42 citations · 151 across the 15 of their papers we have counts for
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Average Elliptic Billiard Invariants with Spatial Integrals
Jair Koiller, Dan Reznik, Ronaldo Garcia
We compare invariants of N-periodic trajectories in the elliptic billiard, classic and new, to their aperiodic counterparts via a spatial integrals evaluated over the boundary of t…
Eighty New Invariants of N-Periodics in the Elliptic Billiard
Dan Reznik, Ronaldo Garcia, Jair Koiller
We introduce several-dozen experimentally-found invariants of Poncelet N-periodics in the confocal ellipse pair (Elliptic Billiard). Recall this family is fully defined by two inte…
The Ballet of Triangle Centers on the Elliptic Billiard
Dan Reznik, Ronaldo Garcia, Jair Koiller
The dynamic geometry of the family of 3-periodics in the Elliptic Billiard is mystifying. Besides conserving perimeter and the ratio of inradius-to-circumradius, it has a stationar…
New Properties of Triangular Orbits in Elliptic Billiards
Ronaldo Garcia, Dan Reznik, Jair Koiller
New invariants in the one-dimensional family of 3-periodic orbits in the elliptic billiard were introduced by the authors in "Can the Elliptic Billiard Still Surprise Us?" (2020),…
Loci of 3-periodics in an Elliptic Billiard: why so many ellipses?
Ronaldo Garcia, Jair Koiller, Dan Reznik
A triangle center such as the incenter, barycenter, etc., is specified by a function thrice- and cyclically applied on sidelengths and/or angles. Consider the 1d family of 3-period…
Can the Elliptic Billiard Still Surprise Us?
Dan Reznik, Ronaldo Garcia, Jair Koiller
Can any secrets still be shed by that much studied, uniquely integrable, Elliptic Billiard? Starting by examining the family of 3-periodic trajectories and the loci of their Triang…