Abstract: I will describe joint work with Daniel Grieser on the behaviour of the eigenvalues for the Dirichlet (or Neumann) problem for the standard Laplace operator on a triangle as the triangle collapses. More precisely we show the existence of a complete asymptotic expansion of the eigenvalues at the boundary of a compactification of the moduli space. This is perhaps more intricate than might at first be supposed and is a good model problem to serve as a guide to many similar (open) questions.