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November 2019 Generating Pythagorean Triples of a Given Height
Jathan Austin
Missouri J. Math. Sci. 31(2): 136-145 (November 2019). DOI: 10.35834/2019/3102136

Abstract

The height of a Pythagorean triple $(a,b,c)$ is defined as the difference $c - b$. In this paper, building on the Height-Excess Enumeration Theorem, we show how to generate primitive Pythagorean triples of a given height using powers of a single matrix. Then, we briefly discuss other matrices that both map any Pythagorean triple to another and also preserve a triple's height. We also note how Pythagorean triples with a given leg difference can be generated using matrices.

Citation

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Jathan Austin. "Generating Pythagorean Triples of a Given Height." Missouri J. Math. Sci. 31 (2) 136 - 145, November 2019. https://doi.org/10.35834/2019/3102136

Information

Published: November 2019
First available in Project Euclid: 16 November 2019

zbMATH: 07276121
MathSciNet: MR4032191
Digital Object Identifier: 10.35834/2019/3102136

Subjects:
Primary: 11A99
Secondary: 11C20, 11D09

Rights: Copyright © 2019 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.31 • No. 2 • November 2019
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