the planes b = c, c = a, a = b. To support cyclicity it must also be invariant under 2π/3 rotations about the line a = b = c. The simplest domain of all is the line (t,t,t) which corresponds to the set of all equilateral triangles.

Each proposition is illustrated with a crudely drawn diagram. Several lines of text in each proposition were left shorter than the remainder of the text lines in order to leave space in the right of the column for the illustrations. The left column has a parallelogram, and two right-angled triangles, while the right has an equilateral triangle, a stone, and two concentric circles.

The structure of The MO diagram of the trihydrogen cation. The three hydrogen atoms in the molecule form an equilateral triangle, with a bond length of 0.90 Å on each side. The bonding among the atoms is a three-center two-electron bond, a delocalized resonance hybrid type of structure. The strength of the bond has been calculated to be around 4.5 eV (104 kcal/mol).

Trianon is a 45-story, skyscraper in the Westend-Süd district of Frankfurt, Germany, completed in 1993. It is the headquarters for DekaBank; other tenants are Deutsche Bundesbank and Franklin Templeton. Atop the building is an inverted pyramid suspended from the three corners. The Trianon's layout is roughly the shape of an equilateral triangle, the corners of which are formed by three-sided towers.

Diagram illustrating the fact that Napoleon's theorem is a special case of Petr–Douglas–Neumann theorem. In the case of triangles, the value of n is 3 and that of n − 2 is 1. Hence there is only one possible value for k, namely 1. The specialisation of the theorem to triangles asserts that the triangle A1 is a regular 3-gon, that is, an equilateral triangle.

The ovate shell is oblong, transverse, equilateral and inequivalve. The beaks are small; that of the left, slightly notched. The valves are white, diaphanous and smooth, indistinctly marked with striae of increase, rounded at the anterior side, strongly truncated at the posterior side. The side is bounded outwardly by an obtuse angle, pretty prominent, extending obliquely from the beak to the lower part of the shell.

Wes Farrell, now employed at Venus Equilateral, uses the Martian power transmitter to construct a matter transmitter. Kingman sues on behalf of Terran Electric, arguing that the matter transmitter is essentially a power transmitter, and thus falls within Terran Electric's licence. Channing successfully argues that the device is not a transmitter by using it as a matter duplicator, to create multiple copies of the judge's antique watch.

Now that it is possible to duplicate money and precious metals, an economy based on scarcity collapses. The people of the Solar System must fall back on barter, and those too poor to buy matter duplicators are left to their own devices. It is not until the staff of Venus Equilateral invents a material that cannot be duplicated that a monetary system can be re-established.

The squadron's patch consists of a white equilateral triangle, bordered in red, superimposed on a circular blue field. A red Arabic numeral "11" sits on silver prop and wings at the center. The triangle superimposed upon the circle is borrowed from the 6th Bomb Wing, the original squadron sponsor. The silver prop and wings symbolize the cadet wing, while the large "11" identified the 11th Cadet Squadron.

There are streaks of fuscous suffusion mixed silvery-white between veins 9-11 towards the costa and a large equilateral triangular white blotch resting on the upper two- thirds of the termen, limited above by vein 8 and cut by ferruginous lines on 5 and 6. The terminal edge is finely blackish. The hindwings are ochreous- whitish thinly strewn with grey hair-scales. The veins are grey.

3D model of a regular icosahedron In geometry, a regular icosahedron ( or ) is a convex polyhedron with 20 faces, 30 edges and 12 vertices. It is one of the five Platonic solids, and the one with the most faces. It has five equilateral triangular faces meeting at each vertex. It is represented by its Schläfli symbol {3,5}, or sometimes by its vertex figure as 3.3.3.3.

In 1853 William Rowan Hamilton published his Lectures on Quaternions which included presentation of biquaternions. The following passage from page 673 shows how Hamilton uses biquaternion algebra and vectors from quaternions to produce hyperboloids from the equation of a sphere: ::... the equation of the unit sphere , and change the vector to a bivector form, such as . The equation of the sphere then breaks up into the system of the two following, :::, ; ::and suggests our considering and as two real and rectangular vectors, such that :::. ::Hence it is easy to infer that if we assume , where is a vector in a given position, the new real vector will terminate on the surface of a double-sheeted and equilateral hyperboloid; and that if, on the other hand, we assume , then the locus of the extremity of the real vector will be an equilateral but single-sheeted hyperboloid.

Construction of the isodynamic point from reflected copies of the given triangle and inwards-pointing equilateral triangles. The circle of Apollonius through vertex A of triangle ABC may be constructed by finding the two (interior and exterior) angle bisectors of the two angles formed by lines AB and AC at vertex A, and intersecting these bisector lines with line BC. The line segment between these two intersection points is the diameter of the circle of Apollonius. The isodynamic points may be found by constructing two of these circles and finding their two intersection points. Another compass and straight-edge construction involves finding the reflection A' of vertex A across line BC (the intersection of circles centered at B and C through A), and constructing an equilateral triangle inwards on side BC of the triangle (the apex A of this triangle is the intersection of two circles having BC as their radius).

Polistes associus. Male, front view Polistes associus can reach a body length of about in females, of about in workers.Erol Yildirim, Hikmet Ozbek Polistinae (Hymenoptera, Vespidae) of Turkey These wasps are characterized by very light eyes, the ocelli arranged according to an equilateral triangle, completely black mandibles and yellow lateral parts (genae) of the head. The dorsal surface of antennae is black in both sexes, with wide and deep longitudinal groove.

The Pembroke Welsh Corgi has erect ears that are in proportion to the equilateral triangle of the head. The breed standard indicates that the ears should be firm, medium in size, and tapered slightly to a rounded point. The head should be "fox-like" in shape and appearance. Pembroke Welsh Corgis differ from the Cardigan Welsh Corgi by being shorter in length, having smaller ears, and being slightly straighter of leg.

In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope. It has six vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and 6 5-cell facets. It has a dihedral angle of cos−1(), or approximately 78.46°. The 5-simplex is a solution to the problem: Make 20 equilateral triangles using 15 matchsticks, where each side of every triangle is exactly one matchstick.

Yilan Plain (), also called the Lanyang Plain (), or historically Kabalan (), Kapsulan (), Komalan () is a plain in Yilan County, Taiwan. The plain has an alluvial fan which formed by Lanyang River. The plain was formed in the shape of nearly equilateral triangle. The broad and flat feature of this plan has made transportation so convenient in the region which drew large population to the towns and city in the area.

The profile of the breed is generally straight. Their water-resistant coat with a dense undercoat developed to help the cat survive in the harsh Scandinavian climate. Hue distribution in bi-colored Norwegian Forest cats varies widely. The head is long with an overall shape similar to an equilateral triangle, a strong chin, and a muzzle of medium length; a square or round-shaped head is considered to be a defect.

The insignia consists of a red St George cross, in the centre a white globe with the monogram of the institutor, two opposite letters C surrounding XIII, in gold. On the reverse the globe has the letter B in gold in an equilateral black and gold edged triangle. The cross is surmounted by a closed golden crown. The insignia is worn around the neck in a red ribbon.

The synchronous component is in the same manner 3 times the deviation from the "inverse equilateral triangle". The directions of these components are correct for the relevant phase. It seems counter intuitive that this works for all three phases regardless of the side chosen but that is the beauty of this illustration. The graphic is from Napoleon's Theorem, which matches a graphical calculation technique that sometimes appears in older references books.

Ainokura, in the Gokayama region, was inscribed on the World Heritage List in December 1995 as one of the three villages of gassho- style houses. Ainokura has 20 gassho-style houses known as minka. Most of them are 100 to 200 years old, and the oldest is said to have been built some 400 years ago. The gassho roof has a slope of about 60 degrees forming a nearly equilateral triangle.

The four principal monuments – the others being the Robert Burns Memorial, Wilfrid Laurier Memorial, and Queen Victoria Diamond Jubilee Fountain – in the square are arranged to form a five equilateral cross with the kiosk towards the Dominion Square Building. On July 8, 2009, the official first shovelful of dirt was lifted in the $23-million project to restore Dorchester Square and Place du Canada near the Boer War memorial monument.

The circle of the current emblem is ringed with ten stars, that represent the islands of Cape Verde, and is similar to the symbolism on the flag of Cape Verde. The plumbob symbolizes righteousness and uprightness which constitute the "key vault" of Cape Verdean constitution. The equilateral triangle symbolizes unity, equality and people's civil rights recognized by the democratic system. The torch symbolizes freedom gained after many years of struggle.

If the faces of a disphenoid are equilateral triangles, it is a regular tetrahedron with Td tetrahedral symmetry, although this is not normally called a disphenoid. When the faces of a disphenoid are isosceles triangles, it is called a tetragonal disphenoid. In this case it has D2d dihedral symmetry. A sphenoid with scalene triangles as its faces is called a rhombic disphenoid and it has D2 dihedral symmetry.

Furthermore, the angle of an Isosceles Triangle or the number of sides of a (regular) Polygon may be altered during life by deeds or surgical adjustments. An equilateral triangle is a member of the craftsman class. Squares and Pentagons are the "gentlemen" class, as doctors, lawyers, and other professions. Hexagons are the lowest rank of nobility, all the way up to (near) Circles, who make up the priest class.

His assignment of the letters P, Q, R, S and T to the various deflections are still used. The term Einthoven's triangle is named after him. It refers to the imaginary inverted equilateral triangle centered on the chest and the points being the standard leads on the arms and leg. After his development of the string galvanometer, Einthoven went on to describe the electrocardiographic features of a number of cardiovascular disorders.

If the horizontal base of the triangle is on top and the opposing vertex below, the child may recognize it as a triangle, but claim it is "upside down". Shapes with rounded or incomplete sides may be accepted as "triangles" if they bear a holistic resemblance to an equilateral triangle. Squares are called "diamonds" and not recognized as squares if their sides are oriented at 45° to the horizontal.

Persicaria perfoliata has a reddish stem that is armed with downward pointing hooks or barbs which are also present on the underside of the leaf blades. The light green leaves are shaped like an equilateral (equal-sided) triangle and alternate along the narrow, delicate stems. Distinctive circular, cup-shaped leafy structures, called ocreass, surround the stem at intervals. Flower buds, and later flowers and fruits, emerge from within the ocreas.

A group of lattice constants could be referred to as lattice parameters. However, the full set of lattice parameters consist of the three lattice constants and the three angles between them. For example, The lattice constant for diamond is at 300 K. The structure is equilateral although its actual shape cannot be determined from only the lattice constant. Furthermore, in real applications, typically the average lattice constant is given.

Hobart, Mike (May 27, 2011) "Craig Taborn, Vortex, London". ft.com. Taborn toured internationally with his own trio,Watson, Walter Ray (April 4, 2012) "Equilateral Triangles: The Challenge of the Modern Piano Trio". npr. Anker's trio,Hobart, Mike (April 18, 2012) "Anker, Taborn, Cleaver, Vortex Jazz Club, London". ft.com. and with Dave Holland's quartet Prism in 2012,Hum, Peter (June 25, 2012) "Prism Filled Air with Vivid, Visceral Music".

An essential element for the band's image is the Slipknot logo. The nonagram was created by the band's members around the same time the band was founded. The nonagram is arguably the best-known sigil of Slipknot and it represents a 9-point star—a symbol of unity, loyalty, friendship and remembrance. The logo is composed of three equilateral triangles each rotated at 0, 40, and 80 degrees.

Structure of boron trifluoride, an example of a molecule with trigonal planar geometry. In chemistry, trigonal planar is a molecular geometry model with one atom at the center and three atoms at the corners of an equilateral triangle, called peripheral atoms, all in one plane. In an ideal trigonal planar species, all three ligands are identical and all bond angles are 120°. Such species belong to the point group D3h.

Dissection of a square and equilateral triangle into each other. No such dissection exists for the cube and regular tetrahedron. In two dimensions, the Wallace–Bolyai–Gerwien theorem states that any two polygons of equal area can be cut up into polygonal pieces and reassembled into each other. David Hilbert became interested in this result as a way to axiomatize area, in connection with Hilbert's axioms for Euclidean geometry.

A rectangle is an equiangular quadrilateral A convex equiangular octagon with 4-fold reflective symmetry A nonconvex equiangular hexagon with 3-fold reflectional symmetry In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths.

They generally have one long axis and concave or convex edges, and it is possible for them to have a gibbosity (hump) or indentations. Triangular microliths may be isosceles, scalene or equilateral. In the case of trapezoid geometric microliths, on the other hand, the notches are not retouched, leaving a portion of the natural edge between them. Trapezoids can be further subdivided into symmetrical, asymmetrical and those with concave edges.

Conditions are known in terms of elliptic curves for an integer triangle to have an integer ratio N of the circumradius to the inradius.MacLeod, Allan J., "Integer triangles with R/r = N", Forum Geometricorum 10, 2010: pp. 149−155.Goehl, John F. Jr., "More integer triangles with R/r = N", Forum Geometricorum 12, 2012: pp. 27−28 The smallest case, that of the equilateral triangle, has N=2.

Icosahedron-20 sided polyhedron. All six genera in the family Phycodnaviridae have similar virion structure and morphology. They are large virions that can range between 100–220 nm in diameter. They have a double-stranded DNA genome, and a protein core surrounded by a lipid bilayer and an icosahedral capsid. The capsid has 2, 3 and 5 fold axis of symmetry with 20 equilateral triangle faces composing of protein subunits.

The portal is constituted by a triangular-shaped pediment upon two round columns. At the centre of the pediment, there is an equilateral triangle, symbol of Trinity, inscribed by "the eye of God." The columns fuse Greek (Ionic, Doric and Corinthian) and Roman (Tuscan and composite) styles, each one with a capital crowned by a finial globe. There are three steps between the columns leading to the Temple entrance.

For example, the square, with its four equilateral sides, is symbolic of the equally important elements of nature: earth, air, fire and water. Without any one of the four, the physical world, represented by a circle that inscribes the square, would collapse upon itself and cease to exist. The second mode is based upon the flowing nature of plant forms. This mode recalls the feminine nature of life giving.

The Sierpiński arrowhead curve is a fractal curve similar in appearance and identical in limit to the Sierpiński triangle. Evolution of Sierpiński arrowhead curve The Sierpiński arrowhead curve draws an equilateral triangle with triangular holes at equal intervals. It can be described with two substituting production rules: (A → B-A-B) and (B → A+B+A). A and B recur and at the bottom do the same thing — draw a line.

Domestic objects represent the transition from tent structure to house. All the houses share a very distinct shape, built according to a complicated geometric pattern. The basis of each of the houses is a circle segment of exactly 60 degrees, constructed in the manner of an equilateral triangle. The tip of the trapezoid base, a shape previously unknown in human settlements, is pointed into the direction of the wind (košava).

Properties of the molecules can be discovered by Coulomb explosion imaging. In this process, a laser ionizes all three atoms simultaneously, which then fly away from each other due to electrostatic repulsion and are detected. The helium trimer is large, being more than 100 Å, which is even larger than the helium dimer. The atoms are not arranged in an equilateral triangle, but instead form random shaped triangles.

The site consists of 3 platform mounds that form an equilateral triangle. Mound A, the southwesternmost of the group, measures in height, with the base being by . Mound B, the northernmost mound, is a dome shaped mound measuring in height, with the base being by . The northernmost mound in the triangle, Mound C, is also a dome shaped mound and measures in height, with the base being by .

Seal of the First Republic The First Philippine Republic featured a seal composed of an equilateral triangle with three stars representing Luzon, Visayas, and "Mindanao and Sulu" and an eight-rayed sun. There were several variations of the seal such as different arrangement of the stars and the presence or absence of a face on the sun. The Republic of Biak- na-Bato, and Malolos Republic also used seals.

The Mukhopadhyay module can form any equilateral polyhedron. Each unit has a middle crease that forms an edge, and triangular wings that form adjacent stellated faces. For example, a cuboctahedral assembly has 24 units, since the cuboctahedron has 24 edges. Additionally, bipyramids are possible, by folding the central crease on each module outwards or convexly instead of inwards or concavely as for the icosahedron and other stellated polyhedra.

The repetitive detail of buttressing, parapeted gable, cross finial and carved skew stones on the small size of the vestry form make this section of the church appear elaborately detailed. The pointed arch entry with hood mould and carved label stops sits below a small equilateral arched window in the gable. An elaborate window on the eastern side of the vestry is of stone tracery within a segmental arch opening.

Top of the 12 edged trunk is surrounded by two-layered stalactite corbel, used as a crossover to the inner cupola, which is folded by stone blocks. Foundations of two minarets attached to portal are prolonged rectangular prisms. Facades of the foundations are treated with patterned placing framed with trilobite equilateral arch. Not tall, octahedral bulk is used as a pedestrian to cylindrical trunks of the minarets built of circle brick.

The diagonal of the unit cube is . This projection of the Bilinski dodecahedron is a rhombus with diagonal ratio . The square root of 3 can be found as the leg length of an equilateral triangle that encompasses a circle with a diameter of 1. If an equilateral triangle with sides of length 1 is cut into two equal halves, by bisecting an internal angle across to make a right angle with one side, the right angle triangle's hypotenuse is length one and the sides are of length and . From this the trigonometric function tangent of 60° equals , and the sine of 60° and the cosine of 30° both equal . The square root of 3 also appears in algebraic expressions for various other trigonometric constants, includingJulian D. A. Wiseman Sin and Cos in Surds the sines of 3°, 12°, 15°, 21°, 24°, 33°, 39°, 48°, 51°, 57°, 66°, 69°, 75°, 78°, 84°, and 87°.

System A used the Dunay-2 designed by V Sosulnikov at NII-37 (which later became NIIDAR) as well as 3 homing radars and an ABM radar. The three homing radars (called RTN (NATO:Hen Egg)) were situated in an equilateral triangle with a length of . It could track missiles from a distance of about . The V-1000 launch position and the ABM radar (called RSV-PR (NATO: Hen Nest)) were located together.

Göbekli Tepe follows a geometric pattern. The pattern is an equilateral triangle that connects enclosures A, B, and D. This means that the people who built Göbekli Tepe had at least some rudimentary knowledge of geometry. The authors of the paper discuss the implications of their findings. The authors suggest that enclosures A, B, and D are all one complex, and within this complex there is a "hierarchy" with enclosure D at the top.

The three collinear Lagrange points (L1, L2, L3) were discovered by Leonhard Euler a few years before Joseph-Louis Lagrange discovered the remaining two. (16MB) In 1772, Lagrange published an "Essay on the three-body problem". In the first chapter he considered the general three-body problem. From that, in the second chapter, he demonstrated two special constant-pattern solutions, the collinear and the equilateral, for any three masses, with circular orbits.

A monochromator can use either the phenomenon of optical dispersion in a prism, or that of diffraction using a diffraction grating, to spatially separate the colors of light. It usually has a mechanism for directing the selected color to an exit slit. Usually the grating or the prism is used in a reflective mode. A reflective prism is made by making a right triangle prism (typically, half of an equilateral prism) with one side mirrored.

Commerzbank Tower is shaped as a wide rounded equilateral triangle with a central, triangular atrium. At nine different levels, the atrium opens up to one of the three sides, forming large sky gardens. These open areas allow more natural light in the building, reducing the need for artificial lighting. At the same time it ensures offices in the building's two other sides have a view of either the city or the garden.

Apart from the trivial cases of equilateral triangles, the triangle with side lengths 17, 13, and 7 is the smallest (by area or perimeter) automedian triangle with integer side lengths. There is only one automedian right triangle, the triangle with side lengths proportional to 1, , and . This triangle is the second triangle in the spiral of Theodorus. It is the only right triangle in which two of the medians are perpendicular to each other.

Carpobrotus dimidiatus (commonly known as Natal sourfig) is a succulent perennial of the family Aizoaceae, native to KwaZulu-Natal, South Africa. The flowers of this Carpobrotus ("Sour-fig") species range bright pink to mauve. It can be difficult to distinguish from the other 5 southern African Sour-fig species, but its leaves are long, thin and equilateral triangular in cross- section. This species's flower base is also strongly and distinctively double- ridged.

Tajug seen here on the roof of Wustho Mangkunegaran Mosque, Surakarta. Tajug is a pyramidal or pyramid square (i.e. an equilateral square base with a peak) ornament which is usually used for sacred buildings in Southeast Asia including Indonesia, such as mosque or cupola graveyard. It is considered derived from Indian and Chinese architecture, which has history since pre- Islamic era, although there's also an element of an influence from Indian mosque.

The darker striae (crosslines) are indistinct and obtusely angulated. The edges of a vague geniculate median band are marked faintly darker, especially as two dark costal spots which form the corners of an equilateral triangle with the discal spot. The forewing fringes are chequered to not chequered. The hindwings are fuscous with only very faint striae and fasciae; even less conspicuously patterned than the forewings but with a clear dark fuscous, shortly linear discal mark.

Equilateral triangle constructed on a Lenart sphere. Other products for studying spherical geometry include visualization software programs such as The Geometer's Sketchpad, GeoGebra and Spherical Easel (see External links for Spherical Easel information, and visit List of interactive geometry software for non-Euclid, and many other interactive Projective geometry apps and programs). Where these products only work on a flat plane, the Lénárt sphere is giving hands-on experience of spherical geometry.

If there are 3 electron pairs surrounding the central atom, their repulsion is minimized by placing them at the vertices of an equilateral triangle centered on the atom. Therefore, the predicted geometry is trigonal. Likewise, for 4 electron pairs, the optimal arrangement is tetrahedral. As a tool in predicting the geometry adopted with a given number of electron pairs, an often used physical demonstration of the principle of minimal electron pair repulsion utilizes inflated balloons.

The shell has an equilateral-triangle profile, being approximately as tall as it is wide. The whorls are slightly inflated and are sculpted with strongly beaded spiral threads and a row of splayed hollow spines along the shoulder. A smaller second row of spines is situated below the shoulder on the last whorl. The base color of the shell is lavender to reddish purple with golden maculations outlined in a darker purple.

A right triangular prism is semiregular or, more generally, a uniform polyhedron if the base faces are equilateral triangles, and the other three faces are squares. It can be seen as a truncated trigonal hosohedron, represented by Schläfli symbol t{2,3}. Alternately it can be seen as the Cartesian product of a triangle and a line segment, and represented by the product {3}x{}. The dual of a triangular prism is a triangular bipyramid.

The rachis (leaf axis) is densely covered in pubescent hairs, but lacks scales. From 15 to 44 pairs of pinnae are present. Each pinna is approximately equilateral in shape, has from 3 to 8 pairs of lobes, which may be cut as shallowly as one-fourth or as deeply as three-fourths of the distance to the costa (pinna axis). The number of lobes and deepness of cutting can vary a great deal between individuals.

A self-made man, Wright respected him and allowed him to design many details including all door hardware, the stainless steel kitchenettes and even the diving board support. This sprawling Usonian is one of Wright's most extensive single-story residences. Three wings spin off a central hexagon much as might have happened had Wingspread been based on an equilateral parallelogram rather than a square. The home is organized around a massive angular fireplace.

The Insignia was designed for the use of the national organization or local chapters. Parts of the Insignia are the equilateral triangle with the words Physical, Intellectual, and Spiritual making up the three sides, an ATA bond of fellowship that ties the sides together, the open book and the lamp of knowledge, supported by two sheaves of wheat. The Insignia is protected by copyright. The official colors of Alpha Tau Alpha are orange and brown.

