Ratios in Heronian triangles. Issue 560 (July 2020)

• Record Type: Journal Article
• Authors: Dolan, Stan
• Is Part Of: Mathematical gazette. Volume 104:Issue 560(2020)
• Page Start: 193
• Page End: 208
• Publication Date: 2020-07
• Subjects: Mathematics -- Periodicals; Mathématique; Mathematik; Mathematics; Periodicals; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); Zeitschrift; Online-Publikation; 510
• DOI: 10.1017/mag.2020.41
• Languages: English
• ISSNs: 0025-5572

Abstract

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].