# How to hear the shape of a billiard table

• Published in 2018
In the collections
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.

### 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}
}