Spore prints are dark brown, sometimes with violet shades. Spores are thick-walled with an apical pore, and elongated ellipsoid to equilateral in face view, and somewhat inequilateral in side view, typically measuring 12.0–12.6–13.1 by 6.8–7.1–7.4 μm. The basidia (spore-bearing cells) are cylindrical, four-spored with sterigmata up to 5.5 μm long, and have dimensions of 27–37 by 9–11 μm. Clamp connections are present in hyphae.

The British decimal twenty pence (20p) coin – often pronounced "twenty pee" – is a unit of currency equal to 20/100 (or 1/5) of a pound sterling. Like the 50p coin, it is an equilateral curve heptagon. Its obverse has featured the profile of Queen Elizabeth II since the coin's introduction on 9 June 1982. Four different portraits of the Queen have been used; the latest design by Jody Clark was introduced in 2015.

For this reason, template racks are almost never used for games where it is common to slow-break (i.e. not create a large spread of balls) since it is significantly more likely that the rack will interfere with slow-rolling balls. The most common shape of a rack is that of an equilateral triangle. Triangular racks are used for eight- ball, straight pool, one-pocket, bank pool, snooker and many other games.

The triangle medians and the centroid. In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid. In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose two adjacent sides are equal in length.

The use of the equilateral triangle was given a theological explanation - the three sides represented the Holy Trinity. In the later years of the flamboyant Gothic the arches and windows often took on more elaborate forms, with tracery circles and multiple forms within forms. Some used a modification of the horseshoe arch, borrowed from Islamic architecture. The Tudor Arch of the Late Gothic style was a variation of the Islamic Four-centred arch.

The boundary of a Reuleaux triangle is a constant width curve based on an equilateral triangle. All points on a side are equidistant from the opposite vertex. A Reuleaux triangle is a shape formed from the intersection of three circular disks, each having its center on the boundary of the other two. Its boundary is a curve of constant width, the simplest and best known such curve other than the circle itself.

Position of some special triangles in an Euler diagram of types of triangles, using the definition that isosceles triangles have at least two equal sides, i.e. equilateral triangles are isosceles. A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°.

In iconography it is represented by the six-pointed star, the two interlocking offset equilateral triangles that form a symmetry. This is the 'sanctum sanctorum' (Sanskrit: garbha gṛha). It later developed into the primordial purity of the lotus which supports the mandala, thangka or the murti of the deity. In temple siting it is the power place or 'spirit of place' that was augured or divined in the sacred geometry of 'geodesy' (Sanskrit: vāstu śāstra).

This invariance is the defining property of a triangle center. It rules out other well-known points such as the Brocard points which are not invariant under reflection and so fail to qualify as triangle centers. All centers of an equilateral triangle coincide at its centroid, but they generally differ from each other on scalene triangles. The definitions and properties of thousands of triangle centers have been collected in the Encyclopedia of Triangle Centers.

E.F.) to close propositions that were not proofs of theorems, but constructions of geometric objects. For example, Euclid's first proposition showing how to construct an equilateral triangle, given one side, is concluded this way. Many times, mathematicians will only utilize () faciendia as a result of the results of previous definitions or demonstradums. An idea of this is expressed within Topics (Aristotle), where he goes over the difference between a proposition and a problem.

An ogive or ogival arch is a pointed, "Gothic" arch, drawn with compasses as outlined above, or with arcs of an ellipse as described. A very narrow, steeply pointed ogive arch is sometimes called a "lancet arch". The most common form is an equilateral arch, where the radius is the same as the width. In the later Flamboyant Gothic style, an "ogee arch", an arch with a pointed head, like S-shaped curves, became prevalent.

The work began modestly as Twenty-Five Women Who Were Eaten Alive, a way in which Chicago could use her "butterfly-vagina" imagery and interest in china painting in a high-art setting. Chicago soon expanded it to include the thirty-nine final women arranged in three groups of thirteen. The triangular shape has significance because it has long been a symbol of the female. It is also an equilateral triangle to represent equality.

A triangular banner appearing to depict a bird (possibly a raven) appears on a penny minted by Olaf Cuaran around 940. The coin features a roughly right isosceles triangular standard, with the two equilateral sides situated at the top and staff, respectively. Along the hypotenuse are a series of five tabs or tassels. The staff is topped by what appears to be a cross; this may indicate a fusion of pagan and Christian symbolism.

The ovate shell is oblong, transverse, equilateral, inequivalve and slightly inflated. it is of a reddish white color, covered with a browner shagreened epidermis, and marked with irregular and more or less numerous striae of increase. The beaks are short, and that of the right valve is notched at its summit to receive that of the left valve. The valves are pretty thick, rounded at the anterior, and truncated at the posterior side.

If the faces are equilateral triangles, it is a deltahedron and a Johnson solid (J13). It can be seen as two pentagonal pyramids (J2) connected by their bases. :200px The pentagonal dipyramid is 4-connected, meaning that it takes the removal of four vertices to disconnect the remaining vertices. It is one of only four 4-connected simplicial well- covered polyhedra, meaning that all of the maximal independent sets of its vertices have the same size.

Instead of using the Montgomery Ward nameplate, however, Montgomery Ward would use the nameplate of its subsidiary brand, The Fair Department Store (a.k.a. "the Fair"), on its anchor store. Randhurst was designed by Victor Gruen, a pioneer of modern shopping mall design. Unlike most shopping malls of the time, which were built in a straight line between two anchoring department stores, Gruen's design was shaped like an equilateral triangle, with an anchoring department store at each angle.

The algorithm is similar to the one which generates a directional spectrum from data on heave (vertical motion), pitch and roll at a single location, as provided by a disc-shaped wave buoy. An array of three vertical radars, having footprints at the vertices of a horizontal, equilateral triangle, can provide the necessary data on water surface elevation. “Directional WaveGuide” is a commercial radar system based on this technique. It is available from the Dutch companies Enraf and Radac.

Some viruses, such as bacteriophages, have developed more complicated structures due to constraints of elasticity and electrostatics. The icosahedral shape, which has 20 equilateral triangular faces, approximates a sphere, while the helical shape resembles the shape of a spring, taking the space of a cylinder but not being a cylinder itself. The capsid faces may consist of one or more proteins. For example, the foot-and-mouth disease virus capsid has faces consisting of three proteins named VP1–3.

Plato (427–347 BCE) took over the four elements of Empedocles. In the Timaeus, his major cosmological dialogue, the Platonic solid associated with air is the octahedron which is formed from eight equilateral triangles. This places air between fire and water which Plato regarded as appropriate because it is intermediate in its mobility, sharpness, and ability to penetrate. He also said of air that its minuscule components are so smooth that one can barely feel them.

Empedocles roots became the four classical elements of Greek philosophy. Plato (427–347 BC) took over the four elements of Empedocles. In the Timaeus, his major cosmological dialogue, the Platonic solid associated with water is the icosahedron which is formed from twenty equilateral triangles. This makes water the element with the greatest number of sides, which Plato regarded as appropriate because water flows out of one's hand when picked up, as if it is made of tiny little balls.

Solutions in which all masses move on the same curve without collisions are called choreographies.Celletti 2008 A choreography for was discovered by Lagrange in 1772 in which three bodies are situated at the vertices of an equilateral triangle in the rotating frame. A figure eight choreography for was found numerically by C. Moore in 1993 and generalized and proven by A. Chenciner and R. Montgomery in 2000. Since then, many other choreographies have been found for .

The building has been nicknamed the 'sliced egg' because of its distinctive shape. A focal point is the diagonal slice which creates a nine-floor high atrium with its glass roof tilted towards the south, maximising daylight and passive solar gain. The structure has three internal concrete cores in the form of an equilateral triangle. Steel was utilised as the building main material; its strength allows for large column-free floors needed in an open plan building.

The Ancient and Mystical Order Rosae Crucis, commonly known as the Rosicrucian Order, AMORC, is the largest Rosicrucian group today, with twenty-three Grand Lodges or Jurisdictions worldwide. There are two primary versions used by the Ancient Mystical Order Rosae Crucis. One is a Gold Latin Cross with a Rose at its center. Another is a downward pointing triangle with a Greek (equilateral) Cross inscribed within the triangle and a top oval reminiscent of an Egyptian Ankh.

The isodynamic points S and S' of a triangle ABC may also be defined by their properties with respect to transformations of the plane, and particularly with respect to inversions and Möbius transformations (products of multiple inversions). Inversion of the triangle ABC with respect to an isodynamic point transforms the original triangle into an equilateral triangle. Inversion with respect to the circumcircle of triangle ABC leaves the triangle invariant but transforms one isodynamic point into the other one.; .

He is restrained by a disbelieving Skinner and then sedated in a hospital. Mulder tells Scully that he saw the monster doing something to the back of his victim's head, begging her to look for similar evidence on Backus's body. Scully finds three puncture marks at the top of Backus's spine, marking the corners of an equilateral triangle. Meanwhile, Mulder, still restrained in his bed at the hospital, sees the silhouette of the monster at the window.

The nearby Highway 49 is a winding, scenic highway that follows the contours of the foothills of the Sierra Nevada Mountain range. The top 70 feet of the bridge columns have an equilateral triangular shape to support the four lanes of proposed superstructure. The initial 2-lanes were placed on the outside radius, so eccentric loading analysis of the columns was necessary. The foundation was excavated rock and is essentially hexagonal in shape to stabilize the column.

The highest symmetry forms are D2d, order 8, while if the underlying rectangular cuboid is distorted into a rhombohedron, the symmetry is reduced to 2-fold rotational symmetry, C2, order 2. It has all 3-valence vertices and its dual has all triangular faces, including the snub disphenoid as a deltahedron with all equilateral triangles.Dual of Snub Disphenoid (J84) However the dual of the snub disphenoid is not space-filling because the pentagons are not right-angled.

Some considered that setting out also involved the > use of equilateral or Pythagorean triangles, pentagons, and octagons. Two > authors believe the Golden Section (or at least its approximation) was used, > but its use in medieval times is not supported by most architectural > historians. The Australian architectural historian John James made a detailed study of the Cathedral of Chartres. In his work The Master Masons of Chartres he says that Bronze, one of the master masons, used the golden ratio.

In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, and is the only such tiling where the constituent shapes are not parallelogons. Because the internal angle of the equilateral triangle is 60 degrees, six triangles at a point occupy a full 360 degrees. The triangular tiling has Schläfli symbol of {3,6}. Conway calls it a deltille, named from the triangular shape of the Greek letter delta (Δ).

69–72 (illustrating examples), Routledge, 2001, , , Google books but this iconography became rare. When the Father is depicted in art, he is sometimes shown with a halo shaped like an equilateral triangle, instead of a circle. The Son is often shown at the Father's right hand. He may be represented by a symbol—typically the Lamb or a cross—or on a crucifix, so that the Father is the only human figure shown at full size.

All the symbols on the shield may be used for jewelry, recognition pins, stationery, and formal clothing. From the upper left to lower right is the "bar" or "band" displaying three Greek sigmas. Above the band in the right third are spreading wings joined by a centered circle, and above these is an equilateral triangle on which is engraved a single Sigma. Below the wings are clasped hands and in the lower left third is a flaming urn.

On the banner below the shield are the words in Greek of the sorority's open motto, "Faithful Unto Death". Adopted in 1903, the badge of the sorority is an equilateral gold triangle bordered with pearls, with a small semi circular indentation on each side. On the gold triangle is a raised black enamel triangle bearing a gold sigma in each corner. In the center of the badge is another symbol of the sorority, a skull and crossbones.

The overall feel of the design is minimalist and brutalist. The exterior of the church building is constructed mostly of red brick, with a massive cast concrete belfry rising from its roof to a height of above the surrounding terrain. In contrast, the interior is light, with white walls and large windows providing natural daylight. The basic shape of the overall floorplan is an equilateral triangle, with two of the three points cut off, forming an irregular pentagon.

The Laser Interferometer Space Antenna (LISA) is a proposed space probe to detect and accurately measure gravitational waves—tiny ripples in the fabric of space-time—from astronomical sources. LISA would be the first dedicated space-based gravitational wave detector. It aims to measure gravitational waves directly by using laser interferometry. The LISA concept has a constellation of three spacecraft arranged in an equilateral triangle with sides 2.5 million km long, flying along an Earth-like heliocentric orbit.

By the law of cosines, every angle of an integer triangle has a rational cosine. If the angles of any triangle form an arithmetic progression then one of its angles must be 60°. For integer triangles the remaining angles must also have rational cosines and a method of generating such triangles is given below. However, apart from the trivial case of an equilateral triangle there are no integer triangles whose angles form either a geometric or harmonic progression.

Between and , there was an enclosed observation deck, entered at and reached via two quick elevators. It was the only tower in the world to have an equilateral triangle as its cross section, and one of very few towers not perched directly into the ground, but standing on its legs. The legs formed a tripod, the symbol of Serbian tripod chair (tronožac). It is one of the small number of towers to be constructed in that manner.

Mountain coral heath was first formally described in 1810 by Lilian Fraser and Joyce Vickery, who gave it the name Epacris microphylla var. rhombifolia. The description was published in Journal and Proceedings of the Linnean Society of New South Wales. The variety was raised to species level in 2015 by Yvonne Menadue and Ron Crowden. The specific epithet (rhombifolia) is derived from the Latin words rhombus meaning "an equilateral parallelogram with unequal pairs of angles" and folium meaning "leaf".

Controversy is associated to the claim that this occurrence was a unique event. Grand trines, where planets are at 120 degree positions forming an equilateral triangle are not uncommon or particularly noteworthy. Traditional astrology does not consider trines to be action points, so the notion of a special shift in world history would not be in the offing under a grand trine. Hence, many traditional astrologers do not regard this occurrence to be of significant importance.

Olympic triangle Traditionally the configuration of the triangle is an equilateral triangle (3 equal sides and 3 equal angles of 60 degrees) with a ratio of the windward leg to a reaching leg being 1:1. In that case the course length for the 9 legs described above is 9 times the length of the windward leg. The angle at each point of the triangle is 60 degrees. The windward leg is generally aligned with the average wind direction.

Atoll Research Bulletin, 190. "Almost-Atoll of Aitutaki: Reef Studies in the Cook Islands", D. R. Stoddard, P. E. Gibbs (eds) August 13, 1975 (12.5 MB) For the lagoon, area figures between are found. Satellite image measurement suggests that the larger figure also includes the reef flat, which is commonly not considered part of a lagoon. The barrier reef that forms the basis of Aitutaki is roughly the shape of an equilateral triangle with sides in length.

The three launchpads are arranged in the form of an equilateral triangle, whose sides point toward the east and the south. The distance between the launchpads is approximately 50 meters. The circular concrete pads on which the Bachem Ba 349s and their launch towers once stood still exist. In the center of each of the three concrete plates is a square hole approximately 50 centimeters deep, which once served as the foundation for the launch tower.

The national flag of Cuba () consists of five alternating stripes (three blue and two white) and a red equilateral triangle at the hoist, within which is a white five-pointed star. It was designed in 1849 and officially adopted May 20, 1902. The flag is referred to as the Estrella Solitaria, or the Lone Star flag. It is one of the two flags of a currently communist country (the other being Laos) that does not use any communist symbolism.

However, cyclic , where the sulfur atoms are arranged in an equilateral triangle with three single bonds (similar to cyclic ozone and cyclopropane), is calculated to be lower in energy than the bent structure experimentally observed. The name thiozone was invented by Hugo Erdmann in 1908 who hypothesized that comprises a large proportion of liquid sulfur. However its existence was unproven until the experiments of J. Berkowitz in 1964. Using mass spectrometry, he showed that sulfur vapour contains the molecule.

The constellation Triangulum Australe, the southern triangle, as it can be seen by the naked eye Triangulum Australe is a small constellation bordered by Norma to the north, Circinus to the west, Apus to the south and Ara to the east. It lies near the Pointers (Alpha and Beta Centauri), with only Circinus in between. The constellation is located within the Milky Way, and hence has many stars. A roughly equilateral triangle, it is easily identifiable.

Another distance measure commonly used in agglomerative clustering is the distance between the centroids of pairs of clusters, also known as the weighted group method. It can be calculated easily in constant time per distance calculation. However, it is not reducible. For instance, if the input forms the set of three points of an equilateral triangle, merging two of these points into a larger cluster causes the inter- cluster distance to decrease, a violation of reducibility.

Burgin, M., Theory of Knowledge: Structures and Processes (Singapore: World Scientific, 2017), p. 468. Examples of this are "the victor in Jena" and "the loser in Waterloo", or "the equilateral triangle" and "the equiangular triangle"; in both cases, both names express different meanings, but designate the same object. There are names which have no meaning, but have the role of designating an object: "Aristotle", "Socrates", and so on. Finally, there are names which designate a variety of objects.

The crossing is separated from the nave by a massive transverse arches. Whole building body have 34 monumental tracery windows, most of them tripled. Nine of them with lancet arch, 14 equilateral arch. The church was primarily constructed as fair faced brick work (Flemish bond), the first brick Gothic building in the region but using also stone (for arches, quoins, dripstones, embrasures, dripstones, water tables, pliths gargoyles) from the local area - Stránská skála quarry – crinoid limestone.

A newer strategy, credited to Felix Shardlow from the Brighton Ultimate team, is called Hexagon Offence. Players spread out in equilateral triangles, creating a hexagon shape with one player (usually not the thrower) in the middle. They create space for each other dynamically, aiming to keep the disc moving by taking the open pass in any direction. This maximizes options, changes the angles of attack rapidly, and hopes to create and exploit holes in the defense.

Triangle and Robert is a webcomic by Patrick Shaughnessy that ran from August 1999 to September 2007. It is about the adventures of two polygons, an equilateral triangle named 'Triangle', and a rhombus named 'Robert'. As Patrick Shaughnessy, appearing in the strip as 'the Cartoonist', has explained on many occasions, he can't draw, and he makes up the story as he goes along. All of the characters are simple shapes that he creates using a cheap paint program.

The plan of the sub-base of the Dome is triangular, equilateral, and with an arch in the centre of each side. The two arches in the sides are those leading from the Rotunda, whilst the arch in the base leads into the Serpentine Passage. This passage, with its curving walls and over-arching vaults, is rich in mosaics of varied design. At the end of the Serpentine Passage, a further arch leads into the Rectangular Chamber.

This 12.3 megapixel resolution is interpolated from the approximately 6 million photodiodes on the Fujifilm 4th generation Super CCD HR sensor. While still a Bayer filter CCD with 3 million green, 1.5 million each red and blue photodiodes, the SuperCCD HR array is tilted 45 degrees. Fujifilm states that its larger equilateral octagonal photodiodes, tilted arrangement, and use of the photoelectric sensing capability of CCD vertical transfer paths enable 12 million output pixels. It has dual memory slots.

The lancet windows at each location are positioned under an equilateral pointed stone arch, with simple hood mould complete with a cube form label stop.Heritas Architecture CMP 2014, pp.14-16 The parapeted gable roof, covered in compressed fibrous cement shingles, has small gabled roof vents - one for each bay - near the ridge line. The eastern parapet is topped with a cross finial, and the skew stones of the parapet are detailed with a trefoil carving.

The Distinguished Public Service Medal is a gold disc 40 mm in height and 36.5 mm in width, with a laurel wreath on the lower half of the rim representing non- military service. Superimposed on the disc is an equilateral triangle which symbolizes the civilian. Displayed on the triangle is the eagle of the Great Seal of the United States. The reverse of the medal bears the inscription AWARDED TO...FOR DISTINGUISHED PUBLIC SERVICE TO THE UNITED STATES ARMY.

After escaping from prison, Hellion Murdoch teams up with Kingman. Kingman will use Terran Electric's research lab to create energy weapons, and Murdoch will mount the weapons in his ship, the Black Widow, and blackmail interplanetary commerce. When news of Murdoch's escape reaches Venus Equilateral, Channing realizes the station will be his first target. The station's staff design a set of missiles that will home in on the Black Widow, and they succeed in destroying it.

Another theory is that the Babylonians subdivided the circle using the angle of an equilateral triangle as the basic unit, and further subdivided the latter into 60 parts following their sexagesimal numeric system. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle. A chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree.

He solved some of them and discussed the conditions of solvability. For example, he was able to solve the problem of inscribing an equilateral pentagon into a square, resulting in a fourth degree equation.Jan Hogendijk (1984) "al-Kuhi's construction of an equilateral pentagon in a given square", Zeitschrift für Gesch. Arab.-Islam. Wiss. 1: 100-144; correction and addendum Volume 4, 1986/87, p.267 He also wrote a treatise on the "perfect compass", a compass with one leg of variable length that allows users to draw any conic section: straight lines, circles, ellipses, parabolas and hyperbolas.Jan Hogendijk (2008) "Two beautiful geometrical theorems by Abu Sahl Kuhi in a 17th century Dutch translation", Ta'rikh-e Elm: Iranian Journal for the History of Science 6: 1-36 It is likely that al-Qūhī invented the device. Alt URL Reviews: Seyyed Hossein Nasr (1998) in Isis 89 (1) pp. 112-113 ; Charles Burnett (1998) in Bulletin of the School of Oriental and African Studies, University of London 61 (2) p.

The recent possible detection of the existence of Iberian lynx in the area between the Cofio and Alberche rivers is testament to the biodiversity of the area. Taking advantage of the orography, there are several reservoirs and dams in the region, with the Santillana reservoir being the largest. Peñalara: The Guadarrama mountain range's highest peak. When looking at a map of the Province of Madrid, it can be seen that it is almost an equilateral triangle, in whose center would be the city.

Therefore, A lies on FP. The lines joining the centers of the circles in Fig. 2 are perpendicular to the line segments AP, BQ and CR. For example, the line joining the center of the circle containing ARB and the center of the circle containing AQC, is perpendicular to the segment AP. So, the lines joining the centers of the circles also intersect at 60° angles. Therefore, the centers of the circles form an equilateral triangle. This is known as Napoleon's Theorem.

The Schläfli symbol is a recursive description, starting with {p} for a p-sided regular polygon that is convex. For example, {3} is an equilateral triangle, {4} is a square, {5} a convex regular pentagon and so on. Regular star polygons are not convex, and their Schläfli symbols {p/q} contain irreducible fractions p/q, where p is the number of vertices, and q is their turning number. Equivalently, {p/q} is created from the vertices of {p}, connected every q.

"Introduction to Chemical and Structural Defects in Crystalline Solids", in Treatise on Solid State Chemistry Volume 1, Springer. The most common example of stacking faults is found in close-packed crystal structures. Face-centered cubic (fcc) structures differ from hexagonal close packed (hcp) structures only in stacking order: both structures have close-packed atomic planes with sixfold symmetry — the atoms form equilateral triangles. When stacking one of these layers on top of another, the atoms are not directly on top of one another.

Atlantis 's main engines during launch Three Space Shuttle Main Engines (SSMEs) were mounted on the orbiter's aft fuselage in the pattern of an equilateral triangle. These three liquid-fueled engines could be swiveled 10.5 degrees vertically and 8.5 degrees horizontally during the rocket-powered ascent of the orbiter in order to change the direction of their thrust. Hence, they steered the entire Space Shuttle, as well as providing rocket thrust towards orbit. The aft fuselage also housed three auxiliary power units (APU).

Using two dimensions, the composition can be represented as an equilateral triangle in which each corner represents one of the pure components. The edges of the triangle represent a mixture of the two components at each end of the edge. Any point inside the triangle represents the composition of a mixture of all three components. The mole fraction of each component would correspond to where a point lies along a line starting at that component's corner and perpendicular to the opposite edge.

