Interesting Esoterica

How to hear the shape of a billiard table

Article by Aaron Calderon and Solly Coles and Diana Davis and Justin Lanier and Andre Oliveira
  • Published in 2018
  • Added on
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}
}