Circuminvariants of 3-Periodics in the Elliptic Billiard

04/06/2020

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by   Dan Reznik, et al.

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A Circumconic passes through a triangle's vertices; an Inconic is tangent to the sides. We introduce the Circumbilliard: the circumellipse of a generic triangle which is an Elliptic Billiard (EB) to the latter. Given a fixed EB, we study varying Circumbilliards obtained from triangles derived from the 3-periodic family. Finally we describe invariants displayed by certain Circumconics and Inconics associated with the family including: axis alignment, aspect ratio, and pairwise focal length ratio.