4 citations · 8 across the 3 of their papers we have counts for
4 papers
On the Motion of Billiards in Ellipses
H. Stachel
For billiards in an ellipse with an ellipse as caustic, there exist canonical coordinates such that the billiard transformation from vertex to vertex is equivalent to a shift of co…
The Geometry of Billiards in Ellipses and their Poncelet Grids
H. Stachel
The goal of this paper is an analysis of the geometry of billiards in ellipses, based on properties of confocal central conics. The extended sides of the billiards meet at points w…
Isometric Billiards in Ellipses and Focal Billiards in Ellipsoids
H. Stachel
Billiards in ellipses have a confocal ellipse or hyperbola as caustic. The goal of this paper is to prove that for each billiard of one type there exists an isometric counterpart o…
Area-Invariant Pedal-Like Curves Derived from the Ellipse
Dan Reznik, Ronaldo Garcia, Hellmuth Stachel
We study six pedal-like curves associated with the ellipse which are area-invariant for pedal points lying on one of two shapes: (i) a circle concentric with the ellipse, or (ii) t…