Calabi triangle triangle or the Calabi triangle. Thus, the Calabi triangle may be defined as a triangle that is not equilateral and has three placements for its largest square. The Calabi triangle is isosceles. The ratio of the base to either leg is which approximates to 1.55138752454. In terms of trigonometric functions, it is It is the largest positive root of and has continued fraction representation [1, 1, 1, 4, 2, 1, 2, 1, 5, 2, 1, 3, 1, 1, 390, ...]. The Calabi triangle is obtuse with base angles 39.1320261...° and third angle 101.7359477...°. Calabi triangle The Calabi triangle is a
Schwarz triangle function hyperbolic upper half plane by Schwarz triangles will be discussed using elementary methods. For triangles without "cusps"—angles equal to zero or equivalently vertices on the real axis—the elementary approach of will be followed. For triangles with one or two cusps, elementary arguments of , simplifying the approach of , will be used: in the case of a Schwarz triangle with one angle zero and another a right angle, the orientation-preserving subgroup of the reflection group of the triangle is a Hecke group. For an ideal triangle in which all angles are zero, so that all vertices lie on the real