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arXiv · 2009.00654

No perfect triangle is isosceles

Mehdi Makhul
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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 $\Delta$ 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.

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Mehdi Makhul. 2020-09-01. No perfect triangle is isosceles. https://arxiv.org/abs/2009.00654

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