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The goal of this paper is an analysis of the geometry of billiards inellipses, based on properties of confocal central conics. The extended sides ofthe billiards meet at points which are located on confocal ellipses andhyperbolas. They define the associated Poncelet grid. If a billiard is periodicthen it closes for any choice of the initial vertex on the ellipse. This givesrise to a continuous variation of billiards which is called billiard's motionthough it is neither a Euclidean nor a projective motion. The extension of thismotion to the associated Poncelet grid leads to new insights and invariants.

The Geometry of Billiards in Ellipses and their Poncelet Grids