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Clifford algebras and Euclid’s parametrization of Pythagorean triples. (English) Zbl 1116.15024
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.

15A66Clifford algebras, spinors
20H05Unimodular groups, congruence subgroups (matrix groups)
22E43Structure and representation of the Lorentz group
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