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arXiv · 2512.02236

Snell meets Fagnano. Path optimization through an imperfect mirror

Maxim Arnold·Jaewoo Park
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Abstract

The renowned Fagnano problem asks for the inscribed triangle of minimal perimeter within a given reference triangle. Equivalently, it seeks a billiard trajectory inside the triangle that closes after three reflections. In this note, we consider a modification of this classical problem: finding the inscribed triangle of minimal weighted perimeter -- or, equivalently, the periodic trajectory of a Snell billiard.

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Maxim Arnold, Jaewoo Park. 2025-12-01. Snell meets Fagnano. Path optimization through an imperfect mirror. https://arxiv.org/abs/2512.02236

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