• Thumbnail for Schwarz triangle
    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...
    78 KB (10,932 words) - 02:21, 20 June 2025
  • Thumbnail for Schwarz triangle function
    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...
    7 KB (1,049 words) - 04:00, 19 July 2025
  • Thumbnail for List of uniform polyhedra by Schwarz triangle
    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...
    97 KB (2,780 words) - 02:08, 22 July 2025
  • Thumbnail for Hypergeometric function
    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...
    39 KB (6,920 words) - 21:33, 14 July 2025
  • 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...
    16 KB (1,771 words) - 01:56, 10 July 2025
  • Thumbnail for Hermann Schwarz
    theorem Schwarz reflection principle Schwarz triangle Schwarz triangle function Cauchy–Schwarz inequality Theorem of Pohlke and Schwarz Schwarz, H. A....
    8 KB (643 words) - 01:16, 18 February 2025
  • 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...
    8 KB (912 words) - 03:15, 27 December 2024
  • Thumbnail for Exceptional object
    exceptional Schwarz triangles (triangles that tile the sphere, or more generally Euclidean plane or hyperbolic plane via their triangle group of reflections...
    25 KB (3,088 words) - 04:00, 21 July 2025
  • 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...
    6 KB (830 words) - 17:56, 29 March 2025
  • Thumbnail for Reuleaux triangle
    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...
    57 KB (6,500 words) - 06:52, 2 June 2025
  • Thumbnail for Heptagonal tiling
    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...
    4 KB (322 words) - 23:56, 14 June 2025
  • 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...
    54 KB (752 words) - 01:11, 22 July 2025
  • Thumbnail for Spherical trigonometry
    trigonometry Great-circle distance or spherical distance Lenart sphere Schwarz triangle Spherical geometry Spherical polyhedron Triangulation (surveying) Todhunter...
    40 KB (6,765 words) - 14:04, 8 July 2025
  • Thumbnail for Uniform star polyhedron
    well-defined densities. The nonconvex forms are constructed from Schwarz triangles. All the uniform polyhedra are listed below by their symmetry groups...
    18 KB (728 words) - 21:53, 20 July 2025
  • Thumbnail for Wythoff symbol
    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...
    12 KB (682 words) - 11:46, 11 July 2025
  • Thumbnail for Triangle inequality
    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...
    35 KB (5,287 words) - 10:38, 18 June 2025
  • Thumbnail for Isosceles triangle
    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...
    38 KB (4,157 words) - 05:19, 12 July 2025
  • Thumbnail for Schwarz lantern
    diverge. The Schwarz lantern demonstrates that sampling a curved surface by close-together points and connecting them by small triangles is inadequate...
    24 KB (2,899 words) - 00:50, 26 March 2025
  • Thumbnail for Order-7 triangular tiling
    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...
    4 KB (423 words) - 20:19, 14 March 2025
  • The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is an upper bound on the absolute value of the inner product between...
    37 KB (5,182 words) - 23:37, 5 July 2025
  • Thumbnail for Tessellation
    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...
    59 KB (6,059 words) - 14:39, 15 July 2025
  • Thumbnail for Small ditrigonal icosidodecahedron
    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...
    3 KB (154 words) - 08:26, 19 January 2024
  • Thumbnail for Hurwitz surface
    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...
    5 KB (645 words) - 02:08, 7 January 2025
  • 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...
    4 KB (629 words) - 20:19, 27 June 2023
  • equivalent to the hypergeometric differential equation and f(z) is the Schwarz triangle function, which can be written in terms of hypergeometric functions...
    46 KB (7,170 words) - 00:44, 17 June 2025
  • Thumbnail for Hyperbolic geometry
    domain triangle, the symmetry group is a hyperbolic triangle group. There are also infinitely many uniform tilings that cannot be generated from Schwarz triangles...
    56 KB (6,970 words) - 13:36, 7 May 2025
  • Charlotte! The First Lady of Saint Louis Television by Patricia Peters Schwarz. Triangle Publishing Co., 1994. Charlotte Peters at St. Louis Media History...
    7 KB (617 words) - 20:35, 2 April 2025
  • triangle Regiomontanus Regiomontanus' angle maximization problem Reuschle's theorem Right triangle Routh's theorem Scalene triangle Schwarz triangle Schiffler's...
    11 KB (634 words) - 12:01, 7 February 2025
  • of uniform polyhedra by Wythoff symbol List of uniform polyhedra by Schwarz triangle Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J...
    38 KB (1,075 words) - 19:11, 24 June 2025
  • Thumbnail for List of Euclidean uniform tilings
    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...
    15 KB (953 words) - 18:19, 31 March 2025