New Properties of Triangular Orbits in Elliptic Billiards

Abstract New invariants in the one-dimensional family of 3-periodic orbits in the elliptic billiard were introduced by the authors in “Can the elliptic billiard still surprise us?” (2020) Math. Intelligencer 42(1): 6–17, some of which were generalized to N > 3. Invariants mentioned there included ratios of radii and/or areas, sum of angle cosines, and a special stationary circle. Here we present some of the proofs omitted there as well as a few new related facts.

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