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arXiv · 1610.07971

On rational triangles via algebraic curves

Mohammad Sadek·Farida shahata
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Abstract

A rational triangle is a triangle with rational side lengths. We consider three different families of rational triangles having a fixed side and whose vertices are rational points in the plane. We display a one-to-one correspondence between each family and the set of rational points of an algebraic curve. These algebraic curves are: a curve of genus 0, an elliptic curve, and a genus 3 curve. We study the set of rational points on each of these curves and describe some of its rational points explicitly.

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Mohammad Sadek, Farida shahata. 2016-10-25. On rational triangles via algebraic curves. https://arxiv.org/abs/1610.07971

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