Hyperbolic triangle the third angle. The triangle where two vertices are ideal points and the remaining angle is right, one of the first hyperbolic triangles (1818) described by Ferdinand Karl Schweikart. The triangle where all vertices are ideal points, an ideal triangle is the largest possible triangle in hyperbolic geometry because of the zero sum of the angles. The relations among the angles and sides are analogous to those of spherical trigonometry; the length scale for both spherical geometry and hyperbolic geometry can for example be defined as the length of a side of an equilateral triangle with fixed angles. The length
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