Uniform polytopes have equal edge-lengths, and all vertices are an equal distance from the center, called the circumradius. Uniform polytopes whose circumradius is equal to the edge length can be used as vertex figures for uniform honeycombs. For example, the regular hexagon divides into 6 equilateral triangles and is the vertex figure for the regular triangular tiling. Also the cuboctahedron divides into 8 regular tetrahedra and 6 square pyramids (half octahedron), and it is the vertex figure for the alternated cubic honeycomb.

Flammability diagram for methane A ternary plot, ternary graph, triangle plot, simplex plot, Gibbs triangle or de Finetti diagram is a barycentric plot on three variables which sum to a constant. It graphically depicts the ratios of the three variables as positions in an equilateral triangle. It is used in physical chemistry, petrology, mineralogy, metallurgy, and other physical sciences to show the compositions of systems composed of three species. In population genetics, it is often called a de Finetti diagram.

Swissair 111 Memorial near Peggy's Cove On September 2, 1998, Swissair Flight 111 crashed into St. Margaret's Bay with the loss of all 229 aboard. One of two memorials to the victims of the disaster is located at The Whalesback, in Indian Harbour. The other is located at Bayswater, Nova Scotia, on the Aspotogan Peninsula on the western shore of the bay. The two monuments and the actual crash site are at the vertices of a roughly equilateral triangle across the bay.

One of the most peculiar properties of this manuscript is its physical shape - an equilateral triangle. Measuring approximately 23.7cm across each of its three sides, it is elegantly bound in leather and gilded on the front. In European grimoire tradition, one frequently finds the practice of conjuring spirits into a triangle drawn on the ground. This particular shape, fortified by the divine names written around it, was thought to force a spirit to answer honestly and perform its duties without tarrying.

The line A'A crosses the similarly constructed lines B'B and C'C at the first isodynamic point. The second isodynamic point may be constructed similarly but with the equilateral triangles erected outwards rather than inwards.. Alternatively, the position of the first isodynamic point may be calculated from its trilinear coordinates, which are. :\sin(A + \pi/3) : \sin(B + \pi/3) : \sin(C + \pi/3). The second isodynamic point uses trilinear coordinates with a similar formula involving -\pi/3 in place of \pi/3.

Creating a semi circular configuration, were the barracks of custody zone which fanned out from the base of the Appellplatz. Sachsenhausen was intended to set a standard for other concentration camps, both in its design and the treatment of prisoners. The camp perimeter is, approximately, an equilateral triangle with a semi circular roll call area centered on the main entrance gate in the boundary running northeast to southwest. Barrack huts lie beyond the roll call area, radiating from the gate.

Graphical representation of Einthoven's triangle Einthoven's triangle is an imaginary formation of three limb leads in a triangle used in electrocardiography, formed by the two shoulders and the pubis. The shape forms an inverted equilateral triangle with the heart at the center. It is named after Willem Einthoven, who theorized its existence. Einthoven used these measuring points, by immersing the hands and foot in pails of salt water, as the contacts for his string galvanometer, the first practical ECG machine.

The Usonian house designed by architect Frank Lloyd Wright in 1948 and was built during 1950–54 for J. Willis Hughes, who lived in it until January 1980. It is on a 30-60 degree triangle, which results in a grid of equilateral parallelograms. The "bedroom wing terminates in a fountain over a pool, which gives the structure its nickname, Fountainhead."The Frank Lloyd Wright Companion,, Revised Edition, by William Allin Storrer, The University of Chicago Press, 2006, p. 316.

The true locations on which the fictional communities were based remain uncertain. According to Murray, the three title communities are however based on real locations one and a half miles from each other at the corners of an equilateral triangle. The real-life locations most frequently cited are Wivelsfield Green (Camberwick Green), Plumpton (Trumpton), and Chailey (Chigley), historically known as Chagley, which are neighbouring communities in a roughly triangular configuration in Sussex. In such an explanation the city of Wellchester could be Chichester.

The cities of Bartow, Lakeland, and Winter Haven form a roughly equilateral triangle pointed downward with Bartow being the south point, Lakeland the west point, and Winter Haven the east point. The other major cities in the county with a population over 10,000 include Haines City, Auburndale, and Lake Wales. Haines City is in the northeast part of the county and has over 20,000 residents. Auburndale is located northwest of Winter Haven and Lake Wales is around 16 miles east of Bartow.

A related construction is a hexadecahedron, 16 triangular faces, 24 edges, and 10 vertices. Starting with the regular octahedron, it is elongated along one axes, adding 8 new triangles. It has 2 sets of 3 coplanar equilateral triangles (each forming a half-hexagon), and thus is not a Johnson solid. If the sets of coplanar triangles are considered a single isosceles trapezoidal face (a triamond), it has 8 vertices, 14 edges, and 8 faces - 4 triangles 20px and 4 triamonds 40px.

Waddell Memorial Presbyterian Church is a historic Presbyterian church located near Rapidan, Orange County, Virginia. It was built in 1874, and is a Carpenter Gothic frame building covered with board-and-batten siding. It features a three-stage tower at the gable end with a ground level with an equilateral-arched doorway, a middle level with a rose window, and a belfry with double pointed windows. and Accompanying photo It was added to the National Register of Historic Places in 1975.

Diagram by Duncan Webb showing the construction of one octant of a Cahill–Keyes projection The Cahill–Keyes projection was designed with four fundamental considerations in mind: visual fidelity to a globe, proportional geocells, 10,000 km lengths for each of its octants' three main joined edges, and an M-shape Master-Map profile. The resulting map comprises 8 octants. Each octant is an equilateral triangle with three segments per side. One side runs along the equator, and the other two run along meridians.

There are no guidelines as to how the main sail is shaped but it may approximate an equilateral triangle. The paraw is also equipped with a foresail or jib and adds to the overall surface area and generated thrust derived from the wind. A variation of the paraw with rectangular sails is the vinta. The mast, commonly made of bamboo, is secured by lines attached to, among other things, the outriggers, the fore (and sometimes, the aft) and various parts of the boat.

Flooding of the Peace River after a hurricane Bartow is located slightly southwest of the geographical centers of both Polk County and peninsular Florida. The city is approximately east of Tampa and southwest of Orlando. The cities of Bartow, Lakeland, and Winter Haven form a roughly equilateral triangle pointed southward, with Bartow being the south point, Lakeland the west point, and Winter Haven the east point. The city is located near the headwaters of the Peace River at Lake Hancock.

Related to polyominoes are polyiamonds, formed from equilateral triangles; polyhexes, formed from regular hexagons; and other plane polyforms. Polyominoes have been generalized to higher dimensions by joining cubes to form polycubes, or hypercubes to form polyhypercubes. In statistical physics, the study of polyominoes and their higher-dimensional analogs (which are often referred to as lattice animals in this literature) is applied to problems in physics and chemistry. Polyominoes have been used as models of branched polymers and of percolation clusters.

In the plane with coordinate axes α and β, α = β is a line dividing the plane in two parts (south border shown in orange in the drawing). δ = β as a curve divides the plane into different sections (north border shown in blue). Both borders enclose a continuous region of the plane whose points map to unique equilateral pentagons. Points outside the region just map to repeated pentagons—that is, pentagons that when rotated or reflected can match others already described.

The tower, an equilateral triangle with rounded corners in section and about 30 metres tall, is built in ashlar sandstone. Its three walls are perpendicular to the ground for then taper to a hexagonal cupola surrounded by a triangular viewing platform reached by an internal helical stairway of 150 steps. It is believed that the three walls under the cupola represented England (including Wales), Scotland and Ireland all under one crown. The exterior is very plain but the interior is more decorative.

Ideally, the secondaries would be positioned at the vertices of an equilateral triangle with the master at the centre. The baseline length, that is, the master-secondary distance, was typically . Each station transmitted a continuous wave signal that, by comparing the phase difference of the signals from the master and one of the secondaries, resulted in a set of hyperbolic lines of position called a pattern. As there were three secondaries there were three patterns, termed Red, Green and Purple.

With the hinge of the two valves oriented towards the top, one side corresponds to the animal's morphological anterior or front, the other is the posterior or rear, the hinge is the dorsal or back/ top region, and the bottom corresponds to the ventral or (as it were) underside/ belly. However, as many scallop shells are more or less bilaterally symmetrical ("equivalved"), as well as symmetrical front/back ("equilateral"), determining which way a given animal is "facing" requires detailed information about its valves.

Each sector was equipped with three huff-duff sets for determining the location of the pip- squeak radios. Although in theory only two were needed, adding a third offered redundancy as well as helping reduce the chance of errors in the plotting. The stations were positioned approximately apart in as close to an equilateral triangular layout as possible. One of the three stations was co-located at the Sector Control center, with the two remote stations communicating with the center over telephone lines.

An equilateral triangle bicentric kite A bicentric isosceles trapezoid A regular pentagon In geometry, a bicentric polygon is a tangential polygon (a polygon all of whose sides are tangent to an inner incircle) which is also cyclic — that is, inscribed in an outer circle that passes through each vertex of the polygon. All triangles and all regular polygons are bicentric. On the other hand, a rectangle with unequal sides is not bicentric, because no circle can be tangent to all four sides.

The cluster has D3h symmetry, consisting of an equilateral triangle of Ru atoms, each of which bears two axial and two equatorial CO ligands.Slebodnick, C.; Zhao, J.; Angel, R.; Hanson, B. E.; Song, Y.; Liu, Z.; Hemley, R. J., "High Pressure Study of Ru3(CO)12 by X-ray Diffraction, Raman, and Infrared Spectroscopy", Inorg. Chem., 2004, vol. 43, 5245-52. Os3(CO)12 has the same structure, whereas Fe3(CO)12 is different, with two bridging CO ligands, resulting in C2v symmetry.

The long radius (center to vertex) of the tesseract is equal to its edge length; thus its diagonal through the center (vertex to opposite vertex) is 2 edge lengths. Only a few polytopes have this property, including the four-dimensional tesseract and 24-cell, the three- dimensional cuboctahedron, and the two-dimensional hexagon. In particular, the tesseract is the only hypercube with this property.Strictly, the hypercubes of 0 dimensions (a point) and 1 dimension (a line segment) are also radially equilateral.

In this species the elytra are not green metallic, but black, with white spots. In addition, the shape of the pronotum side edge is laterally weakly s-shaped, while in Gnorimus nobilis it is imus nobilis simply rounded. Gnorimus nobilis is also rather similar to the more common Cetonia aurata, but in the latter the middle and hind legs are toothed, whereas they are smooth in the Gnorinus nobilis. Moreover in the noble chafer the scutellum forms an equilateral triangle.

IcoSoku is a puzzle invented in 2009 by Andrea Mainini and sold by Recent Toys International, which is based in the Netherlands. It won several awards in 2010. The puzzle frame is a blue plastic icosahedron, and the pieces are 20 white equilateral-triangular snap-in tiles with black dots and 12 yellow pins for the corners. The pins are printed with the numbers from 1 to 12, and the triangular tiles have up to three dots in each of their corners.

Three to five acoustic arrays are set up in a roughly equilateral configuration several hundred meters from each other. Each array detects an impulsive event such as motor/rocket launch and determines the line of bearing from the array to the launch site. The lines of bearing from each array are transmitted via radio link to a central point where the results are combined to establish the location of the firing point through triangulation. Impact points are detected and located the same way.

The simplest shape made of these pyramids, often called "Toshie's Jewel" (shown on the right), is named after origami enthusiast Toshie Takahama. It is a three-unit hexahedron built around the notional scaffold of a flat equilateral triangle (two "faces", three edges); the protruding tab/pocket flaps are simply reconnected on the underside, resulting in two triangular pyramids joined at the base, a triangular bipyramid. The most popular intermediate model is the triakis icosahedron, shown below. It requires 30 units to build.

In quantum mechanics Langmuir states are certain quantum states of Helium that in the classical limit correspond to two parallel circular orbits of electrons one above the other and with the nucleus in between. They are constructed in analogy to circular states of Hydrogen when the electron has the maximum angular momentum and moves on the circle. Because of the magic value of the Helium nucleus charge 2e the triangle nucleus-electron-electron which sweeps the configuration space during the circular motion is equilateral.

Hardy–Weinberg frequency as a function of p. A de Finetti diagram is a ternary plot used in population genetics. It is named after the Italian statistician Bruno de Finetti (1906–1985) and is used to graph the genotype frequencies of populations, where there are two alleles and the population is diploid. It is based on an equilateral triangle, and Viviani's theorem concerning any point within the triangle, and the three lines from that point that are perpendicular to the sides of the triangle.

Each of these radially equilateral polytopes also occurs as cells of a characteristic space-filling tessellation: the tiling of regular hexagons, the rectified cubic honeycomb (of alternating cuboctahedra and octahedra), the 24-cell honeycomb and the tesseractic honeycomb, respectively. Each tessellation has a dual tessellation; the cell centers in a tessellation are cell vertices in its dual tessellation. The densest known regular sphere-packing in two, three and four dimensions uses the cell centers of one of these tessellations as sphere centers. A cuboctahedron has octahedral symmetry.

Using the diagram and summing the incident branches into x1 this equation is seen to be satisfied. As all three variables enter these recast equations in a symmetrical fashion, the symmetry is retained in the graph by placing each variable at the corner of an equilateral triangle. Rotating the figure 120° simply permutes the indices. This construction can be extended to more variables by placing the node for each variable at the vertex of a regular polygon with as many vertices as there are variables.

The wounds were described as consistent with those from a 9mm, and that the three gunshot wounds to the chest were deliberately fired to form the shape of an equilateral triangle, with the victim lying on his back at the time. A gunshot wound just below Mr. Lillelid's nipple was consistent with a .25 caliber weapon, and a final 9mm gunshot wound was located just beneath it. There was a "graze laceration" on the victim's right forearm where a bullet skimmed across the surface.

The seal is a blue inverted equilateral triangle with the face of Dr. Sun Yat-sen placed on top. The words on the seal are marked with a white color. The triangle bears the name “中山中學” which is the Chinese writing of the school's name. The initials “S.Y.S.H.S.” which means “Sun Yat Sen High School” lies at the bottom with “ILOILO” forming an arch under it. Near the corner of the triangle is a vertically-displayed “RP” which means “Republic of the Philippines”.

They have central angles from 104° to 109.5°, where the latter is consistent with a simplistic theory which predicts the tetrahedral symmetry of four sp3 hybridised orbitals. The most common actual angles are 105°, 107°, and 109°: they vary because of the different properties of the peripheral atoms (X). Other cases also experience orbital hybridisation, but in different degrees. AX2E1 molecules, such as SnCl2, have only one lone pair and the central angle about 120° (the centre and two vertices of an equilateral triangle).

He also continued to work at Utrecht University and became a reader in 1927 and began to teach physics to students of medicine. After World War II he began to take an interest in electricity and the human body. He chose a triangle of points for electrical measurement which formed an asymmetric triangle, the so-called Burger's triangle, which departed from the previous idea of Willem Einthoven which was an equilateral triangle. He also pioneered the use of dyes in blood to study circulation.

The only equiangular triangle is the equilateral triangle. Rectangles, including the square, are the only equiangular quadrilaterals (four-sided figures).. For a convex equiangular n-gon each internal angle is 180(1-2/n)°; this is the equiangular polygon theorem. Viviani's theorem holds for equiangular polygons:Elias Abboud "On Viviani’s Theorem and its Extensions" pp. 2, 11 :The sum of distances from an interior point to the sides of an equiangular polygon does not depend on the location of the point, and is that polygon's invariant.

This trihexaflexagon template shows 3 colors of 9 triangles, printed on one side, and folded to be colored on both sides. The two yellow triangles on the ends will end up taped together. The red and blue arcs are seen as full circles on the inside of one side or the other when folded. A hexaflexagon with three faces is the simplest of the hexaflexagons to make and to manage, and is made from a single strip of paper, divided into nine equilateral triangles.

Isotropy is guaranteed by the fourth postulate, that all right angles are equal. For an example of homogeneity, note that Euclid's proposition I.1 implies that the same equilateral triangle can be constructed at any location, not just in locations that are special in some way. The lack of boundaries follows from the second postulate, extensibility of a line segment. One way in which elliptic geometry differs from Euclidean geometry is that the sum of the interior angles of a triangle is greater than 180 degrees.

The Jardin d'Eau et de Lumiere for the 1925 Exposition Internationale des Arts Décoratifs was an equilateral triangle broken up into triangular elements. In the centre were four tiered reflecting pools decorated by Robert Delaunay that sat below a rotating, internally illuminated sphere. These were surrounded by tiered plantings and hemmed in by two low walls of small triangles of glass in white and shades of pink. The sphere and the reflecting surfaces meant that light was reflected in all directions within the garden.

In Macfarlane's paper there is an effort to produce "trigonometry on the surface of the equilateral hyperboloids" through the algebra of hyperbolic quaternions, now re-identified in an associative ring of eight real dimensions. The effort is reinforced by a plate of nine figures on page 181. They illustrate the descriptive power of his "space analysis" method. For example, figure 7 is the common Minkowski diagram used today in special relativity to discuss change of velocity of a frame of reference and relativity of simultaneity.

The form of the Gothic pointed arch in windows and arches was typically based upon an equilateral triangle, in which the three sides have an equal length. This had the great advantage of simplicity. Stone cutters, or hewers, could precisely draw the arc on the stone with a cord and a marker. This allowed arch stones to be cut at the quarry in quantity with great precision, then delivered and assembled at the site, where the layers put them together, with the assurance that they would fit.

At the other extreme, the curve of constant width that has the maximum possible area is a circular disk, which has area \pi s^2 / 4\approx 0.78540s^2. The angles made by each pair of arcs at the corners of a Reuleaux triangle are all equal to 120°. This is the sharpest possible angle at any vertex of any curve of constant width. Additionally, among the curves of constant width, the Reuleaux triangle is the one with both the largest and the smallest inscribed equilateral triangles.

The Kakeya needle problem asks whether there is a minimum area of a region D in the plane, in which a needle of unit length can be turned through 360°. This question was first posed, for convex regions, by . The minimum area for convex sets is achieved by an equilateral triangle of height 1 and area 1/, as Pál showed. Kakeya seems to have suggested that the Kakeya set D of minimum area, without the convexity restriction, would be a three-pointed deltoid shape.

Pi Delta Nu's badge had originally been an oblong square in gold, with a band in the center supporting its letters. This was soon replaced, according to yearbook photos, by a stylized pin in gold, consisting of two equilateral triangles pointing up and down and overlapping, with the letters of the sorority on a center band. Above the letters was a silhouette of a glass beaker used in chemistry called a retort. The pin was surrounded by 22 pearls, eleven above and eleven below.

The vertical walls of the lower part of the building are clad with red Aberdeen Granite composite panels (made by Detail of Concrete, showing marks of timber formwork, Clifton Cathedral Marble Mosaic Ltd), with roofing in lead. Rainwater is channelled through simple gargoyles into a number of semi-hexagonal pools around the building. Inscribed into the outside wall of the turret to the right of the Portal of Saint Paul [see Exterior Plan]. Contained within an equilateral triangle is the symbol ‘√3’ along with the letters PTP.

Zagori (Greek: Ζαγόρι), is a region and a municipality in the Pindus mountains in Epirus, in northwestern Greece. The seat of the municipality is the village Asprangeloi.Kallikratis law Greece Ministry of Interior It has an area of some 1,000 square kilometers and contains 46 villages known as Zagori villages (or Zagorochoria or Zagorohoria), and is in the shape of an upturned equilateral triangle. Ioannina, the provincial capital, is at the southern point of the triangle, while the south-western side is formed by Mount Mitsikeli (1,810m).

The first dorsal fin is triangular with a rounded apex, originating in front of the pelvic fin insertions. The second dorsal fin is only one-half to two- thirds as large as the first; the distance between the dorsal fins is less than the length of the first dorsal fin base. The stout tail comprises about one-third of the total length, terminating in a caudal fin shaped like an equilateral triangle with slightly convex margins. The skin is soft and completely devoid of dermal denticles (scales).

While negotiating with Terran Electric's hardnosed chief lawyer Mark Kingman for a licence on Carroll and Baler's Martian power transmitter, which they had sold to TE, Channing works out a way to use the transmitter to harness solar energy. Channing cuts a deal with Kingman allowing Terran Electric to operate the solar power tube on planetary surfaces while Venus Equilateral operates it in space. It turns out, though, that an atmosphere blocks the tube's reception, so it can't operate on the surface of any inhabited world.

Although that idea was abandoned by Napoleon, grades continued to be used in several fields and many scientific calculators support them. Decigrades () were used with French artillery sights in World War I. An angular mil, which is most used in military applications, has at least three specific variants, ranging from to . It is approximately equal to one milliradian ( ). A mil measuring of a revolution originated in the imperial Russian army, where an equilateral chord was divided into tenths to give a circle of 600 units.

With Charles Joseph Minard, another civil engineer of the Ponts et Chaussées, Lalanne is considered to have made important contributions to rigorous cartography. He first clarified the distinction between an isometric line and an isopleth. Interested in population density and centres, Lalanne plotted innovative maps (1845) with contours of the same population density, and announced an "equilateral law" of equal spacing of the centres (1875), which he found a good fit in France. A paper of 1863 raised general considerations on transport routes and population distributions, direction later covered in work of Walter Christaller.

Smithsonian in Washington, D.C. Major General Keith R. Barney tasked Blakeley with creating the fallout shelter sign in 1961. Blakeley decided that to be most durable the signs must be made from metal. As they needed to be easy to find in the dark, he chose to use orange-yellow and black, with an image created by graphic design firm Blair Inc. and possibly based on an image from on Clarence P. Hornung's Handbook of Designs, consisting of three upside- down equilateral triangles on a black background and the words "Fallout Shelter" in large letters.

In the short story What Dead Men TellAnalog Science-Fiction, November 1949 at The Internet Archive by Theodore Sturgeon, the main action takes place in a seemingly endless corridor with the cross section of an equilateral triangle. At the end the protagonist speculates that the corridor is actually a triangular shape twisted back on itself like a Möbius strip but with the ends rotated 120 degrees before connecting them. This gave an endless corridor in which after three passes one came back to the point where one started.

Bowling pins (with a maximum thickness of at the waist) are "spotted" (placed) in four rows, forming an equilateral triangle with four pins on a side to form a tetractys. Neighboring pins are centered apart, leaving a space of between pins that can be bridged by a bowling ball of regulation diameter (). Pin carry—essentially, the probability of achieving a strike assuming the ball impacts in or near the pocket—varies with several factors. Even before a 2008 USBC pin carry study, it was known that entry angle and ball weight increase strike percentages.

This implies quite a lot of overlap, and the pattern is not efficient. The most efficient pattern uses an equilateral triangular grid, but this may have to be modified to suit the site. The circular search is very popular as it does not require complicated setup and can be done by most divers without a great deal of special training. It is effective where the position of the target is known with reasonable accuracy, where the bottom terrain does not have major snags, and where the depth variation during each arc is acceptable.

John S. Billings in 1876, was a considerable achievement for its day in functional arrangement and fireproofing. I.M. Pei's World Trade Center (1977) is the tallest equilateral pentagonal building in the world at tall. The Harbor East area has seen the addition of two new towers which have completed construction: a 24-floor tower that is the new world headquarters of Legg Mason, and a 21-floor Four Seasons Hotel complex. The streets of Baltimore are organized in a grid pattern, lined with tens of thousands of brick and formstone-faced rowhouses.

