Teorema de Poncelet

Abstract

Poncelet’s theorem is a famous result in projective geometry, dating to the early part of the nineteenth century. It concerns closed polygons inscribed in one conic and circumscribed about another. There are several proofs of the theorem, none of which are elementary. The proof of Poncelet’s theorem that we present in this work requires basic notions of Riemann surfaces, classic results of complex analysis and basic principles of projective geometry. It relates to the theory of elliptic curves and exploits the fact that such curves are endowed with an analytic group structure.