Poncelets theorem and Billiard knots

Let $D$ be any elliptic right cylinder. We prove that every type of knot can be realized as the trajectory of a ball in $D.$ This proves a conjecture of Lamm and gives a new proof of a conjecture of Jones and Przytycki. We use Jacobis proof of Poncelets theorem by means of elliptic functions.

Every knot is a billiard knot

We show that every knot can be realized as a billiard trajectory in a convex prism. This solves a conjecture of Jones and Przytycki.