The Tersane, a medieval drydock built by the Seljuk Turks in 1221, is divided into five vaulted bays with equilateral pointed arches. The Alara Castle and caravanserai near Manavgat, also built under Kayqubad's authority, has been converted into a museum and heritage center. Atatürk's House and Museum, from his short stay in the city on February 18, 1935, is preserved in its historic state and is an example of the interior of a traditional Ottoman villa, with artifacts from the 1930s. The house was built between 1880 and 1885 in the "karniyarik" (stuffed eggplant) style.

It is used in making engineering drawings, commonly called blueprints, blue lines or plans in a specific scale. For example, "one-tenth size" would appear on a drawing to indicate a part larger than the drawing on the paper itself. It is not to be used to measure machined parts to see if they meet specifications. In the United States this scale is divided into decimalized fractions of an inch, but has a cross-section like an equilateral triangle, which enables the scale to have six edges indexed for measurement.

The Three Pagodas of the Chongsheng Temple () are an ensemble of three independent pagodas arranged on the corners of an equilateral triangle, near the old town of Dali, Yunnan province, China, dating from the time of the Kingdom of Nanzhao and Kingdom of Dali in the 9th and 10th centuries. The Three Pagodas are located about north of Dali old town. They are at the east foot of the tenth peak of the massive Cangshan Mountains and face the west shore of the Erhai Lake of ancient Dali.

Given an equilateral triangle, the counterclockwise rotation by 120° around the center of the triangle maps every vertex of the triangle to another one. The cyclic group C3 consisting of the rotations by 0°, 120° and 240° acts on the set of the three vertices. In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure.

Sólido de Johnson J₁₄ In geometry, the elongated triangular bipyramid (or dipyramid) or triakis triangular prism is one of the Johnson solids (J14), convex polyhedra whose faces are regular polygons. As the name suggests, it can be constructed by elongating a triangular bipyramid (J12) by inserting a triangular prism between its congruent halves. The nirrosula, an African musical instrument woven out of strips of plant leaves, is made in the form of a series of elongated bipyramids with non-equilateral triangles as the faces of their end caps..

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.

Resch and his team tiled the egg using a total of 1108 congruent equilateral triangles, 524 concave hexagons (3-pointed stars), 3,512 visible facets, 6,978 nuts and bolts and 177 internal struts. The tiles range in thickness from to and are jointed at angles ranging from 1° at the center to 7° at the tips. These are held together by an internal framework of radiating spokes, which connect the egg's "shell." The pysanka leans at a 30° relative to the base, and turns with the wind similar to the motions of a weather vane.

Huexotla Bridge, west side, see construction protrusion on the right side Huejotla Bridge This structure is represented by a stone masonry pre-Hispanic bridge. Its overall length at the top is about 21.5 meters long by 4.9 meters wide (70 by 16 ft.). It has an equilateral pointed arch type construction, measures some 16 meters long, by 5 meters wide. The bridge top is about 15 meters over the ravine and river below and has a clear span of about 7 meters and it keystone is about 8 meters high.

Screw threads are almost never made perfectly sharp (no truncation at the crest or root), but instead are truncated, yielding a final thread depth that can be expressed as a fraction of the pitch value. The UTS and ISO standards codify the amount of truncation, including tolerance ranges. A perfectly sharp 60° V-thread will have a depth of thread ("height" from root to crest) equal to 0.866 of the pitch. This fact is intrinsic to the geometry of an equilateral triangle — a direct result of the basic trigonometric functions.

In 1958 a proposal was put before Edmonton City Council to build a permanent civic memorial to mark the visit of Queen Elizabeth and Prince Philip in July 1959. Originally there were three projects proposed on a 30.8 metre (94 foot) trilon, a three- sided equilateral prism, which would symbolize the three levels of government. Its likely design would have been as a three-sided obelisk, however, no plans or drawings were able to be located on the proposed structure. Another suggestion was a fountain, and the park itself.

La Géode was designed by architect Adrien Fainsilber and engineer Gérard Chamayou. The geodesic dome is in diameter, composed of 6,433 polished stainless steel equilateral triangles that form the sphere that reflects the sky.Nicolas Janberg's Structurae, La Géode, construction details These triangles are 1.5 meters long and are fixed on a thin metal frame with the same triangular geodesic structure, consisting of 2,580 steel tube bars. The dome stands on a reinforced concrete base, which is attached to Cité des Sciences et de l'Industrie, the largest science museum in Europe.

The structure of the castle is an enclosure, with its building that took place in two stages, the first one with the construction of the tower and the second one with the walls. The tower's plan is formed by a square and an equilateral triangle. The plan of the walls is triangular, with the tower at the top and other smaller towers along the walls. The structure of the castle has been revised several times, as shown, for example, by the raising of the walls, that probably took place in the 14th century.

There are four principal monuments in Dorchester Square, originally arranged to form an equilateral cross with the 'Camellienne' (a multi-purpose kiosk that currently houses a snack bar) at the northern point. However, the cross form was altered first when the Lion of Belfort fountain was disconnected and moved further south along Metcalfe Street. Later, a florist was established at the southwestern corner, further altering the original layout of the square. Under the current renovation plan, the Robert Burns statue will be moved further north along Peel Street and the florist kiosk removed entirely.

Space-based interferometers, such as LISA and DECIGO, are also being developed. LISA's design calls for three test masses forming an equilateral triangle, with lasers from each spacecraft to each other spacecraft forming two independent interferometers. LISA is planned to occupy a solar orbit trailing the Earth, with each arm of the triangle being five million kilometers. This puts the detector in an excellent vacuum far from Earth-based sources of noise, though it will still be susceptible to heat, shot noise, and artifacts caused by cosmic rays and solar wind.

In October the 490 crashed on take off due to fuel starvation, though it was not badly damaged, and Latécoère took the opportunity to increase the fin area during the repairs. The new fin had the shape of an equilateral right angled triangle, and the now deeper rudder was slightly reduced in chord. At that point it was registered as F-AKDD before returning to Villacoublay to complete the tests early in 1932. It was the fastest machine in level flight, though the ANF Les Mureaux 113 climbed faster.

This arrangement combines strength with economy of materials, minimizing weight and thereby reducing loads and expense. Patented in 1848 by its designers James Warren and Willoughby Theobald Monzani, its structure consists of longitudinal members joined only by angled cross- members, forming alternately inverted equilateral triangle-shaped spaces along its length, ensuring that no individual strut, beam, or tie is subject to bending or torsional straining forces, but only to tension or compression. It is an improvement over the Neville truss, which uses a spacing configuration of isosceles triangles.

During the 1970s, feminist art continued to provide a means of challenging women's position in the social hierarchy. The aim was for women to reach a state of equilibrium with their male counterparts. Judy Chicago's work, The Dinner Party (1979), widely regarded as the first epic feminist artwork, emphasizes this idea of a newfound female empowerment through the use of turning a dinner table – an association to the traditional female role – into an equilateral triangle. Each side has an equal number of plate settings dedicated to a specific woman in history.

The Windsor Swastikas used the ancient swastika symbol as their logo. The swastika is an equilateral cross with its arms bent at right angles, in either right-facing () form or its mirrored left-facing () form. Archaeological evidence of swastika-shaped ornaments dates from the Neolithic period and the design is still widely used in many religions around the world. Though once commonly used all over much of the world without stigma, because of its iconic usage in Nazi Germany the symbol has become stigmatized in the Western world, even outlawed in Germany.

In an equilateral triangle the area of the Malfatti circles (left) is approximately 1% smaller than the three area-maximizing circles (right). posed the problem of cutting three cylindrical columns out of a triangular prism of marble, maximizing the total volume of the columns. He assumed that the solution to this problem was given by three tangent circles within the triangular cross-section of the wedge. That is, more abstractly, he conjectured that the three Malfatti circles have the maximum total area of any three disjoint circles within a given triangle.

The difference in area for an equilateral triangle is small, just over 1%, but as pointed out, for an isosceles triangle with a very sharp apex, the optimal circles (stacked one atop each other above the base of the triangle) have nearly twice the area of the Malfatti circles.See also . provided a convincing numerical demonstration that, for every triangle, the Lob–Richmond procedure produces three circles with larger area than the Malfatti circles, so the Malfatti circles are never optimal. followed up with a rigorous mathematical proof of this fact.

Moreover, the formula continues to hold if the walls are slanted and all three measurements are made parallel to the walls. Let P be a point on the circumcircle of an equilateral triangle ABC, on the minor arc AB. Let a be the distance from P to A and b be the distance from P to B. On a line passing through P and the far vertex C, let c be the distance from P to the triangle side AB. ThenPosamentier, Alfred S., and Salkind, Charles T., Challenging Problems in Geometry, Dover Publ.

3D model of a (uniform) triangular prism In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise it is oblique. A uniform triangular prism is a right triangular prism with equilateral bases, and square sides. Equivalently, it is a polyhedron of which two faces are parallel, while the surface normals of the other three are in the same plane (which is not necessarily parallel to the base planes).

The Warsaw radio mast was a guyed steel lattice mast of equilateral triangular cross section, with a face width of . The vertical steel tubes forming the vertices of the mast had a diameter of 245 millimetres (10 in); the thickness of the walls of these tubes varied between 8-34 mm (0.31-1.33 in) depending on height. The mast consisted of 86 elements, each of which had a length of . The mast had 3 arrays of guy wires, each array attached to the mast at 5 levels: , , , , and above ground.

Lake Hancock is located in the Polk Upland area between the Winter Haven Ridge and Lakeland Ridge. As part of the upper Peace River watershed, the lake has ecological importance throughout southwest Florida according to the Southwest Florida Water Management District. At , it is one of the largest lakes in Polk County; the center of the cities of Bartow, Lakeland, and Winter Haven roughly form an equilateral triangle with sides of and Lake Hancock forms over 25% of that triangle. The lake is shallow, with an average depth of and a maximum depth of .

Graduate Reading Room in the Suzzallo Library The library's original architects, Charles H. Bebb and Carl F. Gould, called for three structures built in Collegiate Gothic style and arranged in a roughly equilateral triangle with a bell tower in the center. The proposed bell tower, however, was never built. A terra cotta bas relief of this plan, with the bell tower, can still be found on the wall outside the northeast entrance to Smith Hall. Red Square The first phase, completed 1926, built the wing that forms the west face of the triangle.

Bivalves by definition possess two shells or valves, a "right valve" and a "left valve", that are joined by a ligament. The two valves usually articulate with one another using structures known as "teeth" which are situated along the hinge line. In many bivalve shells, the two valves are symmetrical along the hinge line—when truly symmetrical, such an animal is said to be equivalved; if the valves vary from each other in size or shape, inequivalved. If symmetrical front-to-back, the valves are said to be equilateral, and are otherwise considered inequilateral.

A right pyramid with a regular base has isosceles triangle sides, with symmetry is Cnv or [1,n], with order 2n. It can be given an extended Schläfli symbol ( ) ∨ {n}, representing a point, ( ), joined (orthogonally offset) to a regular polygon, {n}. A join operation creates a new edge between all pairs of vertices of the two joined figures.N.W. Johnson: Geometries and Transformations, (2018) Chapter 11: Finite symmetry groups, 11.3 Pyramids, Prisms, and Antiprisms The trigonal or triangular pyramid with all equilateral triangle faces becomes the regular tetrahedron, one of the Platonic solids.

During the Second Philippine Republic, a more nationalistic policy were adopted and the seal was revised. Foreign components of the Filipino heraldic symbol which previously represented its colonial links to Spain and United States were removed. Instead, salient features of the flag and seal of the short-lived Philippine Republic were incorporated, consisting of the eight-ray mythological sun and three stars located beneath the equilateral triangle. Written within three sets of two marginal lines of the three sides of the triangle were Kalayaan, Kapayapaan, Katarungan (Liberty, Peace, Justice).

The British decimal fifty pence (50p) coin – often informally pronounced fifty pee – is a unit of currency equalling one half of a pound sterling. It is a seven-sided coin formed as an equilateral-curve heptagon, or Reuleaux polygon, a curve of constant width, meaning that the diameter is constant across any bisection. Its obverse has featured the profile of Queen Elizabeth II since the coin's introduction in 1969. Four different portraits of the Queen have been used, with the latest design by Jody Clark being introduced in 2015.

Jessen's icosahedron is vertex-transitive (or isogonal), meaning that it has symmetries taking any vertex to any other vertex. Its dihedral angles are all right angles. One can use it as the basis for the construction of a large family of polyhedra with right dihedral angles, formed by gluing copies of Jessen's icosahedron together on their equilateral-triangle faces. net for Jessen's icosahedron, suitable for making a (shaky) physical model Although it is not a flexible polyhedron, Jessen's icosahedron is also not infinitesimally rigid; that is, it is a "shaky polyhedron".

Many say the inspiration for the idea of using the Triforce in the Zelda series came from the Hōjō clan, and the incorporation of the symbol was similar to how Western games used crossed swords. Another theory holds that the Triforce was based on Gunpei Yokoi's family crest. Another conspicuous use (in equilateral form) is as the symbol for , which has about a dozen shrines in Kantō (Eastern Japan), notably at Kamakura (head shrine) and Inokashira Park in western Tokyo. Some Google logos, or doodles have a hidden triforce.

The pagoda was erected during the Tang Dynasty between the years 742 and 756 AD. The pagoda is made entirely from bricks laid tightly with joint gaps of about one centimeter. The pagoda's floor plan is an equilateral octagon in which all of the eight side walls are curved inwards. These concave walls are another distinguishing feature not found in other pagodas of the period. The main body of the pagoda contains only a single storey and the most elaborate feature of the structure are nine small pagodas that decorate the roof.

Sun cross Sun wheel cross A sun cross, solar cross, or wheel cross is a solar symbol consisting of an equilateral cross inside a circle. The design is frequently found in the symbolism of prehistoric cultures, particularly during the Neolithic to Bronze Age periods of European prehistory. The symbol's ubiquity and apparent importance in prehistoric religion have given rise to its interpretation as a solar symbol, whence the modern English term "sun cross" (a calque of ). The same symbol is in use as a modern astronomical symbol representing the Earth rather than the Sun.

These shapes are rhomboids Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled. A parallelogram with sides of equal length (equilateral) is a rhombus but not a rhomboid. A parallelogram with right angled corners is a rectangle but not a rhomboid. The term rhomboid is now more often used for a rhombohedron or a more general parallelepiped, a solid figure with six faces in which each face is a parallelogram and pairs of opposite faces lie in parallel planes.

On most locations on Earth (except the South Island of New Zealand and the south of Chile and Argentina and further south), this asterism is prominently in the sky from approximately December to March. In the tropics and southern hemisphere, this (then called "summer hexagon") can be extended with the bright star Canopus in the south. Smaller and more regularly shaped is the Winter Triangle, an approximately equilateral triangle that shares two vertices (Sirius and Procyon) with the larger asterism. The third vertex is Betelgeuse, which lies near the center of the hexagon.

According to the astrologer Neil Michelsen's "The American Ephemeris," on 24 August 1987 there was an exceptional alignment of planets in the Solar System. Eight planets were aligned in an unusual configuration called a grand trine. The Sun, Moon and six out of eight planets formed part of the grand trine, that is, they were aligned at the apexes of an equilateral triangle when viewed from the Earth. The Sun, Moon, Mars and Venus were in exact alignment, astrologically called a conjunction at the first degree of Virgo in Tropical Astrology.

The NRHP nomination document describes its front as: > The main facade consists of a central gable pierced by a massive equilateral > arch window, and two flanking towers of differing shapes and heights. These > elements of the exterior announce the three-part division of the interior. A > modest porte-cochere is attached to the square tower at the southwest corner > where a spire achieves a height of 250 feet. The entrance occupies a > centered position, and its arched portion is enveloped by a rather plain > accolade, as is the entrance to the square tower.

It had full span, high aspect ratio ailerons. The wing was supported on each side by a pair of parallel, faired duralumin struts from the lower fuselage longerons to the wing spars and attached centrally, low over the fuselage, on a triangular dural cabane. The engine was mounted in the nose, enclosed in a close fitting cowling which followed the profiles of the two cylinder banks and with its radiator in a long NACA fairing on the cowling below the engine. The fuselage, built around four longerons, had an equilateral triangular section, vertex down.

Nevertheless, many soldiers of the old 39th Division returned home wearing the unauthorized patch. The World War I patch consisted of a dark blue disc bordered red having upon it a steel gray triangle (the Greek Delta symbol). The area within the triangle was divided into four equilateral triangles, with the lower left red, the top white, the lower right blue, and the central triangle the same dark blue as the disk. There are numerous variations of the World War I design, with the colors of the triangles transposed in various combinations.

The deltoid curve is another type of curvilinear triangle, but one in which the curves replacing each side of an equilateral triangle are concave rather than convex. It is not composed of circular arcs, but may be formed by rolling one circle within another of three times the radius. Other planar shapes with three curved sides include the arbelos, which is formed from three semicircles with collinear endpoints,. and the Bézier triangle.. The Reuleaux triangle may also be interpreted as the conformal image of a spherical triangle with 120° angles.

The equilateral pick can be easier for beginners to hold and use since each corner may be used as a playing edge. The shark's fin pick can be used in two ways: normally, employing the blunt end; or the small perturbations can be raked across the strings producing a much fuller chord, or used to apply a "pick scrape" down the strings producing a very harsh, scratching noise. The sharp edged pick is used to create an easier motion of picking across the strings. Some guitar pick shapes are patented.

Bonwill-Triangle of the mandible He examined 4,000 mandibles of corpses and another 6,000 from living people and found that the distance between the condyles was four inches and the distance between each condyle and the contact point of the two lower central incisors, the incisal point of the mandible (lower jaw), corresponded. The latter is also called symphysis. These three points form an equilateral triangle, which does not change throughout life. Bonwill presented these findings in 1864 during a meeting of the Delaware Dental Society to the dental public.

This is the scar remaining from a large cornice, either made of pressed tin or Terra cotta, that was removed from the building after a 1913 fire, harming its architectural integrity greatly. The pilasters continue through the parapet and the central pilasters and recessed within a brick equilateral arch is a Terra cotta wheel window design flanked at the base by Terra cotta fillets filling out the base of the arch. The interior once featured a central courtyard that spanned the top three floors. It was lighted by a set of three large skylights.

In the special case when the polygon is cyclic, the circumcenter of mass coincides with the circumcenter. The circumcenter of mass satisfies an analog of Archimedes' Lemma, which states that if a polygon is decomposed into two smaller polygons, then the circumcenter of mass of that polygon is a weighted sum of the circumcenters of mass of the two smaller polygons. As a consequence, any triangulation with nondegenerate triangles may be used to define the circumcenter of mass. For an equilateral polygon, the circumcenter of mass and center of mass coincide.

Triangulum Australe is a small constellation in the far Southern Celestial Hemisphere. Its name is Latin for "the southern triangle", which distinguishes it from Triangulum in the northern sky and is derived from the almost equilateral pattern of its three brightest stars. It was first depicted on a celestial globe as Triangulus Antarcticus by Petrus Plancius in 1589, and later with more accuracy and its current name by Johann Bayer in his 1603 Uranometria. The French explorer and astronomer Nicolas Louis de Lacaille charted and gave the brighter stars their Bayer designations in 1756.

The sacrococcygeal membrane is a tough fibrous membrane about 10mm long which extends from the inferior tip of the sacrum to the body of the coccyx in humans. It covers the inferior limit of the epidural space and is analogous to the ligamentum flavum found at other levels in the spine. It can be found at the apex of an equilateral triangle whose base is formed by the dimples overlying the sacro-iliac joints. The cornua of the sacrum may be palpated with a finger; the sacrococcygeal membrane lies between and inferior to these.

Primary highways are marked by a black square sign in which is a white equilateral diamond shape with rounded corners that contains the route number. The diamond shape does not alter to accommodate larger route numbers; the numbers are reduced in size to fit within the diamond. Michigan is the only other state, aside from North Carolina, to have a near-identical route shield, but with pointed corners and an M in Michigan's shield. Secondary highways are not signed with route markers; small green or white signs are most commonly used to designate secondary roads.

The shell is greenish brown and roughly an equilateral triangle in profile with a slightly wavy thickened edge on the bottom of the whorl and sculpture consisting of fine diagonal spiral ridges. The single most striking feature is a brilliant spot of reddish-orange at the base of the umbilical pit which is bordered by a dark brown to black outer edge. Average height is 55 mm, and average diameter is 65 mm. Drawing with two views of a shell of Uvanilla olivacea The acute, imperforate shell has a conic shape.

In the worst case, every pair of vertices is connected, giving a complete graph. To immerse the complete graph K_n with all the edges having unit length, we need the Euclidean space of dimension n-1. For example, it takes two dimensions to immerse K_3 (an equilateral triangle), and three to immerse K_4 (a regular tetrahedron) as shown to the right. :\dim K_n = n-1 In other words, the dimension of the complete graph is the same as that of the simplex having the same number of vertices.

Article 13.3 of the Organic Law of Gagauzia describes the coat of arms of Gagauzia as follows :- The coat of arms represents an image of heraldic shield, on the lower part of which there is a yellow (golden) hemisphere of rising sun on blue background. The shield is framed by yellow (golden) spikes enlaced by the flag of Gagauzia. Under the shield there is a conventional image of vine-leaves and vine-bunches. Three five-pointed yellow (golden) stars are arranged in form of an equilateral triangle above the shield.

A pipeclay triangle is a piece of laboratory apparatus that is used to support a crucible being heated by a Bunsen burner or other heat source. It is made of wires strung in an equilateral triangle on which are strung hollow ceramic, normally fire clay, tubes. The triangle is usually supported on a tripod or iron ring. Unlike wire gauze, which primarily supports glassware such as beakers, flasks, or evaporating dishes and provides indirect heat transfer to the glassware, the pipeclay triangle normally supports a crucible and allows the flame to heat the crucible directly.

An equilateral triangle of diameter 1 doesn’t fit inside a circle of diameter 1 Lebesgue's universal covering problem is an unsolved problem in geometry that asks for the convex shape of smallest area that can cover any planar set of diameter one. The diameter of a set by definition is the least upper bound of the distances between all pairs of points in the set. A shape covers a set if it contains a congruent subset. In other words the set may be rotated, translated or reflected to fit inside the shape.

In the Euclidean plane there are 3 regular forms equilateral triangle, squares, and regular hexagons; and 8 semiregular forms; and 4-demiregular forms which can tile the plane with other planigons. All angles of a planigon are whole divisors of 360°. Tilings are made by edge-to-edge connections by perpendicular bisectors of the edges of the original uniform lattice, or centroids along common edges (they coincide). Tilings made from planigons can be seen as dual tilings to the regular, semiregular, and demiregular tilings of the plane by regular polygons.

Inside the temple are other goddesses important to Shakti tradition, for example, the Durga. The entrance to Cave 21 is flanked by large sculptures of the goddesses Ganga and Yamuna representing the two major Himalayan rivers and their significance to the Indian culture. The cave is laid out symmetrically according to the mandapa square principle and has embedded geometric patterns repeated throughout the cave. The Shiva linga at the sanctum sanctorum of the temple is equidistant from the major statues of goddesses Ganga and Yamuna, with all three set in an equilateral triangle.

