Some planar isospectral domains

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# Some planar isospectral domains

**Peter Buser John Conway Peter Doyle
Klaus-Dieter Semmler**

**Version 1.0.1**

15 September 1994

### Abstract:

*We give a number of examples of isospectral pairs of plane domains,
and a particularly simple method of proving isospectrality.
One of our examples
is a pair of domains that are not only isospectral but **homophonic*:
Each domain has a distinguished point such that
corresponding normalized Dirichlet eigenfunctions
take equal values at the distinguished points.
This shows that one really can't hear the shape of a drum.

**Next:** Introduction

*Peter Doyle*