ELLIPTIC BILLIARD SYSTEMS AND THE FULL PONCELET THEOREM IN N-DIMENSIONS

In this work is presented a generalization of Poncelet's theorem to n dimensions which is refered to as the full Poncelet's theorem. The the orem states that if the reflections of a trajectory by a sequence of c onfocal quadrics lead to a closed skew polygon, then there exists an ( n - 1)-parameter family of polygons having the same property. A physic al realization and a projective geometrical proof of this theorem are given. If all the reflecting quadrics coincide, the above theorem redu ces to the n-dimensional Poncelet's theorem presented by Chang and Fri edberg. The geometrical proof is a finite construction based on a prel iminary theorem which extends Hart's lemma. The full Poncelet's theore m may thus be extended to projective geometries over most fields, incl uding discrete ones.