Since the French Revolution had deposed Louis XVI, France had been almost constantly at war with most of Europe. Chronic political instability and the constant rumbles of war created a favourable terrain for a military coup, which General Bonaparte exploited on 18 Brumaire, establishing the French Consulate in the Constitution of the Year VIII, led by an equilateral triumvirate. Two years later, the Constitution was amended into the Constitution of the Year X, making Bonaparte First Consul for life. Finally, on 18 May 1804, the Sénat conservateur passed the Constitution of the Year XII.

With a 1:2 stoichiometric ratio of palladium atoms and acetate ligands, the compound exists as molecular and polymeric forms. Pd achieves approximate square planar coordination in both forms. As prepared by Wilkinson and coworkers in 1965 and later characterized by Skapski and Smart in 1970 by single crystal X-ray diffraction, palladium(II) acetate is a red-brown solid that crystallizes as monoclinic plates. It has a trimeric structure, consisting of an equilateral triangle of Pd atoms each pair of which is bridged with two acetate groups in a butterfly conformation.

The National Flag of the Philippines () is a horizontal flag bicolor with equal bands of royal blue and crimson red, with a white, equilateral triangle at the hoist. In the center of the triangle is a golden-yellow sun with eight primary rays, each representing a Philippine province. At each vertex of the triangle is a five-pointed, golden-yellow star, each of which representing one of the country's three main island groups—Luzon, Visayas (though originally referring to Panay) and Mindanao. The white triangle at the flag represents liberty, equality, and fraternity.

The summit is most easily accessed from Grayson Highlands State Park by following the Appalachian Trail southbound for to a blue-blazed trail leading to the summit, which is covered by trees and marked with four National Geodetic Survey triangulation station disks; a standard station disk marked with an equilateral triangle and three standard reference disks marked with arrows pointing towards the station disk. One reference disk has been obscured by dense overgrowth. Because the Appalachian Trail passes within a half mile of the summit, the area is especially popular with hikers.

It was built at the end of Giacomo della Porta's long courtyard. The dome and cochlear steeple are peculiar, and reflect the idiosyncratic architectural motifs that distinguish Borromini from contemporaries. Inside, the nave has an unusual centralized plan circled by alternating concave and convex-ending cornices, leading to a dome decorated with linear arrays of stars and putti. The geometry of the structure is a symmetric six-pointed star; from the center of the floor, the cornice looks like a two equilateral triangles forming a hexagon, but three of the points are clover-like, while the other three are concavely clipped.

The southeastern wall of the Kaaba in Mecca is aligned with the rising point of Canopus, and is also named Janūb. The Bedouin people of the Negev and Sinai knew Canopus as Suhayl, and used it and Polaris as the two principal stars for navigation at night. Because it disappears below the horizon in those regions, it became associated with a changeable nature, as opposed to always-visible Polaris, which was circumpolar and hence 'steadfast'. The south celestial pole can be approximately located using Canopus and another bright star, Achernar, as the three make an equilateral triangle.

The Avrocar was a disk-shaped aircraft with the same basic shape as a frisbee, the upper surface of the disk being fairly curved, and the bottom much less so. The disk was in diameter and thick. The main structural truss was a large equilateral triangle, to which the various components were attached. The 124-blade "turborotor" sat in the center of the triangle, with most of the rotor's thrust directed straight down through an opening in the lower surface, but some was bled off to power the control system running along the outer rim of the disk.

Other nearby islands (all uninhabited) include Jarvis Island, to the northwest, Vostok Island, to the south- southeast, and Caroline (Millennium) Island, to the southeast. The island has roughly the shape of an equilateral triangle, with on a side, aligned with the southwest side running northwest to southeast. The west and south corners are slightly truncated, shortening the north, east and southwest coasts to about , and adding shorter west and south coasts about 1 to 2 km (½–1 mi) in length. A large, mostly shallow, irregularly shaped lagoon, containing a number of small islets, fills the east central part of the island.

It consists of a revolving solid equilateral triangular prism made of wood. On each of its three faces, a different scene is painted, so that, by quickly revolving the periaktos, another face can appear to the audience. Other solid polygons can be used, such as cubes, but triangular prisms offer the best combination of simplicity, speed and number of scenes per device. A tabletop model of a set with two periaktoi A series of periaktoi positioned one after the other along the stage's depth can produce the illusion of a longer scene, composed by its faces as seen in perspective.

The airfield opened in October 1916 as a Royal Flying Corps aerodrome with three grassed runways laid out in an equilateral triangle. The aerodrome remained busy throughout the First World War as a flying training establishment with a large number of aircraft present, flying mostly a motley assortment of de Havilland DH and Royal Aircraft Factory BE and FE marques. The station was mothballed and placed on a care and maintenance basis between the wars. Surveyed in 1937 as a possible fighter base it was decided that the terrain and location was unsuitable for tarmac runways.

The nonnegative orthant of Rn and the space of all positive semidefinite matrices are self-dual, as are the cones with ellipsoidal base (often called "spherical cones", "Lorentz cones", or sometimes "ice-cream cones"). So are all cones in R3 whose base is the convex hull of a regular polygon with an odd number of vertices. A less regular example is the cone in R3 whose base is the "house": the convex hull of a square and a point outside the square forming an equilateral triangle (of the appropriate height) with one of the sides of the square.

Allegory of the Arithmetic with knotted rope (taken from the Hortus deliciarum (around 1180) The arithmetic rope, or knotted rope, was a widely used arithmetic tool in the Middle Ages that could be used to solve many mathematical and geometrical problems. An arithmetic rope generally has at least 13 knots—therefore, it is often called thirteen-knot-rope—placed at equal intervals. More knots were beneficial, especially for multiplication and division. In medieval architecture, the knotted rope was indispensable for architects, because it allowed the construction of equilateral and right- angled triangles, as well as circles.

The John P. Robarts Research Library, commonly referred to as Robarts Library, is the main humanities and social sciences library of the University of Toronto Libraries and the largest individual library in the university. Opened in 1973 and named for John Robarts, the 17th Premier of Ontario, the library contains more than 4.5 million bookform items, 4.1 million microform items and 740,000 other items. The library building is one of the most significant examples of brutalist architecture in North America. Its towering main structure rests on an equilateral triangular footprint and features extensive use of triangular geometric patterns throughout.

The forewings are light golden brown, at the basal fourth with an outwardly oblique white transverse streak, attenuated towards the dorsum and not quite reaching the dorsal edge. There is an equilateral triangular white spot on the middle of the costa and at apical fourth an inwardly directed triangular white spot. All of these white spots are marginal and continued across the wing by black and metallic-blue scales and terminate on the dorsal edge in small white spots. The apical and terminal edges are broadly velvety black with conspicuous tufts of metallic-blue scales around the margin.

In England in 1848, James Warren and Willoughby Monzani had obtained a British patent for a configuration of repetitive equilateral triangles that could support a road on either its top or bottom chord. Warren's name became synonymous with this form. The first major spans using this configuration were built in England, and English construction firms built prefabricated versions for use in the British colonies, especially India. Thomas Kennard then applied a more detailed analysis of the stress distribution, allowing further economy in the use of iron by varying the cross-sectional area of the top and bottom chords without adversely affecting strength.

The Prince Alfred Bridge over the Murrumbidgee River is a three span, wrought iron, pin jointed Warren truss on cast iron cylindrical piers. A Warren truss, as originally patented, consists of a configuration of repetitive equilateral triangles that support a road on either the top or bottom chord. The trusses of the Prince Alfred Bridge have additional verticals at each cross girder location, designed to provide lateral support to the top chord. The trusses are suspended from a continuous horizontal top chord, supported on a nest of five rollers located on vertical pillars attached to the top of each pier.

Vigilant and Valkyrie II Launched on June 14, 1893, Vigilant beat Colonia, Jubilee, and Pilgrim to win the 1893 American selection trials for the America's Cup defense. In the 1893 America's Cup Vigilant faced Lord Dunraven's British keel cutter Valkyrie II in a best three out of five races format sailed on alternating courses. The races were sailed October 7, 9, and 13, 1893 off Sandy Hook, NJ just south of New York. The first and third races were 15 miles to windward off Scotland Lightship and return to leeward, the second race was a 30-mile equilateral triangle.

Opening page of MS 210, featuring an attribution to Count of St. Germain and a peculiar looking dragon The Triangular Book of St. Germain or The Triangular Manuscript is an untitled 18th-century French text written in code, and attributed to the legendary Count of St. Germain. It takes its name from its physical shape: the binding and sheets of vellum that comprise the manuscript are in the shape of an equilateral triangle. The text, once deciphered, details a magical operation through which a person can perform feats of magic, notably the discovery of treasure and extension of life.

The first section deals with the proposed route of the survey. Greater accuracy is achieved if the triangles are kept regular in shape, and the figure shows that most are close to equilateral, with departures only where the triangles step down in size toward the bases and where they have to stretch over the Channel. Typical sides are about 20 miles but the lines which cross the Channel are up to 45 miles in length. The second part of the report is a thorough examination of the results of Cassini's survey of France between Paris and Dunkirk.

The summit is pyramid-shaped, the culmination of three ridges meeting in an equilateral configuration. The nearest Munro is its "twin summit", Mam Sodhail, about to the southwest, and there are three other Munros on the massif. Beinn Fhionnlaidh ends a spur to the north, and there is a much longer grassy ridge running out to the east, which after leads to Tom a' Choinich () and then after a similar distance culminates in the rather bland summit of Toll Creagach, at . As well as the five Munros topping the massif, there are a further 10 subsidiary minor summits, known as "Munro Tops".

In number theory, the Padovan sequence is the sequence of integers P(n) defined. by the initial values :P(0)=P(1)=P(2)=1, and the recurrence relation :P(n)=P(n-2)+P(n-3). The first few values of P(n) are :1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, ... Spiral of equilateral triangles with side lengths which follow the Padovan sequence. The Padovan sequence is named after Richard Padovan who attributed its discovery to Dutch architect Hans van der Laan in his 1994 essay Dom.

Although still in the early design study phase, the basic parameters are established. Like KAGRA, it will be located underground to reduce seismic noise and "gravity gradient noise" caused by nearby moving objects. The arms will be 10 km long (compared to 4 km for LIGO, and 3 km for Virgo and KAGRA), and like LISA, there will be three arms in an equilateral triangle, with two detectors in each corner. In order to measure the polarization of incoming gravitational waves and avoid having an orientation to which the telescope is insensitive, a minimum of two detectors are required.

Because voussoir domes have lateral support, they can be made much thinner than corresponding arches of the same span. For example, a hemispherical dome can be 2.5 times thinner than a semicircular arch, and a dome with the profile of an equilateral arch can be thinner still. The optimal shape for a masonry dome of equal thickness provides for perfect compression, with none of the tension or bending forces against which masonry is weak. For a particular material, the optimal dome geometry is called the funicular surface, the comparable shape in three dimensions to a catenary curve for a two-dimensional arch.

The Warren truss consists of longitudinal members joined only by angled cross-members, forming alternately inverted Equilateral triangle-shaped spaces along its length. This gives a pure truss: each individual strut, beam, or tie is only subject to tension or compression forces, there are no bending or torsional forces on them. Loads on the diagonals alternate between compression and tension (approaching the centre), with no vertical elements, while elements near the centre must support both tension and compression in response to live loads. This configuration combines strength with economy of materials and can therefore be relatively light.

A lower symmetry case of the triangular pyramid is C3v, which has an equilateral triangle base, and 3 identical isosceles triangle sides. The square and pentagonal pyramids can also be composed of regular convex polygons, in which case they are Johnson solids. If all edges of a square pyramid (or any convex polyhedron) are tangent to a sphere so that the average position of the tangential points are at the center of the sphere, then the pyramid is said to be canonical, and it forms half of a regular octahedron. Pyramids with a hexagon or higher base must be composed of isosceles triangles.

The isoperimetric problem is sometimes simplified by restricting the type of figures to be used. In particular, to find the quadrilateral, or the triangle, or another particular figure, with the largest area amongst those with the same shape having a given perimeter. The solution to the quadrilateral isoperimetric problem is the square, and the solution to the triangle problem is the equilateral triangle. In general, the polygon with sides having the largest area and a given perimeter is the regular polygon, which is closer to being a circle than is any irregular polygon with the same number of sides.

One sleeping drunkard on the left and another with a goat on the right only show their bare backsides. A third satyr who clings to the large column shaft appears to have no good intentions. Only at second glance it becomes clear that the apparent disorder is organized by a strict ordering principle, since all three satyrs embrace the center in the form of an equilateral triangle.Bettina Baumgärtel, Alessandro Magnasco, gen. Il Lissandrino (1667 - 1749), und Clemente Spera (1661 - 1730), Das Satyrfest, 1710 – 1715’ Antique ruins with figures with Sebastiano Ricci Spera also collaborated with other leading figure painters.

Mike Warburton is an amateur mathematician working in probabilistic number theory who was educated at George Heriot's School in Edinburgh. His son's mathematics GCSE coursework involved investigating the growth of equilateral triangles or squares in the Euclidean plane with the rule – a new generation is born if and only if connected to the last by only one-edge. That coursework concluded with a recursive formula for the number of ON cells born in each generation. Later, Warburton found the sharp upper bound formula which he wrote up as a note in the Open University’s M500 magazine in 2002.

Using this equation, the amount of microfouling spores per mm2 can be modeled. Similar to actual shark skin, the patterned nature of Sharklet AF shows microstructural differences in three dimensions with a corresponding ERI of 9.5. This three-dimensional patterned difference imparts a 77% reduction in microfouling settlement. Other artificial nonpatterned nanoscale rough surfaces such as 2-μm-diameter circular pillars (ERI = 5.0) or 2-μm-wide ridges (ERI = 6.1) reduce fouling settlement by 36% and 31%, respectively, while a more patterned surface composed of 2-μm-diameter circular pillars and 10-μm equilateral triangles (ERI = 8.7) reduces spore settlement by 58%.

The surprising answer is that there are many non-circular shapes of constant width. A nontrivial example is the Reuleaux triangle. To construct this, take an equilateral triangle with vertices ABC and draw the arc BC on the circle centered at A, the arc CA on the circle centered at B, and the arc AB on the circle centered at C. The resulting figure is of constant width. The Reuleaux triangle lacks tangent continuity at three points, but constant-width curves can also be constructed without such discontinuities (as shown in the second illustration on the right).

Set square The side lengths of a 30°–60°–90° triangle This is a triangle whose three angles are in the ratio 1 : 2 : 3 and respectively measure 30° (), 60° (), and 90° (). The sides are in the ratio 1 : : 2\. The proof of this fact is clear using trigonometry. The geometric proof is: :Draw an equilateral triangle ABC with side length 2 and with point D as the midpoint of segment BC. Draw an altitude line from A to D. Then ABD is a 30°–60°–90° triangle with hypotenuse of length 2, and base BD of length 1.

The materials for the Price Tower are equally innovative for a mid- twentieth-century skyscraper: cast concrete walls, pigmented concrete floors, aluminum-trimmed windows and doors, and patinated embossed and distressed copper panels. The general geometric element is the equilateral triangle, and all lighting fixtures and ventilation grilles are based upon that form while the angled walls and built-in furniture are based on fractions or multiples of the triangular module. The lobby contains two inscriptions by Walt Whitman. One is from the concluding stanza of Salut au Monde, and the other from Song of the Broad-Axe.

Some of its geological features are natural preservation areas.Nicola Williams, Oliver Berry, Stuart Butler, Jean-Bernard Carillet, Kerry Christiani, Gregor Clark, Emilie Filou, Catherine Le Nevez & Daniel Robinson (2015). Lonely Planet France (Travel Guide) Paperback – 13 Mar 2015 by Lonely Planet. The general shape of the Bassin d'Arcachon is that of an equilateral triangle pointing north, the southwest corner of which is open to the sea, between Cap Ferret and the town of Arcachon (more specifically, one of the suburbs of La Teste- de-Buch, Pyla-sur-Mer), through a 3 km narrow channel (Les Passes).

This arrangement has only m ordinary lines, the lines that connect a vertex v with the point at infinity collinear with the two neighbors of v. As with any finite configuration in the real projective plane, this construction can be perturbed so that all points are finite, without changing the number of ordinary lines. For odd n, only two examples are known that match Dirac's lower bound conjecture, that is, with t_2(n)=(n-1)/2 One example, by , consists of the vertices, edge midpoints, and centroid of an equilateral triangle; these seven points determine only three ordinary lines.

For equal masses, one possible central configuration places the masses at the vertices of a regular polygon (forming a Klemperer rosette), a Platonic solid, or a regular polytope in higher dimensions. The centrality of the configuration follows from its symmetry. It is also possible to place an additional point, of arbitrary mass, at the center of mass of the system without changing its centrality. Placing three masses in an equilateral triangle, four at the vertices of a regular tetrahedron, or more generally masses at the vertices of a regular simplex produces a central configuration even when the masses are not equal.

Fig. 1: Diagram of Gaspard–Rice scattering system showing major parameters. An excellent example system is the "Gaspard–Rice" (GR) scattering system —also known simply as the "three-disc" system—which embodies many of the important concepts in chaotic scattering while being simple and easy to understand and simulate. The concept is very simple: we have three hard discs arranged in some triangular formation, a point particle is sent in and undergoes perfect, elastic collisions until it exits towards infinity. In this discussion, we will only consider GR systems having equally sized discs, equally spaced around the points of an equilateral triangle.

Since then, dissection puzzles have been used for entertainment and maths education, and creation of complex dissection puzzles is considered an exercise of geometric principles by mathematicians and math students. The dissections of regular polygons and other simple geometric shapes into another such shape was the subject of Martin Gardner's November 1961 "Mathematical Games column" in Scientific American. The haberdasher's problem shown in the figure below shows how to divide up a square and rearrange the pieces to make an equilateral triangle. The column included a table of such best known dissections involving the square, pentagon, hexagon, greek cross, and so on.

The "barbed quatrefoil" The barbed quatrefoil is a quatrefoil pierced at the angles by the points of an inscribed square, which gives an image akin to an heraldic rose, which is termed "barbed" due to the stylised thorns which project at the intersection of each pair of petals. The earliest example of the barbed quatrefoil appears on the south transept buttresses of 1260 in the Cathedral of Notre Dame in Paris. Similarly, the trefoil is often combined with an equilateral triangle to form a barbed trefoil. Barbed quatrefoil containing relief of The Sacrifice of Isaac (1401) by Lorenzo Ghiberti for the Baptistry, Florence.

Each FAR could feed data to up to three Zeus sites. By the time the Zeus plans were being finalized in 1957, plans for FAR were deemphasized, and LAR had been upgraded to become the Zeus Acquisition Radar (ZAR) which provided wide area early warning and initial tracking information. This enormously powerful radar was driven by multiple 1.8 MW klystrons and broadcast through three wide antennas arranged as the outside edges of a rotating equilateral triangle. The ZAR spun at 10 RPM, but with three antennas it simulated a single antenna rotating three times as fast.

On the way to the fort at Kothapalem (known as Puttakota in the past), at the foothill of the fort, an embankment is seen which is inferred as a security ring bund to protect the royal family palaces and houses of the main functionaries of the fort. The fort's ruins on the southwest side of the Kondaveedu village is in the shape of an equilateral triangle, and at the turning angles of the triangle at the south west and north east, tower bastions are provided, which form part of the façade wall of the fort. A single wall of length straddles the hills.

Nevertheless, many record companies released stereo "demonstration" records to help promote stereo. These records often included instructions for setting up a stereo system, 'balancing' the speakers, and a variety of ambient recordings to show off the stereo effect. When playing back stereo recordings, the best results are obtained by using two identical speakers, in front of and equidistant from the listener, with the listener located on a center line between the two speakers. In effect, an equilateral triangle is formed, with the angle between the two speakers around 60 degrees as seen from the listener's point of view.

The results regarding the existence of the Napoleon points can be generalized in different ways. In defining the Napoleon points we begin with equilateral triangles drawn on the sides of the triangle ABC and then consider the centers X, Y, and Z of these triangles. These centers can be thought as the vertices of isosceles triangles erected on the sides of triangle ABC with the base angles equal to /6 (30 degrees). The generalizations seek to determine other triangles that, when erected over the sides of the triangle ABC, have concurrent lines joining their external vertices and the vertices of triangle ABC.

In the bill he proposed, without argument, his own method: This appears needlessly convoluted, as an "equilateral rectangle" is, by definition, a square. In simple terms, the assertion is that the area of a circle is the same as that of a square with the same perimeter. This claim results in other mathematical contradictions to which Goodwin attempts to respond. For example, right after the above quotation, the bill goes on to say: In the model circle above, the Archimedean area (accepting Goodwin's values for the circumference and diameter) would be 80, whereas Goodwin's proposed rule leads to an area of 64.

Most of the stories feature Dr. Donald A. Channing, Director of Communications at Venus Equilateral; Walter Franks, Beam Control Engineer; and Arden Westland, Channing's secretary turned fiancée turned wife. Other regular characters include heads of development Charles and Freddie Thomas, Master Mechanic Michael Warren, Martian archeologists Barney Carroll and James Baler, Baler's sister Christine, Terran Electric Company lawyer Mark Kingman, Terran Electric physicist Wesley Farrell, and neurosurgeon-turned- evil-genius Allison "Hellion" Murdoch. A frequent background character is Joe, operator of the "best Bar in Twenty-Seven Million Miles, Minimum!", upon whose tablecloths the engineers do much of their brainstorming.

On the sun there is an equilateral triangle (colored red as opposed to the Flag's white), representing liberty, equality, and fraternity, which were ideals of the Revolution. The stars at the corners of the triangle represent the three major island groups of Luzón, Visayas and Mindanao. At the center of the coat-of-arms is a Sea-lion, which is derived from the coat-of-arms of the City of Manila granted by Philip II of Spain in 1596. It has the upper half of a lion, and the lower half and curled tail of a fish.

The leg footpads formed the vertices of an equilateral triangle with sides when viewed from above, with the long sides of the base forming a straight line with the two adjoining footpads. Instrumentation was attached inside and on top of the base, elevated above the surface by the extended legs. Each lander was enclosed in an aeroshell heat shield designed to slow the lander down during the entry phase. To prevent contamination of Mars by Earth organisms, each lander, upon assembly and enclosure within the aeroshell, was enclosed in a pressurized "bioshield" and then sterilized at a temperature of for 40 hours.

Euler's line (red) is a straight line through the centroid (orange), orthocenter (blue), circumcenter (green) and center of the nine-point circle (red). In geometry, the Euler line, named after Leonhard Euler (), is a line determined from any triangle that is not equilateral. It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle. The concept of a triangle's Euler line extends to the Euler line of other shapes, such as the quadrilateral and the tetrahedron.

This low one-story home is built of Wisconsin limestone, redwood board and batten, and glass. It is one of Wright's diamond module homes, a form he used in the Patrick and Margaret Kinney House, the Richard Smith House and a number of other homes he designed in the late 1940s and early 1950s. In this design, all the angles are either 60°or 120°, forming equilateral parallelogram modules having sides. It was originally built with two wings set at 120° angles which gave the house a V-shaped plan with a living room wing, a bedroom wing, and a central core that contained the fireplace mass, kitchen, and utilities.

