Less than equable Heronian triangles. Issue 549 (17th October 2016)

• Record Type: Journal Article
• Authors: Dolan, Stan
• Is Part Of: Mathematical gazette. Volume 100:Issue 549(2016)
• Page Start: 482
• Page End: 489
• Publication Date: 2016-10-17
• 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.2016.113
• Languages: English
• ISSNs: 0025-5572

Abstract

Abstract : It is well known that there are precisely five integer-sided triangles which have equal area, Δ, and perimeter, P . These triangles are called equable Heronian triangles. A proof of this result was given by Whitworth [1]. Since Whitworth's time, much attention has been given to triangles whose areas are integer multiples of their perimeters, for example [2, 3]. However, as this paper will show, Heronian triangles with areas less than their perimeters have some mathematical interest.