Abstract:
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.
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