|
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 dreznik@gmail.com Ronaldo Garcia Inst. de Matemática e Estatística, Universidade Federal de Goiás, Goiania GO, Brazil ragarcia@ufg.br Jair Koiller Universidade Federal de, Juiz de Fora MG, Brazil jairkoiller@gmail.com 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. [ Fulltext-pdf (1991 KB)] |