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 .
New invariants in the family of 3-periodics in an Elliptic Billiard (EB) were introduced in [ 20 ], stemming from both experimental and theoretical work. These include relationships between radii, angles and areas of triangular members of the family, as well as a special stationary circle. Here we present the proofs promised there as well as a few new related facts .
R
In this paper we present invariants of the 1d
New invariants in the
D
(triangular orbits)
R
, previously mentioned
were introduced in
R
14
20
R
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
stemming from both experimental and theoretical work. These include relationships between radii, angles and areas of triangular members of the family, as well as a special stationary circle. Here we present the proofs promised there as well as a few new related facts