The relativistic Galperin billiard: π becomes a complete elliptic integral

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AUTEUR

Zakaria Gharzouli · Residual Labs, Paris, France

ORCID 0009-0005-7604-4709 · 13 septembre 2026 · CC BY 4.0

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RÉSUMÉ

In Galperin's billiard, the collision count between a heavy block, a light block, and a wall yields the digits of π in the Newtonian regime. When relativistic kinematics are included, the count converges to a complete elliptic integral of the first kind governed by the scaling parameter w = β√M. The Newtonian value f(0) = π is recovered in the zero-velocity limit, with leading corrections determining when each digit of π is lost. Accompanying code reproduces all collision counts, scaling laws, and Abel inversion reconstructions.

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ACCÈS

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DÉMONSTRATION

Trois scènes interactives : le comptage newtonien, la correction relativiste, puis le plafond.

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MOTS-CLÉS