  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 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.

Dynamical Systems;Computational Geometry;Robotics