Introduction to Poncelet Porisms

Abstract

“One of the most important and also most beautiful theorems in classical geometry is that of Poncelet (…) His proof was synthetic and somewhat elaborate in what was to become the predominant style in projective geometry of last century. Slightly thereafter, Jacobi gave another argument based on the addition theorem for elliptic functions. In fact, as will be seen below, the Poncelet theorem and addition theorem are essentially equivalent, so that at least in principle Poncelet gave a synthetic derivation of the group law on an elliptic curve. Because of the appeal of the appeal of the Poncelet theorem it seems reasonable to look for higher-dimensional analogues… Although this has not yet turned out to be the case in the Poncelet-type problems…”