Before revision: 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. We describe these as well as a few related delightful phenomena .
After revision: We analyze the family of 3-periodics in the Elliptic Billiard is mystifying. Besides conserving perimeter and the ratio of inradius-to-circumradius, it has a stationary point. Furthermore, its triangle centers sweep out mesmerizing loci including ellipses, quartics, circles, and a slew of other more complex curves. Here we explore a bevy of new phenomena relating to (i) the shape of 3-periodics and (ii) the kinematics of certain Triangle Centers constrained to the Billiard boundary, specifically the non-monotonic motion some can display with respect to 3-periodics. Hypnotizing is the joint motion of two such non-monotonic Centers, whose many stops-and-gos are akin to a Ballet .