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Download or read book Billiards Mathematically Treated written by George Wirgman Hemming and published by . This book was released on 1904 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: George Wirgman Hemming
Publisher:
Published: 2003
Total Pages: 45
ISBN-13: 9780598414182
DOWNLOAD EBOOKDownload or read book Billiards Mathematically Treated written by George Wirgman Hemming and published by . This book was released on 2003 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Rozikov Utkir A
Publisher: World Scientific
Published: 2018-12-06
Total Pages: 224
ISBN-13: 9813276487
DOWNLOAD EBOOKA mathematical billiard is a mechanical system consisting of a billiard ball on a table of any form (which can be planar or even a multidimensional domain) but without billiard pockets. The ball moves and its trajectory is defined by the ball's initial position and its initial speed vector. The ball's reflections from the boundary of the table are assumed to have the property that the reflection and incidence angles are the same. This book comprehensively presents known results on the behavior of a trajectory of a billiard ball on a planar table (having one of the following forms: circle, ellipse, triangle, rectangle, polygon and some general convex domains). It provides a systematic review of the theory of dynamical systems, with a concise presentation of billiards in elementary mathematics and simple billiards related to geometry and physics.The description of these trajectories leads to the solution of various questions in mathematics and mechanics: problems related to liquid transfusion, lighting of mirror rooms, crushing of stones in a kidney, collisions of gas particles, etc. The analysis of billiard trajectories can involve methods of geometry, dynamical systems, and ergodic theory, as well as methods of theoretical physics and mechanics, which has applications in the fields of biology, mathematics, medicine, and physics.
Download or read book An Introduction To Mathematical Billiards written by Rozikov Utkir A and published by World Scientific. This book was released on 2018-12-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical billiard is a mechanical system consisting of a billiard ball on a table of any form (which can be planar or even a multidimensional domain) but without billiard pockets. The ball moves and its trajectory is defined by the ball's initial position and its initial speed vector. The ball's reflections from the boundary of the table are assumed to have the property that the reflection and incidence angles are the same. This book comprehensively presents known results on the behavior of a trajectory of a billiard ball on a planar table (having one of the following forms: circle, ellipse, triangle, rectangle, polygon and some general convex domains). It provides a systematic review of the theory of dynamical systems, with a concise presentation of billiards in elementary mathematics and simple billiards related to geometry and physics.The description of these trajectories leads to the solution of various questions in mathematics and mechanics: problems related to liquid transfusion, lighting of mirror rooms, crushing of stones in a kidney, collisions of gas particles, etc. The analysis of billiard trajectories can involve methods of geometry, dynamical systems, and ergodic theory, as well as methods of theoretical physics and mechanics, which has applications in the fields of biology, mathematics, medicine, and physics.
Author: Serge Tabachnikov
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 192
ISBN-13: 0821839195
DOWNLOAD EBOOKMathematical 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.
Download or read book Geometry and Billiards written by Serge Tabachnikov and published by American Mathematical Soc.. This book was released on 2005 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author: Valeriĭ Viktorovich Kozlov
Publisher: American Mathematical Soc.
Published: 1991-08-05
Total Pages: 182
ISBN-13: 0821845500
DOWNLOAD EBOOKStarting with the work of G D Birkhoff, billiards have been a popular research topic drawing on such areas as ergodic theory, Morse theory, and KAM theory. Billiard systems are also remarkable in that they arise naturally in a number of important problems of mechanics and physics. This book is devoted to mathematical aspects of the theory of dynamical systems of billiard type. Focusing on the genetic approach, the authors strive to clarify the genesis of the basic ideas and concepts of the theory of dynamical systems with impact intereactions and also to demonstrate that these methods are natural and effective. Recent limit theorems, which justify various mathematical models of impact theory, are key features. Questions of existence and stability of periodic trajectories of elastic billiards occupy a special place in the book, and considerable attention is devoted to integrable billiards. A brief survey is given of work on billiards with ergodic behaviour. Each chapter ends with a list of problems.
Download or read book Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts written by Valeriĭ Viktorovich Kozlov and published by American Mathematical Soc.. This book was released on 1991-08-05 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with the work of G D Birkhoff, billiards have been a popular research topic drawing on such areas as ergodic theory, Morse theory, and KAM theory. Billiard systems are also remarkable in that they arise naturally in a number of important problems of mechanics and physics. This book is devoted to mathematical aspects of the theory of dynamical systems of billiard type. Focusing on the genetic approach, the authors strive to clarify the genesis of the basic ideas and concepts of the theory of dynamical systems with impact intereactions and also to demonstrate that these methods are natural and effective. Recent limit theorems, which justify various mathematical models of impact theory, are key features. Questions of existence and stability of periodic trajectories of elastic billiards occupy a special place in the book, and considerable attention is devoted to integrable billiards. A brief survey is given of work on billiards with ergodic behaviour. Each chapter ends with a list of problems.
