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Journal for Geometry and Graphics 24 (2020), No. 1, 079--101
Copyright Heldermann Verlag 2020

The Ballet of Triangle Centers on the Elliptic Billiard

Dan S. Reznik
Data Science Consulting, Rio de Janeiro, RJ 22210-080, Brazil

Ronaldo Garcia
Inst. de Matemática e Estatística, Universidade Federal de Goiás, Goiania GO, Brazil

Jair Koiller
Universidade Federal de, Juiz de Fora MG, Brazil

We explore a bevy of new phenomena displayed by 3-periodics in the Elliptic Billiard, including (i) their dynamic geometry and (ii) the non-monotonic motion of certain Triangle Centers constrained to the Billiard boundary. Fascinating is the joint motion of certain pairs of centers, whose many stops-and-gos are akin to a Ballet.

Keywords: Elliptic billiard, periodic trajectories, triangle center, loci, dynamic geometry.

MSC: 51N20; 51M04, 51-04, 37-04.

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