English

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 Δ\Delta 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}
}
R2 v1 2026-06-23T18:14:59.006Z