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Pairs of Heron and right triangles with a common area and a common perimeter

Published

Author(s)

Abhishek Juyal, Dustin Moody

Abstract

A Heron triangle is one in which the side lengths and area are integers. An integral right triangle is an example of a Heron triangle. In this paper, we show that there are infinitely many pairs of integral right triangles and Heron triangles with a common area and common perimeter, continuing a line of similar results with other pairs of geometric shapes. This result is established using the theory of elliptic curves.
Citation
Publicationes Mathematicae Debrecen
Volume
100

Keywords

elliptic curve, right triangle, Heron triangle, parallelogram, common area, common perimeter

Citation

Juyal, A. and Moody, D. (2022), Pairs of Heron and right triangles with a common area and a common perimeter, Publicationes Mathematicae Debrecen, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=934575 (Accessed December 5, 2022)
Created May 23, 2022, Updated November 29, 2022