Integer triangle side of the formula are integers it follows that all integer triangles must have an integer value of "16T" and "T" will be rational. By the law of cosines, every angle of an integer triangle has a rational cosine. If the angles of any triangle form an arithmetic progression then one of its angles must be 60°. For integer triangles the remaining angles must also have rational cosines and a method of generating such triangles is given below. However, apart from the trivial case of an equilateral triangle there are no integer triangles whose angles form either a geometric or
Schwarz triangle function since the case of two cusps is obtained by doubling a triangle with one cusp and non-zero angles /"a" and /2. So consider the geodesic triangle in the upper half plane with angles 0, /"a", /"b" with "a", "b" integers greater than one. The interior of such a triangle can be realised as the region "X" in the upper half plane lying outside the unit disk |"z"| ≤ 1 and between two lines parallel to the imaginary axis through points "u" and "v" on the unit circle. Let Γ be the triangle group generated by the three reflections in the