No perfect triangle is isosceles
Number Theory
2020-12-14 v2
Abstract
A perfect triangle is a triangle with rational sides, medians, and area. In this article, we use a similar strategy due to Pocklington to show that if is a perfect triangle, then it cannot be an isosceles triangle. It gives a partial answer to a question of Richard Guy, who asked whether any perfect triangles exist. No example has been found to date. It is widely believed that such a triangle does not exist.
Keywords
Cite
@article{arxiv.2009.00654,
title = {No perfect triangle is isosceles},
author = {Mehdi Makhul},
journal= {arXiv preprint arXiv:2009.00654},
year = {2020}
}