Greg McShane

Continued fractions, codes and identities for lengths

We'll discuss the relationship between the simple geodesics on a once punctured torus and badly approximable real numbers. We explain how this leads to a classification of points in X(gamma) = the set of starting points of complete geodesics perpendicular to a geodesic in the boundary of a hyperbolic surface of type g,n indicating analogies with the theory of continued fractions.