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 Δ has angles /"a", /"b" and /"c" with "a", "b", "c" integers greater than 1. The hyperbolic area of Δ equals – /"a" – /"b" – /"c", so that The construction of a tessellation will first be carried out for the case when "a", "b" and "c" are greater than 2. The original triangle Δ gives a convex polygon "P" with 3 vertices. At each of the three vertices the triangle can be successively reflected through edges emanating from the vertices to produce 2"m" copies of the triangle where the angle at the vertex is /"m". The triangles do not