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
Triangle group of these relations and that Δ("l,m,n") is a discrete group of motions of the corresponding space. Thus a triangle group is a reflection group that admits a group presentation An abstract group with this presentation is a Coxeter group with three generators. Given any natural numbers "l", "m", "n" > 1 exactly one of the classical two-dimensional geometries (Euclidean, spherical, or hyperbolic) admits a triangle with the angles (π/l, π/m, π/n), and the space is tiled by reflections of the triangle. The sum of the angles of the triangle determines the type of the geometry by the Gauss–Bonnet theorem: it