Description
Book SynopsisPoncelet's theorem is a famous result in algebraic geometry, dating to the early part of the nineteenth century. It concerns closed polygons inscribed in one conic and circumscribed about another. This title also discusses the relation between Poncelet's theorem and some aspects of queueing theory and mathematical billiards.
Table of ContentsIntroduction Projective geometry: Basic notions of projective geometry Conics Intersection of two conics Complex analysis: Riemann surfaces Elliptic functions The modular function Elliptic curves Poncelet and Cayley theorems: Poncelet's theorem Cayley's theorem Non-generic cases The real case of Poncelet's theorem Related topics: Billiards in an ellipse Double queues Supplement: Billiards and the Poncelet theorem Appendices: Factorization of homogeneous polynomials Degenerate conics of a conic pencil. Proof of Theorem 4.9 Lifting theorems Proof of Theorem 11.5 Billiards in an ellipse. Proof of Theorem 13.1 References.
