"Poncelet'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. The theorem is of great depth in that it relates to a large and diverse body of mathematics. There are several proofs of the theorem, none of which is elementary. A particularly attractive feature of the theorem, which is easily understood but difficult to prove, is that it serves as a prism through which one can learn and appreciate a lot of beautiful mathematics." "The author's original research in queuing theory and dynamical systems figures prominently in the book. This book stresses the modern approach to the subject and contains much material not previously available in book form. It also discusses the relation between Poncelet's theorem and some aspects of queueing theory and mathematical billiards." "The proof of Poncelet's theorem presented in this book relates it to the theory of elliptic curves and exploits the fact that such curves are endowed with a group structure. The book also treats the real and degenerate cases of Poncelet's theorem. These cases are interesting in themselves, and their proofs require some other considerations. The real case is handled by employing notions from dynamical systems." "The material in this book should be understandable to anyone who has taken the standard courses in undergraduate mathematics. To achieve this, the author has included in the book preliminary chapters dealing with projective geometry, Riemann surfaces, elliptic functions, and elliptic curves. The book also contains numerous figures illustrating various geometric concepts."--Jacket.
Bibliographic references
Includes bibliographical references (p. 237-238) and index.
Contents
Introduction
Basic notions of projective geometry
Conics
Intersection of two conics
Riemann surfaces
Elliptic functions
The modular function
Elliptic curves
Poncelet's theorem
Cayley's theorem
Non-generic cases
The real case of Poncelet's theorem
Billiards in an ellipse
Double queues
Billiards and the Poncelet theorem / S. Tabachnikov.
ISBN
9780821843758 ((alk. paper))
0821843753 ((alk. paper))
LCCN
2008025623
OCLC
232327360
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