New Properties of Triangular Orbits in Elliptic Billiards

01/22/2020

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by   Ronaldo Garcia, et al.

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In this paper we present invariants of the 1d family of 3-periodics (triangular orbits) in an Elliptic Billiard (EB), previously mentioned [14], including: (i) explicit Expressions classic invariants: perimeter and Joachimsthal's quantity; (ii) consevation of Inradius-to-Circumradius; (iii) stationarity of the Cosine Circle of the Excentral Triangle and the fact that it is exterior to the EB. Finally we present an entirely new N=3 invariant.