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arXiv · 2602.20536

Quantizing Pythagorean triples

Hugo Mathevet·Sophie Morier-Genoud·Valentin Ovsienko
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Abstract

We introduce a $q$-deformation of the Pythagoras equation $a^2 + b^2 = c^2$, which is a polynomial version of it different from the standard one. We construct a polynomial analogue, or ``$q$-analogue'', of every primitive Pythagorean triple. We also construct such analogue for a larger class of Pythagorean triples called standard. Our approach is based on the notion of $q$-deformed rational numbers and the modular group $\mathrm{PSL}(2,\mathbb{Z})$.

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Hugo Mathevet, Sophie Morier-Genoud, Valentin Ovsienko. 2026-02-24. Quantizing Pythagorean triples. https://arxiv.org/abs/2602.20536

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