Student Mathematical Library
Volume: 30; 2005; 176 pp; Softcover
MSC: Primary 37; 51; Secondary 49; 70; 78

Print ISBN: 978-0-8218-3919-5
Product Code: STML/30
List Price: $44.00
Individual Price: $35.20

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Electronic ISBN: 978-1-4704-2141-0
Product Code: STML/30.E
List Price: $41.00
Individual Price: $32.80

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Geometry and Billiards

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Serge Tabachnikov

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 book is published in cooperation with Mathematics Advanced Study Semesters

Readership

Advanced undergraduates, graduate students, and research mathematicians interested in ergodic theory and geometry.

Reviews & Endorsements

(This book) is very well written, with nice illustrations. The author presents the results very clearly, with interesting digressions and he mentions applications of billiards to various fields.

-- Zentralblatt MATH

Geometry and Billiards

Base Product Code Keyword List: stml; STML; stml/30; STML/30; stml-30; STML-30

Print Product Code: STML/30

Online Product Code: STML/30.E

Title (HTML): Geometry and Billiards

Author(s) (Product display): Serge Tabachnikov

Affiliation(s) (HTML): Penn State, University Park, PA

Abstract:

This book is published in cooperation with Mathematics Advanced Study Semesters

Book Series Name: Student Mathematical Library

Volume: 30

Publication Month and Year: 2005-09-28

Page Count: 176

Cover Type: Softcover

Print ISBN-13: 978-0-8218-3919-5

Online ISBN 13: 978-1-4704-2141-0

Print ISSN: 1520-9121

Online ISSN: 1520-9121

Primary MSC: 37; 51

Secondary MSC: 49; 70; 78

Textbook?: false

Applied Math?: false

MAA Book?: false

Electronic Media?: false

Apparel or Gift: false

Publisher (non-AMS): Published in cooperation with Mathematics Advanced Study Semesters

SXG Subject: GT; DE

Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/stml-30

Online Price 1 Label: List

Online Price 1: 41.00

Print Price 1 Label: List

Print Price 1: 44.00

Online Price 2 Label: Individual

Online Price 2: 32.80

Print Price 2 Label: Individual

Print Price 2: 35.20

Dual Price 1 Label: List

Dual Price 1: 52

Dual Price 2 Label: Individual

Dual Price 2: 41.6

Print Add to Cart URL: /some/url/at/AMS/STML-30

Electronic Add to Cart URL: /some/url/at/AMS/STML-30.E

Review Copy: https://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-2141-0&pisbn=978-0-8218-3919-5&epc=STML/30.E&ppc=STML/30&title=Geometry%20and%20Billiards&author=Serge%20Tabachnikov&type=R

Readership:

Advanced undergraduates, graduate students, and research mathematicians interested in ergodic theory and geometry.

Reviews:

(This book) is very well written, with nice illustrations. The author presents the results very clearly, with interesting digressions and he mentions applications of billiards to various fields.

-- Zentralblatt MATH

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Cover
- Cover
Title
- Title
Copyright
- Copyright
Contents
- Contents
Foreword: MASS and REU at Penn State University
- Foreword: MASS and REU at Penn State University
Preface
- Preface
Chapter 1. Motivation: Mechanics and Optics
- Chapter 1. Motivation: Mechanics and Optics
Index
- Index

Supplemental Materials

Geometry and Billiards

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Table of Contents

Geometry and Billiards

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Cover

Title

Copyright

Contents

Foreword: MASS and REU at Penn State University

Preface

Chapter 1. Motivation: Mechanics and Optics

Index