  In 1966 Mark Kac asked the famous question 'Can one hear the shape of a
drum?'. While this was later shown to be false in general, it was proved by C.
Durso that one can hear the shape of a triangle. After an introduction to the
general inverse spectral problem we will give a new proof of this fact. The
central point of the argument is to show that area, perimeter and the sum of
the reciprocals of the angles determine a triangle uniquely. This is proved
using convexity arguments and the partial fraction expansion of $\sin^{-2}x$.

Spectral Theory