A geometry where everything is better than nice

摘要

We present a riemannian structure on the disk that has a remarkably richstructure. Geodesics are hypocycloids and the (negative of the) laplacian hasinteger spectrum with multiplicity the Dirichlet divisor function.Eigenfunctions of the laplacian are orthogonal polynomials naturally suited tothe analysis of acoustic scattering in layered media.