  This expository article discusses some connections between the geometry of a
hyperbolic 3-manifold homotopy-equivalent to a surface, and the combinatorial
properties of its end invariants. In particular a necessary and sufficient
condition is stated for the manifold to have arbitrarily short geodesics, in
terms of a sequence of coefficients called subsurface projection distances,
which are analogous in some ways to continued-fraction coefficients. (The proof
of sufficiency appeared in math.GT/9907070)
