The Circumbilliard: Any Triangle can be a 3-Periodic

Abstract

A Circumconic passes through a triangle's vertices. We define the Circumbilliard, a circumellipse to a generic triangle for which the latter is a 3-periodic. We study its properties and associated loci.

arXiv comment14 pages, 8 figures, 4 tables, 7 videos NOTE: this is part I from arXiv:2004.02680 which originally contained two parts and now has been replaced to only contain part II

References in corpus (2)

• Loci of 3-periodics in an Elliptic Billiard: why so many ellipses?
• The Ballet of Triangle Centers on the Elliptic Billiard

Cited by in corpus (1)

• The Geometry of Billiards in Ellipses and their Poncelet Grids