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Projective billiards

Projective billiards are bounded domains whose boundary is endowed with a field of transverse lines called projective lines (see here, here or here for more details).

The following interactive animation shows polygonal examples of projective billiards, in which

Please click and move the points you want !

You can:

You can observe the following properties (which are proved here):

PROP. 1: The trajectories of the projective billiard called right-spherical are periodic of period 3 in the case of a triangle.

PROP. 2: The trajectories of the projective billiards called centrally polygonal are: