New Properties of Triangular Orbits in Elliptic Billiards
This work addresses theoretical properties in mathematical physics, specifically elliptic billiards, and is incremental as it extends prior findings.
The paper presents proofs for previously introduced invariants of 3-periodic orbits in elliptic billiards and adds new related facts, building on earlier work without specifying concrete numerical results.
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), Math. Intelligencer, 42(1): 6--17, some of which were generalized to $N>3$. Invariants mentioned there included ratios of radii and/or areas, sum of angle cosines, and a special stationary circle. Here we present some of the proofs omitted there as well as a few new related facts.