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Zbl 1116.15024
Kocik, Jerzy
Clifford algebras and Euclid's parametrization of Pythagorean triples. (English)
[J] Adv. Appl. Clifford Algebr. 17, No. 1, 71-93 (2007). ISSN 0188-7009; ISSN 1661-4909/e

The author proves that the space of Euclid's parameters for Pythagorean triples is endowed with a natural symplectic structure. This space can be considered as a spinor space for the Clifford algebra $\Bbb R_{12}$ build over a 3-dimensional Minkowski space whose integer light-like vectors represent the Pythagorean triples. An extension to more variables is proposed and explicit formulae for generating all Pythagorean quadruples and hexads are provided.
[Georgi Hristov Georgiev (Shumen)]

MSC 2000:: *15A66 Clifford algebras
20H05 Congruence subgroups (matrix groups)
22E43 Structure and representation of the Lorentz group

Keywords: Pythagorean triples; Clifford algebra, spinors; Minkowski space; Euclid's parametrization; pseudo-quaternions; unimodular group; Hall matrices; Apollonian gasket; Lorentz group; Pythagorean quadruples

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