1409 W. Green St., Urbana, Illinois 6181,
University if Illinois at Urbana-Champaign
Circular Billiard Tables, Conjugate Loci, and a Cardioid
2003, vol. 8, no. 1, pp. 83-95
Some of the major concepts of Riemannian geometry are explained in terms of billiards on a circular billiard table: conjugate loci, exponential map, Morse theory on the path space. The conjugate loci are related to the caustics of classical optics of a circular reflector. The change in form of those conjugate loci and caustics as the source point moves is classified and illustrated with many pictures based on numerical data.