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Geometry and Billiards
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Bibliographic Detail
Publisher Amer Mathematical Society
Publication date September 28, 2005
Pages 176
Binding Paperback
Book category Adult Non-Fiction
ISBN-13 9780821839195
ISBN-10 0821839195
Dimensions 0.50 by 5.50 by 8.25 in.
Weight 0.50 lbs.
Original list price $41.00
Amazon.com says people who bought this book also bought:
Principles of Mathematical Analysis
Summaries and Reviews
Amazon.com description: Product Description: 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 Poincaré 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. This volume has been copublished with the Mathematics Advanced Study Semesters program at Penn State.

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Paperback
Book cover for 9780821839195
 
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from Amer Mathematical Society (September 28, 2005)
9780821839195 | details & prices | 176 pages | 5.50 × 8.25 × 0.50 in. | 0.50 lbs | List price $41.00
About: 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.

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