# How to hear the shape of a billiard table

- Published in 2018
- Added on

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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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### BibTeX entry

@article{Howtoheartheshapeofabilliardtable, title = {How to hear the shape of a billiard table}, 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.}, url = {http://arxiv.org/abs/1806.09644v1 http://arxiv.org/pdf/1806.09644v1}, year = 2018, author = {Aaron Calderon and Solly Coles and Diana Davis and Justin Lanier and Andre Oliveira}, comment = {}, urldate = {2018-06-27}, archivePrefix = {arXiv}, eprint = {1806.09644}, primaryClass = {math.DS}, collections = {Basically physics,Easily explained,Geometry,Fun maths facts} }