We analyze the family of 3-periodic  trajectories in an Elliptic Billiard. Taken as a continuum of rotating triangles, its Triangle Centers (Incenter, Barycenter, etc.) sweep remarkable loci: ellipses, circles, quartics, sextics, and even a stationary point. Here we present a systematic method to prove 29 out of the first 100 Centers listed in Clark Kimberling's Encyclopedia are elliptic. We also derive conditions under which loci are algebraic . Finally, we informally describe a variety of delightful phenomena involving loci of orbit-derived centers and vertices .
We analyze the family of 3-periodic (triangular) trajectories in an Elliptic Billiard. Its Triangle Centers (Incenter, Barycenter, etc.) sweep remarkable loci: ellipses, circles, quartics, sextics, and even a stationary point. Here we present a systematic method to prove 29 out of the first 100 Centers listed in Clark Kimberling's Encyclopedia are elliptic. We also derive conditions under which loci are algebraic .
A
(triangular)
R
Taken as a continuum of rotating triangles, its
Its
D
. Finally, we informally describe a variety of delightful phenomena involving loci of orbit-derived centers and vertices