Ten-pin bowling is a type of bowling in which a bowler rolls a bowling ball down a wood or synthetic lane toward ten pins positioned evenly in four rows in an equilateral triangle at the far end of the lane. The objective is to knock down all ten pins on the first roll of the ball (a strike), or failing that, on the second roll (a spare). An approximately long approach area used by the bowler to impart speed and apply rotation to the ball ends in a foul line. The , lane is bordered along its length by gutters (channels) that collect errant balls.

Three famous questions of Greek geometry were how: # ... with compass and straight- edge to trisect any angle, # to construct a cube with a volume twice the volume of a given cube # to construct a square equal in area to that of a given circle. For more than 2,000 years unsuccessful attempts were made to solve these problems; at last, in the 19th century it was proved that the desired constructions are logically impossible.Nagel and Newman p. 8 A fourth problem of the ancient Greeks was to construct an equilateral polygon with a specified number n of sides, beyond the basic cases n = 3, 4, 5 that they knew how to construct.

The Fermat point of a triangle with largest angle at most 120° is simply its first isogonic center or X(13), which is constructed as follows: # Construct an equilateral triangle on each of two arbitrarily chosen sides of the given triangle. # Draw a line from each new vertex to the opposite vertex of the original triangle. # The two lines intersect at the Fermat point. An alternative method is the following: # On each of two arbitrarily chosen sides, construct an isosceles triangle, with base the side in question, 30-degree angles at the base, and the third vertex of each isosceles triangle lying outside the original triangle.

He predicts that the next month will see one final killing. In the meantime, the detective's office receives an anonymous tip to view the locations of the murders on a map, revealing that each coincides to the point of an equilateral triangle. Recognizing that the southern end of the city has yet to be terrorized, Lönnrot extrapolates that the complete pattern will create a rhombus (the south appears frequently in Borges's writings as an allusion to the Argentine frontier, and by extension, as a symbol of solitude, lawlessness, and fate). Lönnrot arrives at the site a day in advance, prepared to surprise the murderers.

The airfield opened in November 1916 as a Royal Flying Corps training aerodrome with three grassed runways laid out in an equilateral triangle, unusually oriented to the north.Opening and runways The aerodrome remained busy throughout the First World War as a flying training establishment with a large number of aircraft present, flying mostly a motley assortment of de Havilland DH marques and Sopwith Camels. de Havilland DH-9 bomber The Royal Flying Corps' No.98 Squadron formed at Harlaxton from elements drawn from the training squadrons. After training at the station and Old Sarum Airfield the squadron was deployed to France in a day-bombing role flying DH-9s.

Star of David The Star of David (✡︎), known in Hebrew as the Shield of David or Magen David (Hebrew ; Biblical Hebrew Māḡēn Dāwīḏ , Tiberian , Modern Hebrew , Ashkenazi Hebrew and Yiddish Mogein Dovid or Mogen Dovid), is a generally recognized symbol of modern Jewish identity and Judaism.Yacov Newman, Gavriel Sivan, Judaism A-Z Its shape is that of a hexagram, the compound of two equilateral triangles. The identification of the term "Star of David" or "Shield of David" with the hexagram shape dates to the 17th century. The term "Shield of David" is also used in the Siddur (Jewish prayer book) as a title of the God of Israel.

The ratio of 1:2, in the square separator theorem above, is the best that can be guaranteed: there are collections of shapes that cannot be separated in a better ratio using a separator that crosses only O(sqrt(n)) shapes. Here is one such collection (from theorem 34 of ): Consider an equilateral triangle. At each of its 3 vertices, put N/3 shapes arranged in an exponential spiral, such that the diameter increases by a constant factor every turn of the spiral, and each shape touches its neighbours in the spiral ordering. For example, start with a 1-by-Φ rectangle, where Φ is the golden ratio.

The traditional way to construct a regular polygon, or indeed any other figure on the plane, is by compass and straightedge. Constructing some regular polygons in this way is very simple (the easiest is perhaps the equilateral triangle), some are more complex, and some are impossible ("not constructible"). The simplest few regular polygons that are impossible to construct are the n-sided polygons with n equal to 7, 9, 11, 13, 14, 18, 19, 21,... Constructibility in this sense refers only to ideal constructions with ideal tools. Of course reasonably accurate approximations can be constructed by a range of methods; while theoretically possible constructions may be impractical.

Oval plan churches spread outside of Rome following Vignola's innovation with the church of Santa Anna dei Palafrenieri. Giovan Battista Aleotti built both in Argenta and San Carlo Borromeo in Ferrara between 1609 and 1621. The oval plans synthesize longitudinal and central plan church layouts, allowing clear views of the altar from all points. Francesco Borromini's dome of San Carlo alle Quattro Fontane (1638–41) has a novel oval plan that approximates an ellipse using four circular arcs based on the vertices of two large equilateral triangles; a complex geometrical coffer pattern of crosses, octagons, and lozenges is repeated eight times on the dome's inner surface.

The Golden Triangle is an informal designation for a region renowned as one of the premier fly fishing locations in the United States. The region is named for its approximate boundaries that form an equilateral triangle having an apex at Glacier National Park and encompassing Yellowstone National Park and the eastern portion of Idaho. Superior fly fishing also exists in the surrounding areas of the Rocky Mountains in Idaho and western Montana. Because of a large number of major rivers such as the Yellowstone, Madison, Gallatin, and the Blackfoot, many hundreds of fast, clear-running streams and high alpine lakes, the region contains a large number of trout.

In it, Stephens expressed his conviction that the "Everlasting Truth sealed by the Grand Architect of the Universe" is that "everything of value, or merit, is the result of creative Industry." Rituals included lectures on the nobility of labor and the evils of wage slavery, monopoly, and over-accumulation of wealth. Stephens created an equilateral triangle within a circle as the new order’s emblem, embellishing it with symbolism from the various lodges to which he belonged. The Knights of Labor elected Stephens as the first local Master Workman, the first District Master Workman, and the first Grand Master Workman, the highest position in the organization.

Grid cells derive their name from the fact that connecting the centers of their firing fields gives a triangular grid. To detect grid cell activity in a typical rat experiment, an electrode which can record single-neuron activity is implanted in the dorsomedial entorhinal cortex and collects recordings as the rat moves around freely in an open arena. The resulting data can be visualized by marking the rat's position on a map of the arena every time that neuron fires an action potential. These marks accumulate over time to form a set of small clusters, which in turn form the vertices of a grid of equilateral triangles.

Now, form the next row of spheres. Again, the centers will all lie on a straight line with x-coordinate differences of 2r, but there will be a shift of distance r in the x-direction so that the center of every sphere in this row aligns with the x-coordinate of where two spheres touch in the first row. This allows the spheres of the new row to slide in closer to the first row until all spheres in the new row are touching two spheres of the first row. Since the new spheres touch two spheres, their centers form an equilateral triangle with those two neighbors' centers.

The symmetric group S3, consisting of the 6 permutations of three elements, has three conjugacy classes: :no change (abc → abc) :transposing two (abc → acb, abc → bac, abc → cba) :a cyclic permutation of all three (abc → bca, abc → cab) These three classes also correspond to the classification of the isometries of an equilateral triangle. numbered list). Each row contains all elements of the conjugacy class and each column contains all elements of . The symmetric group S4, consisting of the 24 permutations of four elements, has five conjugacy classes, listed with their cycle structures and orders: :(1)4 no change (1 element: { (1, 2, 3, 4) }).

He says: "[...] Does it not require some pains and skill to form the general idea of a triangle (which is yet none of the most abstract, comprehensive and difficult) for it must be neither oblique nor rectangle, neither equilateral, equicrural, nor scalenon, but all and none of these at once?" (A Treatise Concerning the Principles of Human Knowledge, Introduction, section 13.) Berkeley is here criticizing John Locke, demonstrating that each representation is particular (i.e., individual). Whether there is a meaning or not depends on the individual person: it is possible that a sentence has a meaning according to A, whereas B can't discern any.

Conway calls it a kisrhombille for his kis vertex bisector operation applied to the rhombille tiling. More specifically it can be called a 3-6 kisrhombille, to distinguish it from other similar hyperbolic tilings, like 3-7 kisrhombille. The related rhombille tiling becomes the kisrhombille by cutting each rhombic face along its diagonals into four triangular faces It can be seen as an equilateral hexagonal tiling with each hexagon divided into 12 triangles from the center point. (Alternately it can be seen as a bisected triangular tiling divided into 6 triangles, or as an infinite arrangement of lines in six parallel families.) It is labeled V4.6.

For twenty years, he had a successful column, "Perplexities", in The Strand Magazine, edited by the former editor of Tit-Bits, George Newnes. Dudeney continued to exchange puzzles with fellow recreational mathematician Sam Loyd for a while, but broke off the correspondence and accused Loyd of stealing his puzzles and publishing them under his own name. Some of Dudeney's most famous innovations were his 1903 success at solving the Haberdasher's Puzzle (Cut an equilateral triangle into four pieces that can be rearranged to make a square) and publishing the first known crossnumber puzzle, in 1926. He has also been credited with discovering new applications of digital roots.

All four of the cut center flaps from each pinwheel square are extended outward; each of the eight new faces is formed by overlapping one flap each from three adjacent faces to form an equilateral triangle. Originally, the overlapped triangle was glued together, although it is possible to construct a triangular face hinge that does not require glue. The folding pattern for this form was documented by Isao Honda in 1933 alongside the simple cube. It was also documented by Harry Houdini as a "Japanese hexagon puzzle box" in 1922 without the simple cube version, in the company of several other traditional models which he learned from a Japanese acquaintance.

Papers three and four are "Fundamental Theorems of Analysis Generalized for Space" and "On the definition of the Trigonometric Functions", which he had presented the previous year in Chicago at the Congress of Mathematicians held in connection with the World's Columbian Exhibition. He follows George Salmon in exhibiting the hyperbolic angle, argument of hyperbolic functions. The fifth paper is "Elliptic and Hyperbolic Analysis" which considers the spherical law of cosines as the fundamental theorem of the sphere, and proceeds to analogues for the ellipsoid of revolution, general ellipsoid, and equilateral hyperboloids of one and two sheets, where he provides the hyperbolic law of cosines. In 1900 Alexander published "Hyperbolic Quaternions"A.

The national flag of Djibouti (, , ) is a horizontal flag bicolor with equal bands of light blue and light green, with a white, equilateral triangle at the hoist. In the center of the triangle is a red star. The flag combines the basic layout and colors from the flag of the Front de Libération de la Côte des Somalis. The light blue represents the sky and the sea, as well as the Issa Somalis, green represents the everlasting green of the earth, as well as the Afars, white represents the colour of peace and the red star represents the unity and the blood shed by the martyrs of independence.

In Italy, driving schools' cars are tagged with the words "Scuola guida" (driving school), and private cars with beginner drivers are tagged with a "P" capital letter: both signs are black on white reflective background. In Finland, a white triangle (equilateral with 16–25 cm sides) is used by driving schools' cars. Between 1972–1996, new drivers were limited to only drive up to in the first year, and had to use a yellow round "80" plaque (colloquially kahdeksankympin lätkä) in rear window or as a sticker on back of the cars. Today, plaques like this are used only by cars that are technically restricted to 80 km/h.

To construct a Reuleaux triangle The Reuleaux triangle may be constructed either directly from three circles, or by rounding the sides of an equilateral triangle.. The three-circle construction may be performed with a compass alone, not even needing a straightedge. By the Mohr–Mascheroni theorem the same is true more generally of any compass-and-straightedge construction,. but the construction for the Reuleaux triangle is particularly simple. The first step is to mark two arbitrary points of the plane (which will eventually become vertices of the triangle), and use the compass to draw a circle centered at one of the marked points, through the other marked point.

Upperside: The antennae are about an inch (25 mm) long, slender, setaceous, and gradually diminishing from the base to the extremities. The head is small. The thorax is clothed with long soft hair, and, with the abdomen, is of a darkish brown. A remarkable straight narrow line, or bar, of a cream colour, arises from the middle of the anterior edge of each of the forewings, and, crossing both anterior and posterior wings, ends at the abdominal edges, about half an inch below the abdomen; so that, when the wings are extended, as in the figure, these lines, with the anterior edges, form an equilateral triangle.

The cluster has D3h symmetry, consisting of an equilateral triangle of Os atoms, each of which bears two axial and two equatorial CO ligands. The Os–Os bond distance is 2.88 Â (288 pm).Corey, E. R.; Dahl, L. F. “The Molecular and Crystal Structure of Os3(CO)12” Inorganic Chemistry 1962, volume 1, pages 521–526; . Ru3(CO)12 has the same structure, whereas Fe3(CO)12 is different, with two bridging CO ligands resulting in C2v symmetry. Os3(CO)12 is prepared by the direct reaction of OsO4 with carbon monoxide at 175 °C:Drake, S. R.; Loveday, P. A. “Dodecarbonyltriosmium” Inorganic Syntheses, 1990, volume 28, pages 230–231. .

The eikosany vertices when scaled by a 1/3 move to the centres of the 2D faces of the 5-simplex. In a 3D cube 111 when scaled by 1/3 moves to the midpoint of 100 010 001, where each edge vector subtends the same distance along the long diagonal of the cube. 11100 moves to the centre of the equilateral triangle with cords 10000 01000 00100 and similarly for all the other eikosany vertices. The geometric figure for the eikosany is the face dual of the 5-simplex or birectified 5-simplex, the dual of its 2D faces, as it also has 3D and 4D facets.

The Palais de Rumine, one of the former buildings of the University of Lausanne. The milliradian (approximately 6283.185 in a circle) was first used in the mid nineteenth century by Charles-Marc Dapples (1837–1920), a Swiss engineer and professor at the University of Lausanne. Degrees and minutes were the usual units of angular measurement but others were being proposed, with "grads" (400 gradians in a circle) under various names having considerable popularity in much of northern Europe. However, Imperial Russia used a different approach, dividing a circle into equilateral triangles (60° per triangle, 6 triangles in a circle) and hence 600 units to a circle.

The white, equilateral triangle with the point facing downwards in a red disc was a completely new design and had (other than the flag or coats of arms) no prior basis. The airmens' barracks at Aspern were the only new barracks built in Vienna between the wars. The Austrian government planned the establishment of an air base in the Tulln Basin, however this plan was realised only by the German armed forces (nowadays: Brumowski Air base, near Langenlebarn). The uniform departed from all traditions and followed the international model: Grey jacket with four buttons as well as rocker emblem on the chest, and soft garrison caps more reminiscent of British models.

The same sequence of shapes, converging to the Sierpinski triangle, can alternatively be generated by the following steps: #Start with any triangle in a plane (any closed, bounded region in the plane will actually work). The canonical Sierpinski triangle uses an equilateral triangle with a base parallel to the horizontal axis (first image). #Shrink the triangle to height and width, make three copies, and position the three shrunken triangles so that each triangle touches the two other triangles at a corner (image 2). Note the emergence of the central hole—because the three shrunken triangles can between them cover only of the area of the original.

A distinctive landmark in the Helsinki cityscape, with its tall, green dome surrounded by four smaller domes, the building is in the neoclassical style. It was designed by Carl Ludvig Engel as the climax of his Senate Square layout: it is surrounded by other, smaller buildings designed by him. The church's plan is a Greek cross (a square centre and four equilateral arms), symmetrical in each of the four cardinal directions, with each arm's façade featuring a colonnade and pediment. Engel originally intended to place a further row of columns on the western end to mark the main entrance opposite the eastern altar, but this was never built.

Valkyrie II was launched on April 29, 1893, a week after Britannia, and sailed to the U.S. that October to compete in the eighth America's Cup where she faced Vigilant in a best three out of five races format sailed on alternating courses. The races were sailed October 7, 9, and 13, 1893 off Sandy Hook, NJ just south of New York. The first and third races were 15 miles to windward off Scotland Lightship and return to leeward, the second race was a 30-mile equilateral triangle. In the first race on October 7, Valkyrie II won the 11:25 am start by 15 seconds and one boat length.

They showed that rather than the traditional ruler and compass construction, it was possible to create girih designs using a set of five "girih tiles", all equilateral polygons, secondarily decorated with lines (for the strapwork). In 2016, Ahmad Rafsanjani described the use of Islamic geometric patterns from tomb towers in Iran to create auxetic materials from perforated rubber sheets. These are stable in either a contracted or an expanded state, and can switch between the two, which might be useful for surgical stents or for spacecraft components. When a conventional material is stretched along one axis, it contracts along other axes (at right angles to the stretch).

The medal is a bronze hexagon 1 3/8 inches (3.49 cm) in height and 1 1/4inches (3.18 cm) in width, with the eagle from the Great Seal of the United States displayed upon an equilateral triangle. The reverse of the medal is inscribed “DEPARTMENT OF THE ARMY CIVILIAN SERVICE COMMENDATION” at top and contains two crossed laurel branches at bottom. The medal is suspended from a ribbon 1 3/8 inches in width consisting of the following vertical stripes: 1/16” Green, 1/8” White, 5/16” Green, 1/32” White, 5/16” Green, 1/32”White, 5/16” Green, 1/8” White and 1/16” Green.

Then BGCL is a parallelogram, the two triangles BGL and CLG into which it may be subdivided are both similar to ABC, G is the midpoint of AL, and the Euler line of the triangle is the perpendicular bisector of AL. When generating a primitive automedian triangle from a primitive Pythagorean triple using the Euclidean parameters m, n, then m>n and it follows that b \ge a \ge c. As non- primitive automedian triangles are multiples of their primitives the inequalities of the sides apply to all integer automedian triangles. Equality occurs only for trivial equilateral triangles. Furthermore, because m+n is always odd, all the sides a, b, c have to be odd.

Tau Zero, a hard science fiction novel by Poul Anderson, has a spaceship using a constant acceleration drive. The spacecraft of George O. Smith's Venus Equilateral stories are all constant acceleration ships. Normal acceleration is 1 g, but in "The External Triangle" it is mentioned that accelerations of up to 5 g are possible if the crew is drugged with gravanol to counteract the effects of the g-load. Spacecraft in Joe Haldeman's novel The Forever War make extensive use of constant acceleration; they require elaborate safety equipment to keep their occupants alive at high acceleration (up to 25 g), and accelerate at 1 g even when "at rest" to provide humans with a comfortable level of gravity.

If these faces are aligned with a congruent patch of faces on the icosidodecahedron, then the hexagonal face will lie in the plane midway between two opposing triangular faces of the icosidodecahedron. The triangular hebesphenorotunda also has clusters of faces that can be aligned with corresponding faces of the rhombicosidodecahedron: the three lunes, each lune consisting of a square and two antipodal triangles adjacent to the square. The faces around each (33.5) vertex can also be aligned with the corresponding faces of various diminished icosahedra. Johnson uses the prefix hebespheno- to refer to a blunt wedge-like complex formed by three adjacent lunes, a lune being a square with equilateral triangles attached on opposite sides.

30–60–90 triangle In recreational mathematics, a polydrafter is a polyform with a 30°–60°–90° right triangle as the base form. This triangle is also called a drafting triangle, hence the name.. This triangle is also half of an equilateral triangle, and a polydrafter's cells must consist of halves of triangles in the triangular tiling of the plane; consequently, when two drafters share an edge that is the middle of their three edge lengths, they must be reflections rather than rotations of each other. Any contiguous subset of halves of triangles in this tiling is allowed, so unlike most polyforms, a polydrafter may have cells joined along unequal edges: a hypotenuse and a short leg.

300px There is a simple neusis construction using a marked ruler for a length which is the cube root of 2 times another length. #Mark a ruler with the given length; this will eventually be GH. #Construct an equilateral triangle ABC with the given length as side. #Extend AB an equal amount again to D. #Extend the line BC forming the line CE. #Extend the line DC forming the line CF #Place the marked ruler so it goes through A and one end, G, of the marked length falls on ray CF and the other end of the marked length, H, falls on ray CE. Thus GH is the given length. Then AG is the given length times .

Thomas Hutcheson published an article in the Mathematics Teacher that used a string instead of a compass and straight edge. A string can be used as either a straight edge (by stretching it) or a compass (by fixing one point and identifying another), but can also wrap around a cylinder, the key to Hutcheson's solution. Hutcheson constructed a cylinder from the angle to be trisected by drawing an arc across the angle, completing it as a circle, and constructing from that circle a cylinder on which a, say, equilateral triangle was inscribed (a 360-degree angle divided in three). This was then "mapped" onto the angle to be trisected, with a simple proof of similar triangles.

The three stars of θ2 Orionis within the Orion Nebula θ2 Orionis consists of three stars in a line, each about an arc-minute from the next. In addition to the well-known three stars, the Washington Double Star Catalog confusingly lists a component D which is actually θ1 Orionis C. There is one other star brighter than 10th magnitude in the region. V1073 Orionis is a B9.5 Orion variable that forms an equilateral triangle with θ2 Ori B and C. Bizarrely, θ2 Orionis C has a second entry in the Washington Double Star Catalog under the name S490. The companion is 10th magnitude and actually lies between θ2 Ori B and V1073 Ori.

Coordinates were measured in grades on official French terrestrial ordnance charts from the French revolution well into the 20th century. 1 grade (or in modern symbology 1 gon) = 0.9° or 0.01 right angle. One advantage of this measure is that the distance between latitude lines 0.01 gon apart at the equator is almost exactly 1 kilometer (and would be exactly 1 km if the original definition of 1 meter = quarter-meridian had been adhered to). One disadvantage is that common angles like 30° and 60° are expressed by fractional values (33 and 66 respectively) so this "decimal" unit failed to displace the "sexagesimal" units equilateral-vertex – degree – minute – second invented by Babylonian astronomers.

The Moser spindle embedded as a unit distance graph in the plane, together with a seven-coloring of the plane. As a unit distance graph, the Moser spindle is formed by two rhombi with 60 and 120 degree angles, so that the sides and short diagonals of the rhombi form equilateral triangles. The two rhombi are placed in the plane, sharing one of their acute-angled vertices, in such a way that the remaining two acute-angled vertices are a unit distance apart from each other. The eleven edges of the graph are the eight rhombus sides, the two short diagonals of the rhombi, and the edge between the unit-distance pair of acute-angled vertices.

The building stands at a prominent triangular intersection in the center of Dover-Foxcroft, where Pleasant Street diverges from East Main Street (Maine State Route 15). The building itself is a roughly triangular two-story wood frame structure, presenting a narrow three-bay front to the junction. Its roof is one of its most unusual features, beginning at the front with a nearly equilateral triangular gable pitch, which flattens out toward the rear of the building, giving an effect similar to an inverted ship's hull. The front facade has a doorway flanked by sash windows on the first floor, and a pair of symmetrically-placed windows on the second, and a smaller sash window in the gable.

The essential design of Phi Mu Alpha's official membership pin was adopted at the 1st National Convention in 1901. The design consisted of an upward-pointing equilateral triangle with a gold old-English S on a field of black enamel, surrounded by twelve pearls and six rubies. The pattern of the jeweling was three pearls at each tip, with two rubies separated by one pearl on each side. The design was modified slightly in 1910 by reducing the size of the old-English S to allow room for the Greek letters Φ, Μ, and Α, with Φ in the top corner, Μ in the lower left corner, and Α in the lower right corner.

The Schönhardt polyhedron is combinatorially equivalent to the regular octahedron: its vertices, edges, and faces can be placed in one-to-one correspondence with the features of a regular octahedron. However, unlike the regular octahedron, three of its edges have concave dihedral angles, and these three edges form a perfect matching of the graph of the octahedron; this fact is sufficient to show that it cannot be triangulated. The six vertices of the Schönhardt polyhedron can be used to form fifteen unordered pairs of vertices. Twelve of these fifteen pairs form edges of the polyhedron: there are six edges in the two equilateral triangle faces, and six edges connecting the two triangles.

