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February 2009 Generalized Pythagorean Triples and Pythagorean Triple Preserving Matrices
Mohan Tikoo, Haohao Wang
Missouri J. Math. Sci. 21(1): 3-12 (February 2009). DOI: 10.35834/mjms/1316032675

Abstract

Traditionally, Pythagorean triples (PT) consist of three positive integers, $(x, y, z) \in \mathbb{Z}^3_+$, such that $x^2 + y^2 = z^2$, and Pythagorean triple preserving matrices (PTPM) $A$ are $3 \times 3$ matrices with entries in the real numbers $\R$, such that the product $(x, y, z)A$ is also a Pythagorean triple. In this paper, we study PT and PTPM from the view of projective geometry, and extend the results concerning PT and PTPM from integers to any commutative ring with identity. In particular, we use the method of polynomial parametrization for projective conics to obtain the general form of PT over any commutative ring with identity. In addition, we view the PTPM as projective transformations and formulate the general form of a PTPM over any commutative ring with identity.

Citation

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Mohan Tikoo. Haohao Wang. "Generalized Pythagorean Triples and Pythagorean Triple Preserving Matrices." Missouri J. Math. Sci. 21 (1) 3 - 12, February 2009. https://doi.org/10.35834/mjms/1316032675

Information

Published: February 2009
First available in Project Euclid: 14 September 2011

zbMATH: 1210.11041
MathSciNet: MR2503169
Digital Object Identifier: 10.35834/mjms/1316032675

Subjects:
Primary: 13-01
Secondary: 14-01

Rights: Copyright © 2009 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.21 • No. 1 • February 2009
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