Integral Isosceles Triangle-Parallelogram and Heron triangle-Rhombus Pairs with a Common Area and Common Perimeter

Published

June 6, 2017

Author(s)

Pradeep Das, Abhishek Juyal, Dustin Moody

Abstract

In this paper we show that there are in nitely many pairs of integer isosceles triangles and integer parallelograms with a common (integral) area and common perimeter. We also show that there are in nitely many Heron triangles and integer rhombuses with common area and common perimeter. As a corollary, we show there does not exist any Heron triangle and integer square which have a common area and common perimeter.

Citation

Journal of Number Theory

Volume

180

Pub Type

Journals

Download Paper

https://doi.org/10.1016/j.jnt.2017.04.009

Local Download

Keywords

Elliptic Curve, Isosceles Triangle, Heron Triangle, Rhombus, Parallelogram

Citation

Das, P. , Juyal, A. and Moody, D. (2017), Integral Isosceles Triangle-Parallelogram and Heron triangle-Rhombus Pairs with a Common Area and Common Perimeter, Journal of Number Theory, [online], https://doi.org/10.1016/j.jnt.2017.04.009, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=923308 (Accessed October 2, 2025)