Da Vinci developed the concept of dividing the surface of the globe into eight spherical equilateral triangles, each section bounded by the Equator and two meridians separate by 90°. This was the first map of this type. Some critics believe that the existing map was not really an autograph work, since the precision and expertise in the drawing does not reflect the usual high standards of da Vinci. They suggest that it was probably done by a trusted employee or copyist at Leonardo's workshop. Da Vinci's authorship would be demonstrated by Christopher Tyler in his paper entitled "Leonardo da Vinci’s World Map", in which he provides examples of derivative maps in a similar projection to da Vinci's.

As a result of origami study through the application of geometric principles, methods such as Haga's theorem have allowed paperfolders to accurately fold the side of a square into thirds, fifths, sevenths, and ninths. Other theorems and methods have allowed paperfolders to get other shapes from a square, such as equilateral triangles, pentagons, hexagons, and special rectangles such as the golden rectangle and the silver rectangle. Methods for folding most regular polygons up to and including the regular 19-gon have been developed. A regular n-gon can be constructed by paper folding if and only if n is a product of distinct Pierpont primes, powers of two, and powers of three.

The current induced alternates at the same frequency as the transmitter coil and the composite signal can be separated out to determine the distance from each individual coil, thus determining the position of the sensor in space. In two-dimensional articulography, transmitter coils are placed in an equilateral triangle along the midsagittal plane at the forehead, chin, and neck. Because of the geometric orientation of the transmitter coils, accurate readings are able to be taken as long as the sensor coils placed on the tongue stay within about a centimeter of the midsagittal plane and are not angled at more than 30 degrees. Articulographs able to measure in three dimensions use six transmitter coils organized in a spherical configuration.

The first six triangular numbers A triangular number or triangle number counts objects arranged in an equilateral triangle (thus triangular numbers are a type of figurate numbers, other examples being square numbers and cube numbers). The th triangular number is the number of dots in the triangular arrangement with dots on a side, and is equal to the sum of the natural numbers from 1 to . The sequence of triangular numbers , starting at the 0th triangular number, is :0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666...

3D model of a great icosahedron In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol {3,} and Coxeter-Dynkin diagram of . It is composed of 20 intersecting triangular faces, having five triangles meeting at each vertex in a pentagrammic sequence. The great icosahedron can be constructed analogously to the pentagram, its two-dimensional analogue, via the extension of the (n-1)-D simplex faces of the core nD polytope (equilateral triangles for the great icosahedron, and line segments for the pentagram) until the figure regains regular faces. The grand 600-cell can be seen as its four-dimensional analogue using the same process.

Skewness based on equilateral volume If the accuracy is of the highest concern then hexahedral mesh is the most preferable one. The density of the mesh is required to be sufficiently high in order to capture all the flow features but on the same note, it should not be so high that it captures unnecessary details of the flow, thus burdening the CPU and wasting more time. Whenever a wall is present, the mesh adjacent to the wall is fine enough to resolve the boundary layer flow and generally quad, hex and prism cells are preferred over triangles, tetrahedrons and pyramids. Quad and Hex cells can be stretched where the flow is fully developed and one- dimensional.

The "Bulwagga" is essentially a modified fluke style anchor which made itself known at the very beginning of the 2000s. Rather than two flukes in a symmetrical configuration, it adds a third for an equilateral triangular arrangement. This concept is an improvement over the Danforth in terms of general purpose usage, but is slightly comparatively inefficient (on account of the fact that one fluke is always unused), and is difficult to stow. New Zealander Peter Smith in the early 2000s took elements of the Spade and other types, and developed unique solutions of his own, in order to design the "Rocna" anchor, a general purpose type which uses a concave fluke, a self-righting roll-bar, and setting skids.

Runge's Farbenkugel (color sphere) Runge's interest in color was the natural result of his work as a painter and of having an enquiring mind. Among his accepted tenets was that "as is known, there are only three colors, yellow, red, and blue" (letter to Goethe of July 3, 1806). His goal was to establish the complete world of colors resulting from mixture of the three, among themselves and together with white and black. In the same lengthy letter, Runge discussed in some detail his views on color order and included a sketch of a mixture circle, with the three primary colors forming an equilateral triangle and, together with their pair-wise mixtures, a hexagon.

Two central configurations are considered to be equivalent if they are similar, that is, they can be transformed into each other by some combination of rotation, translation, and scaling. With this definition of equivalence, there is only one configuration of one or two points, and it is always central. In the case of three bodies, there are three one-dimensional central configurations, found by Leonhard Euler. The finiteness of the set of three- point central configurations was shown by Joseph-Louis Lagrange in his solution to the three-body problem; Lagrange showed that there is only one non-collinear central configuration, in which the three points form the vertices of an equilateral triangle.

The usual depiction of the Father as an older man with a white beard may derive from the biblical Ancient of Days, which is often cited in defense of this sometimes controversial representation. However, in Eastern Orthodoxy the Ancient of Days is usually understood to be God the Son, not God the Father (see below) — early Byzantine images show Christ as the Ancient of Days,Cartlidge, David R., and Elliott, J.K.. Art and the Christian Apocrypha, pp. 69–72 (illustrating examples), Routledge, 2001, , , Google books but this iconography became rare. When the Father is depicted in art, he is sometimes shown with a halo shaped like an equilateral triangle, instead of a circle.

Thus for all triangles R ≥ 2r, with equality holding for equilateral triangles. If we denote that the orthocenter divides one altitude into segments of lengths u and v, another altitude into segment lengths w and x, and the third altitude into segment lengths y and z, then uv = wx = yz. The distance from a side to the circumcenter equals half the distance from the opposite vertex to the orthocenter. The sum of the squares of the distances from the vertices to the orthocenter H plus the sum of the squares of the sides equals twelve times the square of the circumradius: :AH^2+BH^2+CH^2+a^2+b^2+c^2=12R^2.

This article discusses the geometric figure; for the science-fiction character see Spidron (character). First spidron created by Dániel Erdély in 1979, consisting of equilateral triangles and the symmetrical obtuse isosceles triangles which together form right triangles In geometry, a spidron is a continuous flat geometric figure composed entirely of triangles, where, for every pair of joining triangles, each has a leg of the other as one of its legs, and neither has any point inside the interior of the other. A deformed spidron is a three-dimensional figure sharing the other properties of a specific spidron, as if that spidron were drawn on paper, cut out in a single piece, and folded along a number of legs.

The internal magazine of the M98 system consists of an integral box machined to match the cartridge for which the rifle was being chambered, with a detachable floorplate, that can hold up to 5 rifle cartridges. The German military M98 system internal magazine boxes feature an internal magazine length of to store maximal overall length 7.92×57mm Mauser cartridges without dimensional issues. The cartridges are stored in the magazine box in a staggered column at a stacking angle of 30 degrees, so viewed from the end, three cartridges touching each other form the points of an equilateral triangle. The magazine can be loaded with single rounds by pushing the cartridges into the receiver top opening or via stripper clips.

Up until the eve of World War II, Flag Day was celebrated on annually on October 30, commemorating the date the ban on the flag was lifted. The Commonwealth of the Philippines was inaugurated in 1935. On March 25, 1936, President Manuel L. Quezon issued Executive Order No. 23 which provided for the technical description and specifications of the flag. Among the provisions of the order was the definition of the triangle at the hoist as an equilateral triangle, the definition of the aspect ratio at 1:2, the precise angles of the stars, the geometric and aesthetic design of the sun, and the formal elimination of the mythical face on the sun.

The badge of the Order of Prince Yaroslav the Wise I degree is worn on the chain of the Order, one star of the Order - on the left side of the chest, the other - on the ribbon over the right shoulder below the bow. The insignia of the Order of the I degree is made of silver and is an equilateral cross with rounded ends, topped with miniature crosses. The sides of the cross are covered with white and blue enamel, between them diverge curly rays. At the upper end of the sign is a bracket in the shape of a wreath of oak leaves, on which is superimposed the Old Slavic letter "U" (Ukraine) of blue enamel.

In any triangle, the radius of the incircle is one-third of the harmonic mean of the altitudes. For any point P on the minor arc BC of the circumcircle of an equilateral triangle ABC, with distances q and t from B and C respectively, and with the intersection of PA and BC being at a distance y from point P, we have that y is half the harmonic mean of q and t. In a right triangle with legs a and b and altitude h from the hypotenuse to the right angle, is half the harmonic mean of and .Voles, Roger, "Integer solutions of a^{-2}+b^{-2}=d^{-2}," Mathematical Gazette 83, July 1999, 269–271.

The intersection of the three octahedra is a convex polyhedron with 14 vertices and 24 faces, a tetrakis hexahedron, formed by attaching a low square pyramid to each face of the central cube. Thus, the compound can be seen as a stellation of the tetrakis hexahedron. A different form of the tetrakis hexahedron, formed by using taller pyramids on each face of the cube, is non-convex but has equilateral triangle faces that again lie on the same planes as the faces of the three octahedra; it is another of the known isohedral deltahedra. A third isohedral deltahedron sharing the same face planes, the compound of six tetrahedra, may be formed by stellating each face of the compound of three octahedra to form three stellae octangulae.

Construction of the castle was further hindered by its location, which required large amounts of stone to be hauled uphill. The location of Brahehus harmonised visually with Brahe's other two castles – Västanå Manor south of Gränna and Visingsborg Castle on Visingsö; the three of them were intended to form an equilateral triangle surrounding Gränna. The architecture of the castle was inspired by Renaissance castles in the Mälaren Valley, which syncretised native elements with the Palladian style, while the location on a hilltop emulated castles in the Rhine Valley. Brahehus consisted of a square main building with a side of , as well as two spired side towers, one to the north and one to the south, each connected to the main building by a side wall.

The Iron Triangle was an area of relatively flat terrain, shaped like an equilateral triangle, in the mountains of east central North Korea. It is situated above the 38th Parallel, halfway across the peninsula, and northeast of Seoul. It is bounded at its three corners by the towns of Ch'orwon at its western base, Kumhwa-eup at its eastern base, and P'yonggang at its northern apex. The area was an important North Korean rail and road communication center, linking east and west coastal areas with each other, and in turn connecting them with the communication net leading south through central South Korea. On 11 October the ROK 8th Division and the 7th Regiment of the 6th Division converged on P'yonggang.

Subutai Ahmad and Steve Omohundro developed biologically realistic neural models of selective attention.Subutai Ahmad and Stephen M. Omohundro, “Equilateral Triangles: A Challenge for Connectionist Vision“, Proceedings of the 12th Annual meeting of the Cognitive Science Society, MIT, (1990).Subutai Ahmad and Stephen M. Omohundro, “A Network for Extracting the Locations of Point Clusters Using Selective Attention“, ICSI Technical Report No. TR-90-011, (1990).Subutai Ahmad and Stephen M. Omohundro, “Efficient Visual Search: A Connectionist Solution“, Proceedings of the 13th Annual meeting of the Cognitive Science Society, Chicago, (1991).Bartlett Mel and Stephen M. Omohundro, “How Receptive Field Parameters Affect Neural Learning” in Advances in Neural Information Processing Systems 3, edited by Lippmann, Moody, and Touretzky, Morgan Kaufmann Publishers, Inc.

The isodynamic points S and S' as common intersection points of circles of Apollonius. The blue and red lines are the interior and exterior angle bisectors, used to construct the circles. In Euclidean geometry, the isodynamic points of a triangle are points associated with the triangle, with the properties that an inversion centered at one of these points transforms the given triangle into an equilateral triangle, and that the distances from the isodynamic point to the triangle vertices are inversely proportional to the opposite side lengths of the triangle. Triangles that are similar to each other have isodynamic points in corresponding locations in the plane, so the isodynamic points are triangle centers, and unlike other triangle centers the isodynamic points are also invariant under Möbius transformations.

A Warren truss The Warren truss was patented in 1848 by James Warren and Willoughby Theobald Monzani, and consists of longitudinal members joined only by angled cross-members, forming alternately inverted equilateral triangle-shaped spaces along its length, ensuring that no individual strut, beam, or tie is subject to bending or torsional straining forces, but only to tension or compression. Loads on the diagonals alternate between compression and tension (approaching the center), with no vertical elements, while elements near the center must support both tension and compression in response to live loads. This configuration combines strength with economy of materials and can therefore be relatively light. The girders being of equal length, it is ideal for use in prefabricated modular bridges.

A pentagonal rosette as described in Larry Niven's novel Ringworld. The term "Klemperer rosette" (often misspelled "Kemplerer rosette") is often used to mean a configuration of three or more equal masses, set at the points of an equilateral polygon and given an equal angular velocity about their center of mass. Klemperer does indeed mention this configuration at the start of his article, but only as an already known set of equilibrium systems before introducing the actual rosettes. In Larry Niven's novel Ringworld, the Puppeteers' "Fleet of Worlds" is arranged in such a configuration (5 planets spaced at the points of a pentagon), which Niven calls a "Kemplerer rosette"; this (possibly intentional) misspelling (and misuse) is one possible source of this confusion.

The vesica piscis is the intersection of two congruent disks, each centered on the perimeter of the other. The vesica piscis is a type of lens, a mathematical shape formed by the intersection of two disks with the same radius, intersecting in such a way that the center of each disk lies on the perimeter of the other.. In Latin, "vesica piscis" literally means "bladder of a fish", reflecting the shape's resemblance to the conjoined dual air bladders ("swim bladder") found in most fish. In Italian, the shape's name is mandorla ("almond"). Euclid's Elements This figure appears in the first proposition of Euclid's Elements, where it forms the first step in constructing an equilateral triangle using a compass and straightedge.

Periodic tiling by the sphinx With pentagons that are not required to be convex, additional types of tiling are possible. An example is the sphinx tiling, an aperiodic tiling formed by a pentagonal rep- tile. The sphinx may also tile the plane periodically, by fitting two sphinx tiles together to form a parallelogram and then tiling the plane by translates of this parallelogram, a pattern that can be extended to any non-convex pentagon that has two consecutive angles adding to 2, thus satisfying the condition(s) of convex Type 1 above. It is possible to divide an equilateral triangle into three congruent non-convex pentagons, meeting at the center of the triangle, and to tile the plane with the resulting three-pentagon unit.

The flag of Palestine () is a tricolor of three equal horizontal stripes (black, white, and green from top to bottom) overlaid by a red triangle issuing from the hoist. This flag is derived from the Pan-Arab colors and is used to represent the State of Palestine and the Palestinian people. It was first adopted on 28 May 1964 by the Palestinian Liberation Organization. The flag is almost identical to that of the Hashemite Kingdom of Hejaz, which is the western portion of the Arabian peninsula, and the Arab Socialist Ba'ath Party (both use a 2:3 ratio as opposed to the Palestine's 1:2) as well as the short-lived Arab Federation of Iraq and Jordan (which had an equilateral triangle at the hoist).

This tiling is uniform but not regular (it is by scalene triangles), and often regular tilings are used instead. A quotient of any tiling in the (2,3,7) family can be used (and will have the same automorphism group); of these, the two regular tilings are the tiling by 24 regular hyperbolic heptagons, each of degree 3 (meeting at 56 vertices), and the dual tiling by 56 equilateral triangles, each of degree 7 (meeting at 24 vertices). The order of the automorphism group is related, being the number of polygons times the number of edges in the polygon in both cases. :24 × 7 = 168 :56 × 3 = 168 The covering tilings on the hyperbolic plane are the order-3 heptagonal tiling and the order-7 triangular tiling.

Men from Soraken wearing upe, a headdress representing the transition to adulthood which later became a national symbol of Bougainville According to the Bougainville Flag, Emblem and Anthem (Protection) Act 2018, the flag consists of "a depiction of an upe superimposed over concentric discs of black and white on a cobalt blue field". The upe is a traditional headdress worn by Bougainvillean men as a symbol of adulthood. The black disc "represents the distinctive skin colour of the Bougainvillean people", while the white disc represents the kapkap, a traditional symbol of authority made from mother of pearl. The 24 green equilateral triangles within the kapkap symbolise "the importance of land to the Bougainvillean people", the blue field represents the ocean.

A shape is a circle because it looks like a sun; a shape is a rectangle because it looks like a door or a box; and so on. A square seems to be a different sort of shape than a rectangle, and a rhombus does not look like other parallelograms, so these shapes are classified completely separately in the child’s mind. Children view figures holistically without analyzing their properties. If a shape does not sufficiently resemble its prototype, the child may reject the classification. Thus, children at this stage might balk at calling a thin, wedge-shaped triangle (with sides 1, 20, 20 or sides 20, 20, 39) a "triangle", because it's so different in shape from an equilateral triangle, which is the usual prototype for "triangle".

The sides are not straight but are curved so that the centre of curvature is the opposite apex of the coin - this is an equilateral curve which allows the coin to roll freely in slot machines. It was of the same shape and size of the British coin of the same denomination, as both nations' pounds were pegged until 1979. The coin used the woodcock design from the pre-decimal farthing coin, introduced to the Irish Free State in 1928. Dublin Millennium 50 pence coin On 31 May 1988 a special design was circulated for the "Dublin Millennium", although Dublin is thought to have been founded by the Vikings in around 841 – the issue was regarded for publicity and collectors only.

The Schönhardt polyhedron can be formed by two congruent equilateral triangles in two parallel planes, such that the line through the centers of the triangles is perpendicular to the planes. The two triangles should be twisted with respect to each other, so that they are neither translates of each other nor 180-degree reflections of each other. The convex hull of these two triangles forms a convex polyhedron that is combinatorially equivalent to a regular octahedron; along with the triangle edges, it has six edges connecting the two triangles to each other, with two different lengths, and three interior diagonals. The Schönhardt polyhedron is formed by removing the three longest connecting edges, and replacing them by the three diagonals of the convex hull.

Geometry problem of the surface of a heptagon divided into triangles, on a clay tablet belonging to a school for scribes; Susa, the first half of the 2nd millennium BCE The United Kingdom currently (2020) has two heptagonal coins, the 50p and 20p pieces, and the Barbados Dollar are also heptagonal. The 20-eurocent coin has cavities placed similarly. Strictly, the shape of the coins is a Reuleaux heptagon, a curvilinear heptagon to make them curves of constant width: the sides are curved outwards so that the coin will roll smoothly when inserted into a vending machine. Botswana pula coins in the denominations of 2 Pula, 1 Pula, 50 Thebe and 5 Thebe are also shaped as equilateral-curve heptagons.

The only integer triangle with three rational angles (rational numbers of degrees, or equivalently rational fractions of a full turn) is the equilateral triangle. This is because integer sides imply three rational cosines by the law of cosines, and by Niven's theorem a rational cosine coincides with a rational angle if and only if the cosine equals 0, ±1/2, or ±1. The only ones of these giving an angle strictly between 0° and 180° are the cosine value 1/2 with the angle 60°, the cosine value –1/2 with the angle 120°, and the cosine value 0 with the angle 90°. The only combination of three of these, allowing multiple use of any of them and summing to 180°, is three 60° angles.

In astronomy, Lagrangian points are five positions in the orbital plane of two large orbiting bodies where a small object affected only by gravity can maintain a stable position relative to the two large bodies. The first three Lagrangian points (L1, L2, L3) lie along the line connecting the two large bodies, while the last two points (L4 and L5) each form an equilateral triangle with the two large bodies. The L4 and L5 points, although they correspond to maxima of the effective potential in the coordinate frame that rotates with the two large bodies, are stable due to the Coriolis effect. The stability can result in orbits around just L4 or L5, known as tadpole orbits, where trojans can be found.

A Besicovitch set can be created by combining three rotations of a Perron tree created from an equilateral triangle. Adapting this method further, we can construct a sequence of sets whose intersection is a Besicovitch set of measure zero. One way of doing this is to observe that if we have any parallelogram two of whose sides are on the lines x = 0 and x = 1 then we can find a union of parallelograms also with sides on these lines, whose total area is arbitrarily small and which contain translates of all lines joining a point on x = 0 to a point on x = 1 that are in the original parallelogram. This follows from a slight variation of Besicovich's construction above.

Pairs of paddlers sit facing forward in the boat, and use a specific type of paddle which, unlike equipment used in rowing, is not rigged to the boat in any way. Because the paddlers face the direction of boat-movement, dragon boaters "paddle," and do not "row." The paddle now accepted by the International Dragon Boat Organization has a standardized, fixed blade surface area and distinctive shape derived from the paddle shapes characteristic of that used by inhabitants of the Pearl River delta region of Guangdong Province, China adjacent to Hong Kong. The IDBF Paddle Specification 202a (PS202a) has straight flared edges and circular arced shoulders, based geometrically on an equilateral triangle positioned between the blade face and the neck of the shaft.

The forewings are pale straw-ochreous, with a black spot at the extreme base which is produced outward in a thin line along the costa, nearly to the middle, and is narrowly margined beneath with whitish ochreous. Before the middle of the wing is a group of four conspicuous black spots, three on the cell arranged as an equilateral triangle with the apex outward, the fourth on the fold below and a little beyond the lower of the three. Beyond these at the end of the cell are two similar spots, the upper a little beyond the lower and there is a series of six to eight much smaller black spots along the termen and around the apex. The hindwings are greyish cinereous.

Isaac Asimov's short story "Left to Right" concerns an unknown "change in parity", and mentions biological incompatibilities due to chirality as one possible consequence. In one of George O. Smith's Venus Equilateral stories, an experimental teleporter that has killed several teleported animals is discovered to have inverted their chemical chirality; in the climax, two newborn babies are successfully teleported to a hospital on Earth through the simple measure of teleporting them twice, cancelling out the inversion. In Dorothy L. Sayers's novel The Documents in the Case, a murder is committed that is designed to appear as accidental death from eating poisonous mushrooms containing muscarine. The case is proved to be murder because the muscarine found in the deceased's stomach is racemic and therefore synthetic.

At the Lagrange points the gravitational forces of the two large bodies cancel out in such a way that a small object placed in orbit there is in equilibrium relative to the center of mass of the large bodies. There are five such points, labeled L1 to L5, all in the orbital plane of the two large bodies. L1, L2, and L3 are on the line through the centers of the two large bodies, while L4 and L5 each act as the third vertex of an equilateral triangle formed with the centers of the two large bodies. L1, L2, L3 are unstable equilibria, whereas L4 and L5 are stable, which implies that objects can orbit around them in a rotating coordinate system tied to the two large bodies.

Magnified view of a delta-gun shadow mask color CRT Magnified view of a Trinitron color CRT Spectra of constituent blue, green and red phosphors in a common CRT Color tubes use three different phosphors which emit red, green, and blue light respectively. They are packed together in stripes (as in aperture grille designs) or clusters called "triads" (as in shadow mask CRTs). Color CRTs have three electron guns, one for each primary color, arranged either in a straight line or in an equilateral triangular configuration (the guns are usually constructed as a single unit). (The triangular configuration is often called "delta-gun", based on its relation to the shape of the Greek letter delta Δ.) A grille or mask absorbs the electrons that would otherwise hit the wrong phosphor.