Author: Gary Clarke
Publisher: Paragon Publishing
Published: 2008
Total Pages: 276
ISBN-13: 1899820469
DOWNLOAD EBOOKA Billiards & Snooker Compendium A Billiards & Snooker Compendium is the most extensive work on the literature of billiards and snooker ever published and took over two years to compile. It contains bibliographical information on over 650 books, a detailed description of each book's content, tips on identifying different editions, notes on scarce dustjackets, plus the estimated values of 1st editions. These values have been calculated using a variety of well respected sources. This essential reference book is easy to use, is clearly laid out, and includes both an author and title index. Each book has its own unique reference number and entries are fully cross referenced. It will appeal to all collectors of billiards and snooker memorabilia, book dealers and collectors, fans of both sports, and those simply wishing to add a few books to their sports collection. About the author Gary Clarke has been playing and watching snooker for over 25 years and has a great knowledge and deep affection for the game. He is also an avid reader and book lover and this work combines two of his most passionate interests. The author currently lives in his home town of Ipswich and this is his first work of non-fiction.
Download or read book A Billiards and Snooker Compendium written by Gary Clarke and published by Paragon Publishing. This book was released on 2008 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Billiards & Snooker Compendium A Billiards & Snooker Compendium is the most extensive work on the literature of billiards and snooker ever published and took over two years to compile. It contains bibliographical information on over 650 books, a detailed description of each book's content, tips on identifying different editions, notes on scarce dustjackets, plus the estimated values of 1st editions. These values have been calculated using a variety of well respected sources. This essential reference book is easy to use, is clearly laid out, and includes both an author and title index. Each book has its own unique reference number and entries are fully cross referenced. It will appeal to all collectors of billiards and snooker memorabilia, book dealers and collectors, fans of both sports, and those simply wishing to add a few books to their sports collection. About the author Gary Clarke has been playing and watching snooker for over 25 years and has a great knowledge and deep affection for the game. He is also an avid reader and book lover and this work combines two of his most passionate interests. The author currently lives in his home town of Ipswich and this is his first work of non-fiction.
Download or read book The Speaker written by and published by . This book was released on 1899 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Nikolai Chernov
Publisher: American Mathematical Society
Published: 2023-09-18
Total Pages: 330
ISBN-13: 1470474425
DOWNLOAD EBOOKThis book covers one of the most exciting but most difficult topics in the modern theory of dynamical systems: chaotic billiards. In physics, billiard models describe various mechanical processes, molecular dynamics, and optical phenomena. The theory of chaotic billiards has made remarkable progress in the past thirty-five years, but it remains notoriously difficult for the beginner, with main results scattered in hardly accessible research articles. This is the first and so far only book that covers all the fundamental facts about chaotic billiards in a complete and systematic manner. The book contains all the necessary definitions, full proofs of all the main theorems, and many examples and illustrations that help the reader to understand the material. Hundreds of carefully designed exercises allow the reader not only to become familiar with chaotic billiards but to master the subject. The book addresses graduate students and young researchers in physics and mathematics. Prerequisites include standard graduate courses in measure theory, probability, Riemannian geometry, topology, and complex analysis. Some of this material is summarized in the appendices to the book.
Download or read book Chaotic Billiards written by Nikolai Chernov and published by American Mathematical Society. This book was released on 2023-09-18 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers one of the most exciting but most difficult topics in the modern theory of dynamical systems: chaotic billiards. In physics, billiard models describe various mechanical processes, molecular dynamics, and optical phenomena. The theory of chaotic billiards has made remarkable progress in the past thirty-five years, but it remains notoriously difficult for the beginner, with main results scattered in hardly accessible research articles. This is the first and so far only book that covers all the fundamental facts about chaotic billiards in a complete and systematic manner. The book contains all the necessary definitions, full proofs of all the main theorems, and many examples and illustrations that help the reader to understand the material. Hundreds of carefully designed exercises allow the reader not only to become familiar with chaotic billiards but to master the subject. The book addresses graduate students and young researchers in physics and mathematics. Prerequisites include standard graduate courses in measure theory, probability, Riemannian geometry, topology, and complex analysis. Some of this material is summarized in the appendices to the book.
Download or read book Educational Times written by and published by . This book was released on 1899 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bulletin of the American Mathematical Society written by and published by . This book was released on 1899 with total page 1052 pages. Available in PDF, EPUB and Kindle. Book excerpt:
