Loci of Triangular Orbits in an Elliptic Billiard: Elliptic? Algebraic?

01/22/2020

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by   Ronaldo Garcia, 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. Here we present a systematic method to prove 29 out of the first 100 Centers listed in Clark Kimberling's Encyclopedia are elliptic. We also derive conditions under which loci are algebraic.