The design for the three iron truss spans of the Prince Alfred Bridge are based on the British pin-jointed Warren and Kennard trusses, and have the unique feature of the trusses being suspended from a continuous horizontal top chord, supported on roller bearings on vertical posts at each pier. The end roller detail has five rollers placed between the extended upper chord and a pillar which rises from the pier top. A similar detail is provided at the central pier, where each upper chord is continued from one span to the next across a nest of rollers. The Warren truss, as originally patented, consisted of a configuration of repetitive equilateral triangles but the Prince Alfred Bridge has additional verticals at each cross girder location, designed to provide lateral support to the top chord.

In Book V, after an interesting preface concerning regular polygons, and containing remarks upon the hexagonal form of the cells of honeycombs, Pappus addresses himself to the comparison of the areas of different plane figures which have all the same perimeter (following Zenodorus's treatise on this subject), and of the volumes of different solid figures which have all the same superficial area, and, lastly, a comparison of the five regular solids of Plato. Incidentally, Pappus describes the thirteen other polyhedra bounded by equilateral and equiangular but not similar polygons, discovered by Archimedes, and finds, by a method recalling that of Archimedes, the surface and volume of a sphere. According to the preface, Book VI is intended to resolve difficulties occurring in the so-called "Lesser Astronomical Works" (Μικρὸς Ἀστρονοµούµενος), i.e., works other than the Almagest.

For example, the first and fourth of Euclid's postulates, that there is a unique line between any two points and that all right angles are equal, hold in elliptic geometry. Postulate 3, that one can construct a circle with any given center and radius, fails if "any radius" is taken to mean "any real number", but holds if it is taken to mean "the length of any given line segment". Therefore any result in Euclidean geometry that follows from these three postulates will hold in elliptic geometry, such as proposition 1 from book I of the Elements, which states that given any line segment, an equilateral triangle can be constructed with the segment as its base. Elliptic geometry is also like Euclidean geometry in that space is continuous, homogeneous, isotropic, and without boundaries.

In its most formal sense, the threefold model claims that any single gamemaster (GM) decision (about the resolution of in-game events) can be made in order to further the goals of Drama, or Simulation, or Game. By extension, a series of decisions may be described as tending towards one or two of the three goals, to a greater or lesser extent. This can be visualised as an equilateral triangle, with a goal at each vertex, and the points between them representing different weightings of the different goals. As a consequence, a player or GM can characterise their preferred gaming style as a point on this triangle, or (since no real precision is implied) in words such as 'mostly gamist' or 'dramatist with a bit of simulationist' or 'right in the middle'.

The molecules are made by an expanding supersonic jet of neon gas. The neon dimer has an average distance of 3.3 Å between atoms. The neon trimer is shaped approximately like an equilateral triangle with sides 3.3 Å long. However the shape is floppy and isosceles triangle shapes are also common. The first excited state of the neon trimer is 2 meV above the ground state. The neon tetramer takes the form of a tetrahedron with sides around 3.2 Å. Van der Waals molecules with metals include LiNe. More Van der Waals molecules include CF4Ne and CCl4Ne, Ne2Cl2, Ne3Cl2, I2Ne, I2Ne2, I2Ne3, I2Ne4, I2NexHey (x=1-5, y=1-4). Van der Waals molecules formed with organic molecules in gas include aniline, dimethyl ether, 1,1-difluoroethylene, pyrimidine, chlorobenzene, cyclopentanone, cyanocyclobutane, and cyclopentadienyl.

'Mary, the woman of Faith', bronze, by Terry Jones, Clifton Cathedral The votive candelabra hanging in the Lady Chapel [H on Plan] is made from twenty stainless steel equilateral triangles (a regular icosahedron) and was designed and made by Brother Patrick, of Prinknash Abbey in Gloucestershire.History Tour, Clifton Cathedral site It features in a pop music video (see Appearances in Media section). Also in the Lady Chapel is a Lampedusa Cross [J on Plan]. This is made from wood from migrant boats destroyed in the Mediterranean and recovered from Lampedusa, Italy between 2012 and 2016. It is similar to the British Museum’s Lampedusa Cross and is intended to reflect Pope Francis’s 2017 ‘Share the Journey’ exhortation for the Church to care for, and show solidarity to, all migrants and asylum seekers.

The Kagome crest; six-pointed star The Kagome crest, eight-pointed star is also known as Ashthalakshmi or Star of Lakshmi The Kagome crest or is a star- shaped crest related to the kagome lattice design. The Kagome crest can be depicted as, either, a six-pointed star (a hexagram) and as an eight-pointed star (an octagram): # The six-pointed star version (a hexagram) is composed of two interlocking equilateral triangles, similar to/interchangeable with the Hindu Shatkona (Sanskrit: षट्कोण, Ṣaṭkoṇa, lit. Six-Sided), which represents the represents the union between opposites, similar to Yin and yang) and to the Jewish Star of David. # The eight-pointed star version (an octagram) is composed of two interlocking squares, similar to/interchangeable with the Hindu Star of Lakshmi (which represents the Ashtalakshmi (Sanskrit: अष्टलक्ष्मी, Aṣṭalakṣmi, lit.

Rainbow lattice sunstone with hematite and magnetite equilateral triangle inclusions Rainbow lattice is a type of feldspar which is predominantly moonstone that is made up of 75% orthoclase and 25% albite. The inclusions are the result of crystallographically oriented exsolution crystals within the feldspar mass. Whilst the initial testing of the stones inclusions conducted in 1989 concluded that the inclusions were made up of ilmenite (for the black blades and triangles) and hematite (for the orange platelets), with the advancement in technology over the last 3 decades, a recently conducted more in depth analysis has found the black blades and triangle inclusions in Rainbow Lattice to be magnetite. Hematite (Fe2O3) which are small mainly yellow to deep orange platelets which can be hexagonal shape and are generally in one plane within the feldspar.

Hoppe wrote over 250 scientific publications, including one of the first textbooks on differential geometry. His accomplishments in geometry include rediscovering the higher-dimensional regular polytopes (previously discovered by Ludwig Schläfli),. and coining the term "polytope".. In 1880 he published a closed-form expression for all triangles with consecutive integer sides and rational area, also known as almost-equilateral Heronian triangles.. He is sometimes credited with having proven Isaac Newton's conjecture on the kissing number problem, that at most twelve congruent balls can touch a central ball of the same radius, but his proof was incorrect, and a valid proof was not found until 1953.. Hoppe published several works on a formula for the m-fold derivative of a composition of functions. The formula, now known as "Hoppe's formula", is a variation of Faà di Bruno's formula.

The work in its final execution displays the stereotypes of Late Baroque Catholic religious painting. To either side are arranged groups of angels directing the attention to the central scene, dominated by the symbol of the Christianity Trinity and Godhead: an equilateral triangle inscribed with the Tetragrammaton in Hebrew. Because the various groups are situated at different altitudes, the final impression is rather static, dominated by a composition in the shape of an "X", the result of Goya's intention to have the lines of force coming in from the corners and crossing in the centre. Various sketches and preparatory drawings for the work have been preserved which display more accomplishment than the painting on the cupola shows in actuality, although it must be borne in mind that the fresco has been restored no less than four times, in 1887, 1947, 1967 and 1991.

Symbolically, Tn = (S1)n. The configuration space of unordered, not necessarily distinct points is accordingly the orbifold Tn/Sn, which is the quotient of the torus by the symmetric group on n letters (by permuting the coordinates). For n = 2, the quotient is the Möbius strip, the edge corresponding to the orbifold points where the two coordinates coincide. For n = 3 this quotient may be described as a solid torus with cross-section an equilateral triangle, with a twist; equivalently, as a triangular prism whose top and bottom faces are connected with a 1/3 twist (120°): the 3-dimensional interior corresponds to the points on the 3-torus where all 3 coordinates are distinct, the 2-dimensional face corresponds to points with 2 coordinates equal and the 3rd different, while the 1-dimensional edge corresponds to points with all 3 coordinates identical.

The apparatus used in the colour vision experiments is depicted in Fig. 1. It was constructed by joining a box of (AK) with a box of (KN) at a 100-degree angle. A mirror at M reflects light coming through the opening at BC towards a lens at L. Two equilateral prisms at P diffract light coming from the three slits at X, Y, and Z. This illuminated the prisms with the combination of the spectral colors created by the diffraction of the light from the slits. This light was also visible through the lens at L. The observer then peered through the slit at E while the operator adjusted the position and width of each slit at X, Y, and Z until the observer could not distinguish the prism light from the pure white light reflected by the mirror.

Like all regular hypercubic honeycombs, the tesseractic honeycomb corresponds to a sphere packing of edge-length-diameter spheres centered on each vertex, or (dually) inscribed in each cell instead. In the hypercubic honeycomb of 4 dimensions, vertex-centered 3-spheres and cell-inscribed 3-spheres will both fit at once, forming the unique regular body-centered cubic lattice of equal-sized spheres (in any number of dimensions). Since the tesseract is radially equilateral, there is exactly enough space in the hole between the 16 vertex-centered 3-spheres for another edge-length-diameter 3-sphere. (This 4-dimensional body centered cubic lattice is actually the union of two tesseractic honeycombs, in dual positions.) This is the same densest known regular 3-sphere packing, with kissing number 24, that is also seen in the other two regular tessellations of 4-space, the 16-cell honeycomb and the 24-cell-honeycomb.

Viewed as a pattern, ignoring the colors of the fish, in the hyperbolic plane, the woodcut has three-fold and four-fold rotational symmetry at the centers of its triangles and squares, respectively, and order-three dihedral symmetry (the symmetry of an equilateral triangle) at the points where the white curves cross. In John Conway's orbifold notation, this set of symmetries is denoted 433. Each fish provides a fundamental region for this symmetry group. Contrary to appearances, the fish do not have bilateral symmetry: the white curves of the drawing are not axes of reflection symmetry.. Conway wrote that "The work Circle Limit III is equally intriguing" (in comparison to Circle Limit IV, which has a different symmetry group), and uses is it as an example of this symmetry group.. Paper presented to the 8th International Conference on Geometry, Nahsholim (Israel), March 7–14, 1999.

Postcard sent in June 1910. This card was among those made by the Stanford Card Co. in Brooklyn, New York The swastika (from Sanskrit svástika; also known outside the Indian subcontinent as the Hakenkreuz, gammadion cross, cross cramponnée, croix gammée, fylfot, or tetraskelion) is an ancient Indo- European religious symbol with the earliest known example found in Mezine, modern Ukraine, that generally takes the form of an equilateral cross with four legs each bent at 90 degrees in either right-facing (卐) form or its mirrored left-facing (卍) form. It is considered to be a sacred and auspicious symbol in Hinduism, Buddhism, and Jainism and dates back at least 11,000 years. The swastika (gammadion, "fylfot") symbol became a popular symbol of luck in the Western world in the early 20th century, as it had long been in Asia, and was often used for ornamentation.

This early conception then went through various iterations, in which the block was first divided into the three geometrical shapes composing the Czech flag, and was then, in a subsequent design, merged with the shape of a "Czech hedgehog" - an anti-tank obstacle most familiar to English-speakers from its use by the Germans on the beaches of Normandy but invented in Czechoslovakia and used throughout Europe in World War II. The flag motif, though eventually simplified, remained a basic element of the finished composition. It was incorporated into the design of the central column, which, being triangular in cross-section, corresponds to the equilateral triangle in the Czech flag. This simplification was necessitated by the somewhat awkward shape of the memorial site. The central column was clad in corten, a form of weathered steel, symbolizing the destruction of Czech statehood and the subjugation of the entire nation.

The Technical Member (and the only engineer) on the Decimal Currency Board was Hugh Conway, at that time President of the Institution of Mechanical Engineers and Managing Director of Bristol Siddeley Engines, Bristol. He had found in a mathematical textbook a formula for a non- circular shape of constant breadth and asked the design office at Patchway, near Bristol, which normally worked on the engines for aircraft such as Concorde, Vulcan and Harrier to draw out the shape. However, this turned out to be a wavy-edged form with re-entrant sides which would not roll and which could not be measured easily. A designer, Colin Lewis, suggested a much simpler shape which in its basic form is an equilateral triangle with a small circle centred on each apex and with a larger circular arc centred on each apex but tangential to each of the two opposite small circles.

The gate lies about 150 yards east of the edge of the plateau, which there terminates in an almost unbroken vertical precipice of several hundred feet in height and receding in a north-easterly direction. No wall was built along about three hundred yards of this part which is absolutely unscalable, but for the rest of the way the walling is continued along the edge of the cliff in a north-east direction for about another three hundred yards. Here it turns still following the cliff to the south-east for another seven hundred yards, and then gradually rounds to the westward covering four hundred and fifty yards more till it meets the gateway. But for the break of the inaccessible precipice this outer wall would form a nearly equilateral triangle with the corners rounded off, the side being of some six hundred and fifty yards.

Designed by Jean Omer Marchand and John A. Pearson, the tower is a campanile whose height reaches 92.2 m (302 ft 6 in), over which are arranged a multitude of stone carvings, including approximately 370 gargoyles, grotesques, and friezes, keeping with the Victorian High Gothic style of the rest of the parliamentary complex. The walls are of Nepean sandstone and the roof is of reinforced concrete covered with copper. One of four grotesques at the corners of the Peace Tower At its base is a porte-cochère within four equilateral pointed arches, the north of which frames the main entrance of the Centre Block, and the jambs of the south adorned by the supporters of the Royal Arms of Canada. Near the apex, just below the steeply pitched roof, are the tower's 4.8 m (16 ft) diameter clock faces, one on each of the four facades.

Gravitational accelerations at The and points lie at the third corners of the two equilateral triangles in the plane of orbit whose common base is the line between the centers of the two masses, such that the point lies behind () or ahead () of the smaller mass with regard to its orbit around the larger mass. The triangular points ( and ) are stable equilibria, provided that the ratio of is greater than 24.96.Actually ≈ , Neil J. Cornish with input from Jeremy Goodman This is the case for the Sun–Earth system, the Sun–Jupiter system, and, by a smaller margin, the Earth–Moon system. When a body at these points is perturbed, it moves away from the point, but the factor opposite of that which is increased or decreased by the perturbation (either gravity or angular momentum-induced speed) will also increase or decrease, bending the object's path into a stable, kidney bean-shaped orbit around the point (as seen in the corotating frame of reference).

In the Euclidean plane, two circles that are concentric necessarily have different radii from each other.. However, circles in three-dimensional space may be concentric, and have the same radius as each other, but nevertheless be different circles. For example, two different meridians of a terrestrial globe are concentric with each other and with the globe of the earth (approximated as a sphere). More generally, every two great circles on a sphere are concentric with each other and with the sphere.. By Euler's theorem in geometry on the distance between the circumcenter and incenter of a triangle, two concentric circles (with that distance being zero) are the circumcircle and incircle of a triangle if and only if the radius of one is twice the radius of the other, in which case the triangle is equilateral. The circumcircle and the incircle of a regular n-gon, and the regular n-gon itself, are concentric.

The interior consists of chancel, nave, transepts and south porch, and is formed of rough materials, now largely plastered and whitewashed. The large chancel was restored around 1475, primarily it would appear by extending it and adding new red sandstone Perpendicular segmental-pointed side windows, one three-light and one single- light to the south and one three-light to the north – all now with nineteenth century tracery and stained glass. The window is Gothic equilateral. South transept, east side, showing join to crossing and chancel An inscription in the left side window jamb of the east window in the south wall of the chancel may be a contemporary memorial to William Stratford;The jam-stones, four- centred heads and cills are believed to be original, with the mullions and heads of the lights being renewed in 1882–84; W. Gwyn Thomas, "The Chancel of Llanbadarn Fawr Church" (1978) 127 Archaeologia Cambrensis 127–129, at 129.

In Nazi concentration camps, each prisoner was required to wear a downward-pointing, equilateral triangular cloth badge on their chest, the color of which identified the reason for their imprisonment.See Nazi concentration camp table of inmate markings Early on, homosexual male prisoners were variously identified with a green triangle (indicating criminals) or red triangle (political prisoners), the number 175 (referring to Paragraph 175, the section of the German penal code criminalizing homosexual activity), or the letter A (which stood for Arschficker, literally "ass fucker"). Later, the use of a pink triangle was established for prisoners identified as homosexual men, which also included bisexual men and transgender women. (Lesbian and bisexual women and trans men were not systematically imprisoned; some were, and classified as "asocial", wearing a black triangle.) The pink triangle was also assigned to others considered sexual deviants, including more sexual minorities such as zoophiles and pedophiles in addition to sex offenders.

Present were John Cardinal Heenan (Archbishop of Westminster), and twenty-nine bishops from around the United Kingdom, with Bishop Joseph Rudderham (7th Bishop of Clifton); Civic Officials and Councillors of Bristol; the Italian and Belgian Consuls; the architects; Sir William 'Kirby' Laing (representing John Laing Construction Ltd); the Anglican Bishops of Bristol, of Bath and Wells, and of Salisbury.Press Release & Order of Service Mass of Consecration 29 June 1973, Clifton Diocesan Trustees, Clifton Diocesan Archives The pro-Cathedral was closed and its sale provided fund for the new parish school, SS Peter and Paul on Aberdeen Road, Clifton. Inscribed into the outside wall of the turret to the right of the Portal of Saint Paul and contained within an equilateral triangle is the symbol ‘√3’ along with the letters PTP. This engraving makes a reference to the architects [Percy Thomas Partnership] and to the controlling mathematical formula used by Ronald Weeks in the design.

Imagination Imagination A research project, Project Genesis, searches for evidence confirming the Steady State Theory of continuous creation in the area within and surrounding an unnamed American Midwestern city, according to which, 125,000 newly created neutrons (also called neoneutrons, which decay into hydrogen atoms consisting of protons and electrons while giving off hard gamma radiation - here called creation-radiation) should be called into existence in an Earth-sized volume in a twenty-four-hour period. The monitored area is an equilateral triangle with thickness of and an area of which should, by a proportional estimate, register twenty-one neoneutronic creation signatures in that same period. Suddenly, not merely twenty-one, but millions of neoneutrons are called into existence in this monitoring area, fusing some of the sensor equipment. After replacing and refusing of the sensor elements, the locus of the phenomenon is traced to a rail-yard on the edge of the zone, and further, apparently emanating from a young drug-user and hobo, Milton Bradford.

The Philippine national flag has a rectangular design that consists of a white equilateral triangle, symbolizing liberty, equality and fraternity; a horizontal blue stripe for peace, truth, and justice; and a horizontal red stripe for patriotism and valor. In the center of the white triangle is an eight-rayed golden sun symbolizing unity, freedom, people's democracy, and sovereignty. Each ray represents a province with significant involvement in the 1896 Philippine Revolution against Spain; these provinces are Manila, Bulacan, Cavite, Pampanga, Morong (modern-day province of Rizal), Laguna, Batangas, and Nueva Ecija (some sources specify other provinces as alternatives to some of these).Philippine Declaration of Independence However, according to the Declaration of Independence and a research by Ateneo de Manila University Professor Ambeth Ocampo, the rays of the sun symbolized the first eight provinces of the Philippines which was declared under martial law during the Philippine Revolution (Batangas, Bulacan, Cavite, Manila, Laguna, Nueva Ecija, Pampanga and Tarlac).

Example of microphone positioning in a Decca Tree setup A Decca Tree setup uses three omnidirectional microphones arranged in a "T" pattern outlining a triangle, often equilateral; the center microphone is mixed with the two spaced microphones to fill the "hole in the middle" in their imaging; it points the sound source. The placement can be done with three separate microphone stands or using one or more bars. In contrast to the ORTF stereo technique, the Decca Tree size is not fixed and may vary considerably; distances between the two back microphones are seen between 0.6 and 1.2 m; the front microphone is set proportionally and can be mounted slightly lower than the outside pair. The recording engineer arbitrarily adjusts these dimensions accordingly to the size of the ensemble, the dimensions of the room and the type of music. Microphone manufacturer Schoeps advises to put the three microphones at least 1.5 m apart to reduce crosstalk and excessive correlation at low frequencies (for example, setting the microphone width to 2 m and the depth to 1.5 m).

Standardized rules and organization of nine-pins were developed by the American Bowling Congress in 1895. Nine-pins was the most popular form of bowling in much of the United States from colonial times until the 1830s, when several cities in the United States banned nine-pin bowling out of moral panic over the supposed destruction of the work ethic, gambling, and organized crime. Tenpin bowling is said to have been invented in order to meet the letter of these laws, even with evidence of outdoor bowling games in 1810 England being bowled with ten pins set in an equilateral triangle as is done today in tenpin bowling. Today, nine-pins has disappeared from all of the United States except Texas, where, by 1837, ninepin alleys were numerous enough that rather than a ban, the 1st Congress of the Republic of Texas chose to subject them to an annual tax of $150, and all forms of bowling have remained legal and subject to taxation in Texas ever since.

Nine-point hyperbola: One branch bisects BA, BC, and BP. The other branch bisects PA, PC, and AC, as well as passing through BA.PC and AP.BC. In plane geometry with triangle ABC, the nine-point hyperbola is an instance of the nine-point conic described by Maxime Bôcher in 1892. The celebrated nine-point circle is a separate instance of Bôcher's conic: :Given a triangle ABC and a point P in its plane, a conic can be drawn through the following nine points: :: the midpoints of the sides of ABC, :: the midpoints of the lines joining P to the vertices, and :: the points where these last named lines cut the sides of the triangle. The conic is an ellipse if P lies in the interior of ABC or in one of the regions of the plane separated from the interior by two sides of the triangle; otherwise, the conic is a hyperbola. Bôcher notes that when P is the orthocenter, one obtains the nine-point circle, and when P is on the circumcircle of ABC, then the conic is an equilateral hyperbola.

This shape was called a Siamese dodecahedron in the paper by Hans Freudenthal and B. L. van der Waerden (1947) which first described the set of eight convex deltahedra.. The dodecadeltahedron name was given to the same shape by , referring to the fact that it is a 12-sided deltahedron. There are other simplicial dodecahedra, such as the hexagonal bipyramid, but this is the only one that can be realized with equilateral faces. Bernal was interested in the shapes of holes left in irregular close-packed arrangements of spheres, so he used a restrictive definition of deltahedra, in which a deltahedron is a convex polyhedron with triangular faces that can be formed by the centers of a collection of congruent spheres, whose tangencies represent polyhedron edges, and such that there is no room to pack another sphere inside the cage created by this system of spheres. This restrictive definition disallows the triangular bipyramid (as forming two tetrahedral holes rather than a single hole), pentagonal bipyramid (because the spheres for its apexes interpenetrate, so it cannot occur in sphere packings), and icosahedron (because it has interior room for another sphere).

533 Juan de Mata Terreforte, an exiled veteran of "El Grito de Lares" and Vice-President of the Puerto Rican Revolutionary Committee, in New York City, adopted with its members the flag of Lares as the flag of Puerto Rico, until 1895, when the current design, modeled after the Cuban flag, was unveiled and adopted by the committee. The new flag, which consisted of five equal horizontal bands of red (top and bottom) alternating with white; a blue isosceles triangle based on the hoist side bears a large, white, five-pointed star in the center, was first flown in Puerto Rico on March 24, 1897, during the "Intentona de Yauco" revolt. (This is contrasted by the usage of three blue and two white equal horizontal stripes and a red equilateral triangle at the hoist with a five-pointed star in the Cuban flag.) The use and display of the Puerto Rican flag was outlawed and the only flags permitted to be flown in Puerto Rico were the Spanish flag (1492 to 1898) and the American flag (1898 to 1952). In 1952, the Commonwealth of Puerto Rico adopted the 1895 flag design as its official standard.