Ratios in Heronian triangles. Issue 560 (July 2020) - Dolan, Stan
Abstract : Heronian triangles are triangles with integer sides and area. In [1], a classical result about squares in arithmetic progression was obtained by proving that it is not possible for the altitude of a Heronian triangle to divide the base in the ratio of 1 : 2. In this article we shall investigate general ratios of the form 1 : n, where n is a positive integer. These base ratios do not appear to have received previous attention despite the wealth of results about other aspects of Heronian triangles [2].