On rational triangles via algebraic curves
Number Theory
2018-07-23 v1
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.
Cite
@article{arxiv.1610.07971,
title = {On rational triangles via algebraic curves},
author = {Mohammad Sadek and Farida shahata},
journal= {arXiv preprint arXiv:1610.07971},
year = {2018}
}