The relativistic Galperin billiard: π becomes a complete elliptic integral
Year: 2026
Type: preprint
Abstract: 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.
Author: Gharzouli, Zakaria
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212445755
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