Integral isosceles triangle-parallelogram and Heron triangle-rhombus pairs with a common area and common perimeter

Das, Pradeep; Juyal, Abhishek; Moody, Dustin

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

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Journal Article

Integral isosceles triangle-parallelogram and Heron triangle-rhombus pairs with a common area and common perimeter

Documentation Topics

Published: November 1, 2017
Citation: Journal of Number Theory vol. 180, (November 2017) pp. 208-218

Author(s)

Pradeep Das (Harish-Chandra Research Institute), Abhishek Juyal (Motilal Nehru National Institute of Technology), Dustin Moody (NIST)

Abstract

In this paper we show that there are infinitely many pairs of integer isosceles triangles and integer parallelograms with a common (integral) area and common perimeter. We also show that there are infinitely 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.

Keywords

Elliptic curve; Isosceles triangle; Heron triangle; Parallelogram; Rhombus; Common area; Common perimeter

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Documentation

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

Supplemental Material:
None available

Document History:
11/01/17: Journal Article (Final)

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