The origin of the Beauregard–Suryanarayan product on Pythagorean triples

Shaul Zemel

doi:10.1007/s11565-019-00319-0

The origin of the Beauregard–Suryanarayan product on Pythagorean triples

Shaul Zemel^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show how the multiplicative structure on Pythagorean triples defined by Beauregard–Suryanarayan arises from automorphisms of the hyperbolic plane, and how the structure theorem of this product follow naturally from this connection. We also show how the natural involution on Pythagorean triples is related to Pell’s equation with the parameter 2, and prove a generalization of this phenomenon.

Original language	English
Pages (from-to)	389-409
Number of pages	21
Journal	Annali dell'Universita di Ferrara
Volume	65
Issue number	2
DOIs	https://doi.org/10.1007/s11565-019-00319-0
State	Published - 1 Nov 2019

Bibliographical note

Publisher Copyright:
© 2019, Università degli Studi di Ferrara.

Keywords

Binary quadratic forms
Pell’s equation
Pythagorean triples

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10.1007/s11565-019-00319-0

Cite this

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The origin of the Beauregard–Suryanarayan product on Pythagorean triples

Abstract

Bibliographical note

Keywords

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