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Poncelet’s Theorem
About this Title
Leopold Flatto
Publication: Miscellaneous Books
Publication Year:
2009; Volume 56
ISBNs: 978-0-8218-4375-8 (print); 978-1-4704-1595-2 (online)
DOI: https://doi.org/10.1090/mbk/056
MathSciNet review: MR2465164
MSC: Primary 37-01; Secondary 14H52, 14H70, 35E05, 37D40, 37D50, 51-01, 51A05
Table of Contents
Front/Back Matter
Chapters
- Chapter 1. Introduction
Part 1. Projective geometry
- Chapter 2. Basic notions of projective geometry
- Chapter 3. Conics
- Chapter 4. Intersection of two conics
Part II. Complex analysis
- Chapter 5. Riemann surfaces
- Chapter 6. Elliptic functions
- Chapter 7. The modular function
- Chapter 8. Elliptic curves
Part III. Poncelet and Cayley theorems
- Chapter 9. Poncelet’s theorem
- Chapter 10. Cayley’s theorem
- Chapter 11. Non-generic cases
- Chapter 12. The real case of Poncelet’s theorem
Part IV. Related topics
- Chapter 13. Billiards in an ellipse
- Chapter 14. Double queues
Supplement
- Chapter 15. Billiards and the Poncelet theorem
Appendices
- Appendix A. Factorization of homogeneous polynomials
- Appendix B. Degenerate conics of a conic pencil. Proof of Theorem 4.9
- Appendix C. Lifting theorems
- Appendix D. Proof of Theorem 11.5
- Appendix E. Billiards in an ellipse. Proof of Theorem 13.1