  This note begins with an introduction to the inverse isospectral problem
popularized by M. Kac's 1966 article in the American Mathematical Monthly, "Can
one hear the shape of a drum?" Although the answer has been known for some
twenty years now, many open problems remain. Intended for general audiences,
readers are challenged to complete exercises throughout this interactive
introduction to inverse spectral theory. Following the introduction, the main
techniques used in inverse isospectral problems are collected and discussed.
These are then used to prove that one can hear the shape of: parallelograms,
acute trapezoids, and the regular n-gon. Finally, we show that one can
realistically hear the shape of the regular n-gon amongst all convex n-gons
because it is uniquely determined by a finite number of eigenvalues; the sound
of symmetry can really be heard!
