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arXiv · 1806.09644

How to hear the shape of a billiard table

Aaron Calderon·Solly Coles·Diana Davis·Justin Lanier·Andre Oliveira
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Abstract

The bounce spectrum of a polygonal billiard table is the collection of all bi-infinite sequences of edge labels corresponding to billiard trajectories on the table. We give methods for reconstructing from the bounce spectrum of a polygonal billiard table both the cyclic ordering of its edge labels and the sizes of its angles. We also show that it is impossible to reconstruct the exact shape of a polygonal billiard table from any finite collection of finite words from its bounce spectrum.

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Aaron Calderon, Solly Coles, Diana Davis, Justin Lanier, Andre Oliveira. 2018-06-25. How to hear the shape of a billiard table. https://arxiv.org/abs/1806.09644

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