Geometry and Billiards (Student Mathematical Library)

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9780821839195: Geometry and Billiards (Student Mathematical Library)
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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. This volume has been copublished with the Mathematics Advanced Study Semesters program at Penn State.

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Tabachnikov, Serge
Editorial: American Mathematical Society (2005)
ISBN 10: 0821839195 ISBN 13: 9780821839195
Nuevos Paperback Cantidad: > 20
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Sequitur Books
(Boonsboro, MD, Estados Unidos de America)
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Descripción American Mathematical Society, 2005. Paperback. Estado de conservación: New. Brand new. We distribute directly for the publisher. 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. Nº de ref. de la librería 1006100146

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Tabachnikov, Serge
Editorial: American Mathematical Society, United States (2005)
ISBN 10: 0821839195 ISBN 13: 9780821839195
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Descripción American Mathematical Society, United States, 2005. Paperback. Estado de conservación: New. Illustrated edition. 213 x 140 mm. Language: English . Brand New Book. 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. Nº de ref. de la librería AAN9780821839195

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Descripción Estado de conservación: New. Depending on your location, this item may ship from the US or UK. Nº de ref. de la librería 97808218391950000000

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Tabachnikov, Serge
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Descripción American Mathematical Society, United States, 2005. Paperback. Estado de conservación: New. Illustrated edition. 213 x 140 mm. Language: English . Brand New Book. 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. Nº de ref. de la librería AAN9780821839195

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Tabachnikov, Serge
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ISBN 10: 0821839195 ISBN 13: 9780821839195
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Descripción American Mathematical Society, 2005. Estado de conservación: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: 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. This volume has been copublished with the Mathematics Advanced Study Semesters program at Penn State. Nº de ref. de la librería ABE_book_new_0821839195

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Tabachnikov, Serge
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Descripción American Mathematical Society, 2005. Paperback. Estado de conservación: New. book. Nº de ref. de la librería 0821839195

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Descripción American Mathematical Society, 2005. Paperback. Estado de conservación: NEW. 9780821839195 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0698306

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Descripción American Mathematical Society. Paperback. Estado de conservación: new. BRAND NEW, Geometry and Billiards (Illustrated edition), 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 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. Nº de ref. de la librería B9780821839195

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Tabachnikov, Serge
Editorial: American Mathematical Society (2005)
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Descripción American Mathematical Society, 2005. Paperback. Estado de conservación: New. Nº de ref. de la librería DADAX0821839195

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Tabachnikov, Serge
Editorial: American Mathematical Society (2005)
ISBN 10: 0821839195 ISBN 13: 9780821839195
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Descripción American Mathematical Society, 2005. Estado de conservación: New. Describes billiards and their relation with differential geometry, classical mechanics, and geometrical optics. This book covers such topics as variational principles of billiard motion, and symplectic geometry of rays of light and integral geometry. It is suitable for students interested in ergodic theory and geometry. Series: Student Mathematical Library. Num Pages: 176 pages, Illustrations. BIC Classification: PBM; PBW; WSJZ. Category: (P) Professional & Vocational. Weight in Grams: 242. . 2005. Paperback. . . . . . Nº de ref. de la librería V9780821839195

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