Loci of 3-Periodics in an Elliptic Billiard: Intriguing Phenomena

01/30/2020

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by   Dan Reznik, et al.

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We analyze the family of 3-periodic (triangular) trajectories in an Elliptic Billiard. Its Triangle Centers (Incenter, Barycenter, etc.) sweep remarkable loci: ellipses, circles, quartics, sextics, and even a stationary point. We describe these as well as a few related delightful phenomena.