|
Geometry and Billiards (Student Mathematical Library,) Posters
Photos Art
Search for Posters Art Prints, photos and get
results from all the many categories from Amazon including
books, videos, dvds, toys, video games, and more.
|
|
|
Posters Art
Prints Photos collectables |
|
|
|
|
|
|
If for some reason you can't find what the
poster or art print your looking for try using the search boxes
below
|
|
 |
|
|
|
|
List Price: $35.00Amazon.com's Price: $34.30 You Save: $0.70 ( 2%)Prices subject to change.
Availability: Usually ships in 24 hours
Buy Now!
Binding: Paperback
EAN: 9780821839195
ISBN: 0821839195
Label: American Mathematical Society
Manufacturer: American Mathematical Society
Number Of Items: 1
Number Of Pages: 176
Publication Date: 2005-09
Publisher: American Mathematical Society
Sales Rank: 1004736
Studio: American Mathematical Society
Related Items:
Browse for similar items by category:
Editorial Review:
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.
|
