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

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Keywords

Binary quadratic forms
Pell’s equation
Pythagorean triples

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11565-019-00319-0

Cite this

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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{\textquoteright}s equation with the parameter 2, and prove a generalization of this phenomenon.",

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AB - 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.

KW - Binary quadratic forms

KW - Pell’s equation

KW - Pythagorean triples

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The origin of the Beauregard–Suryanarayan product on Pythagorean triples

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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