In geometry, a Schwarz triangle, named after Hermann Schwarz, is a spherical triangle that can be used to tile a sphere (spherical tiling), possibly overlapping...
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complex analysis, the Schwarz triangle function or Schwarz s-function is a function that conformally maps the upper half plane to a triangle in the upper half...
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the acute and obtuse Schwarz triangles. The numbers that can be used for the sides of a non-dihedral acute or obtuse Schwarz triangle that does not necessarily...
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Hypergeometric function (redirect from Schwarz s-map)
to the Schwarzian derivative (Hille 1976, pp. 307–401). The Schwarz triangle maps or Schwarz s-functions are ratios of pairs of solutions. s k ( z ) = ϕ...
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triangle can be an ordinary Euclidean triangle, a triangle on the sphere, or a hyperbolic triangle. Each triangle group is the symmetry group of a tiling...
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theorem Schwarz reflection principle Schwarz triangle Schwarz triangle function Cauchy–Schwarz inequality Theorem of Pohlke and Schwarz Schwarz, H. A....
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functions. The upper half-plane is mapped to a triangle with circular arcs for edges by the Schwarz triangle map. The upper half-plane is mapped to the square...
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Exceptional object (section Schwarz triangles)
exceptional Schwarz triangles (triangles that tile the sphere, or more generally Euclidean plane or hyperbolic plane via their triangle group of reflections...
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construct the triangle group, start with a hyperbolic triangle with angles π/2, π/3, and π/7. This triangle, the smallest hyperbolic Schwarz triangle, tiles...
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A Reuleaux triangle [ʁœlo] is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. It is formed...
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3,7) triangle group, and a fundamental domain for this action is the (2,3,7) Schwarz triangle. This is the smallest hyperbolic Schwarz triangle, and thus...
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t-notation. Simple tiles are generated by Möbius triangles with whole numbers p,q,r, while Schwarz triangles allow rational numbers p,q,r and allow star polygon...
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Spherical trigonometry (redirect from Spherical triangle)
trigonometry Great-circle distance or spherical distance Lenart sphere Schwarz triangle Spherical geometry Spherical polyhedron Triangulation (surveying) Todhunter...
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well-defined densities. The nonconvex forms are constructed from Schwarz triangles. All the uniform polyhedra are listed below by their symmetry groups...
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Wythoff construction of a uniform polyhedron or plane tiling within a Schwarz triangle. It was first used by Coxeter, Longuet-Higgins and Miller in their...
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In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length...
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In geometry, an isosceles triangle (/aɪˈsɒsəliːz/) is a triangle that has two sides of equal length and two angles of equal measure. Sometimes it is specified...
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diverge. The Schwarz lantern demonstrates that sampling a curved surface by close-together points and connecting them by small triangles is inadequate...
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3,7) triangle group, and a fundamental domain for this action is the (2,3,7) Schwarz triangle. This is the smallest hyperbolic Schwarz triangle, and thus...
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The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is an upper bound on the absolute value of the inner product between...
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with the property of tiling space only aperiodically. A Schwarz triangle is a spherical triangle that can be used to tile a sphere. It is possible to tessellate...
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constructed from Schwarz triangle (3 3 5⁄2) with Wythoff symbol 3 | 5⁄2 3. Its hexagonal vertex figure alternates equilateral triangle and pentagram faces...
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contexts, the "(2,3,7) triangle group" most often refers, not to the full triangle group Δ(2,3,7) (the Coxeter group with Schwarz triangle (2,3,7) or a realization...
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of two solutions of the hypergeometric equation is also known as a Schwarz triangle map. The Picard–Fuchs equation can be cast into the form of Riemann's...
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Schwarzian derivative (redirect from Schwarz derivative)
equivalent to the hypergeometric differential equation and f(z) is the Schwarz triangle function, which can be written in terms of hypergeometric functions...
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Hyperbolic geometry (section Triangles)
domain triangle, the symmetry group is a hyperbolic triangle group. There are also infinitely many uniform tilings that cannot be generated from Schwarz triangles...
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Charlotte! The First Lady of Saint Louis Television by Patricia Peters Schwarz. Triangle Publishing Co., 1994. Charlotte Peters at St. Louis Media History...
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triangle Regiomontanus Regiomontanus' angle maximization problem Reuschle's theorem Right triangle Routh's theorem Scalene triangle Schwarz triangle Schiffler's...
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of uniform polyhedra by Wythoff symbol List of uniform polyhedra by Schwarz triangle Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J...
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symbols, or Coxeter-Dynkin diagrams, each operating upon one of three Schwarz triangle (4,4,2), (6,3,2), or (3,3,3), with symmetry represented by Coxeter...
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