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2018 On rational triangles via algebraic curves
Mohammad Sadek, Farida Shahata
Rocky Mountain J. Math. 48(1): 325-343 (2018). DOI: 10.1216/RMJ-2018-48-1-325

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 explicitly describe some of its rational points.

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Mohammad Sadek. Farida Shahata. "On rational triangles via algebraic curves." Rocky Mountain J. Math. 48 (1) 325 - 343, 2018. https://doi.org/10.1216/RMJ-2018-48-1-325

Information

Published: 2018
First available in Project Euclid: 28 April 2018

zbMATH: 06866712
MathSciNet: MR3795745
Digital Object Identifier: 10.1216/RMJ-2018-48-1-325

Subjects:
Primary: 11G05, 11G30

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 1 • 2018
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