  A number of questions related to the length spectrum of surfaces are
discussed and in particular the existence of pairs of surfaces which though not
isometric are isospectral. Here by isospectral we mean that a pair of bodies
have the same distribution of chord lengths. In the Euclidean setting, we study
isospectral convex dodecagons found by Mallows and Clark in the 1970's.
Starting from their idea, we give constructions for isospectral pairs of
hyperbolic surfaces that have no common cover. Since the work of Mallows and
Clark is probably unfamiliar to readers with a background in
topology/hyperbolic geometry we include expository material on other related
topics about the distribution of chord lengths.

Geometric Topology