Nearly Isosceles Triangles Where the Vertex Angle is a Multiple of the Base Angle

Abstract

Let a triangle in which the vertex angle is a positive integral multiple n of a base angle be called an α — nα triangle. We find integral solutions for the lengths of the sides by a recursive method. We note that, for any particular α for which there is an integral α — nα triangle, cos α must be a rational number by the law of cosines.