Geometry and Billiards
Language: English
Published by American Mathematical Society, US, 2005
- Softcover
- New
Seller: Rarewaves.com USA, London, London, United KingdomRarewaves.com USA
AbeBooks seller since June 11, 2025
Condition: New
£ 55.76
Quantity: 1 available
Add to basketItem description from seller
Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. Topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards.The book is based on an advanced undergraduate topics course. Minimum prerequisites are the standard material covered in the first two years of college mathematics (the entire calculus sequence, linear algebra). However, readers should show some mathematical maturity and rely on their mathematical common sense. A unique feature of the book is the coverage of many diverse topics related to billiards, for example, evolutes and involutes of plane curves, the four-vertex theorem, a mathematical theory of rainbows, distribution of first digits in various sequences, Morse theory, the Poincare recurrence theorem, Hilbert's fourth problem, Poncelet porism, and many others. There are approximately 100 illustrations. The book is suitable for advanced undergraduates, graduate students, and researchers interested in ergodic theory and geometry.…
Seller Inventory # LU-9780821839195
- Title
- Geometry and Billiards
- Author
- Serge Tabachnikov
- Publisher
- American Mathematical Society, US
- Publication year
- 2005
- Condition
- New
- Binding
- Paperback
- Language
- English
- ISBN 10
- 0821839195
- ISBN 13
- 9780821839195
- Edition
- illustrated Edition.
- Item weight
- 242 grams
- Dimensions
- 13.97 x 1.27 x 20.96 cm
"Synopsis" may belong to another edition of this title.
Rarewaves.com USA
London, London, United Kingdom
AbeBooks seller since June 11, 2025
Shipping rates from United Kingdom to U.S.A.
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