  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 Triangular Centers, one obtains a beautiful and
variegated gallery of curves: ellipses, quartics, sextics, circles, and even a
stationary point. Secondly, one notices this family conserves an intriguing
ratio: Inradius-to-Circumradius. In turn this implies three conservation
corollaries: (i) the sum of bounce angle cosines, (ii) the product of excentral
cosines, and (iii) the ratio of excentral-to-orbit areas. Monge's Orthoptic
Circle's close relation to 4-periodic Billiard trajectories is well-known. Its
geometry provided clues with which to generalize 3-periodic invariants to
trajectories of an arbitrary number of edges. This was quite unexpected.
Indeed, the Elliptic Billiard did surprise us!
