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 case the region in the sector between the radii "OA" and "OB" outside the edge "AB" is convex as the intersection of three convex regions. By induction the angles at "A" and "B" are greater than or equal to /3. Thus the geodesics to "C" from "A" and "B" start off in the region; by convexity, the triangle "ABC" lies wholly inside the region. The quadrilateral "OACB" has all its angles less than (since "OAB" is a geodesic triangle), so is convex. Hence the radius "OC" lies inside the angle of the triangle "ABC" near "C". Thus the angles between