Geometry And Billiards

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Geometry and Billiards

Author : Serge Tabachnikov
Publisher : American Mathematical Soc.
ISBN 13 : 0821839195
Total Pages : 192 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometry and Billiards by : Serge Tabachnikov

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.

An Introduction To Mathematical Billiards

Author : Rozikov Utkir A
Publisher : World Scientific
ISBN 13 : 9813276487
Total Pages : 224 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis An Introduction To Mathematical Billiards by : Rozikov Utkir A

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.

Chaotic Billiards

Author : Nikolai Chernov
Publisher : American Mathematical Society
ISBN 13 : 1470474425
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Chaotic Billiards by : Nikolai Chernov

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.

Poncelet Porisms and Beyond

Author : Vladimir Dragović
Publisher : Springer Science & Business Media
ISBN 13 : 3034800150
Total Pages : 293 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Poncelet Porisms and Beyond by : Vladimir Dragović

Download or read book Poncelet Porisms and Beyond written by Vladimir Dragović and published by Springer Science & Business Media. This book was released on 2011-05-02 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to present, in a complete and comprehensive way, areas of current research interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, and classical projective geometry of pencils of quadrics. The most important results and ideas, classical as well as modern, connected to the Poncelet theorem are presented, together with a historical overview analyzing the classical ideas and their natural generalizations. Special attention is paid to the realization of the Griffiths and Harris programme about Poncelet-type problems and addition theorems. This programme, formulated three decades ago, is aimed to understanding the higher-dimensional analogues of Poncelet problems and the realization of the synthetic approach of higher genus addition theorems.

An Introduction to Mathematical Billiards

Author : Utkir A. Rozikov
Publisher :
ISBN 13 : 9789813276475
Total Pages : 223 pages
Book Rating : 4.2/5 (764 download)

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Book Synopsis An Introduction to Mathematical Billiards by : Utkir A. Rozikov

Download or read book An Introduction to Mathematical Billiards written by Utkir A. Rozikov and published by . This book was released on 2018 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Integrable Hamiltonian Systems

Author : A.V. Bolsinov
Publisher : CRC Press
ISBN 13 : 0203643429
Total Pages : 752 pages
Book Rating : 4.2/5 (36 download)

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Book Synopsis Integrable Hamiltonian Systems by : A.V. Bolsinov

Download or read book Integrable Hamiltonian Systems written by A.V. Bolsinov and published by CRC Press. This book was released on 2004-02-25 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,

Mostly Surfaces

Author : Richard Evan Schwartz
Publisher : American Mathematical Soc.
ISBN 13 : 0821853686
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mostly Surfaces by : Richard Evan Schwartz

Download or read book Mostly Surfaces written by Richard Evan Schwartz and published by American Mathematical Soc.. This book was released on 2011 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.

The Illustrated Principles of Pool and Billiards

Author : David G. Alciatore
Publisher : Union Square & Co.
ISBN 13 : 1454927917
Total Pages : 272 pages
Book Rating : 4.4/5 (549 download)

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Book Synopsis The Illustrated Principles of Pool and Billiards by : David G. Alciatore

Download or read book The Illustrated Principles of Pool and Billiards written by David G. Alciatore and published by Union Square & Co.. This book was released on 2017-05-01 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master one of the world’s most popular games with the help of a mechanical engineering professor who has a passion for pool. More than 80 principles of the game, presented with 250-plus precisely scaled illustrations and photographs, offer players of all levels a thorough overview of the fundamentals of 8-ball and 9-ball, including grip and stance, basic shots, position play and strategy, bank and kick shots, and advanced techniques such as carom and jump shots. Organized for quick study, this must-have guide features extensive cross-references and is supplemented with video clips, interesting mathematical formulas, and other resources also available at www.engr.colostate.edu/pool.

Billiards

Author : Serge Tabachnikov
Publisher : SMF
ISBN 13 : 9782856290309
Total Pages : 142 pages
Book Rating : 4.2/5 (93 download)

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Book Synopsis Billiards by : Serge Tabachnikov

Download or read book Billiards written by Serge Tabachnikov and published by SMF. This book was released on 1995 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:

How To Play Pool

Author : Tim Ander
Publisher : CRB Publishing
ISBN 13 : 8827502343
Total Pages : pages
Book Rating : 4.8/5 (275 download)

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Book Synopsis How To Play Pool by : Tim Ander

Download or read book How To Play Pool written by Tim Ander and published by CRB Publishing. This book was released on 2018-03-10 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Take Your Pool Skills to the Next Level and Win Big! Inside How to Play Pool, you’ll discover the rules for many popular variations of the game: Eight-Ball Nine-Ball One-Pocket and Snooker With this book, you can strengthen your pool game with the right posture, physics, and geometry. You’ll learn to execute many different types of shots, such as straight, angled, and spin shots. For example, you’ll learn to combine top/back with left/right spin and get all kinds of impressive results! How to Play Pool explains how you can use your cunning to plan ahead and out-strategize your opponents. You’ll find out why to use just the right amount of force to avoid reflections and “own” pockets. By targeting clumps of balls, you can set yourself up for a great endgame layout. If you pay close attention to the cue ball’s trajectory after it hits the target ball, you’ll set yourself up for shot after easy shot. With these simple and powerful pool-playing tips and techniques, you’ll dominate the table – and the competition! You’ll even learn how to pull off a variety of crowd-pleasing trick shots: Pocketing the Eight-Ball on the Break Jumping Over Obstacles Sinking the 4-in-a-Line Shot Don’t wait – Take the plunge and become a pool shark today with How to Play Pool! It’s fast and easy to order – just scroll up and click the BUY NOW WITH ONE CLICK button on the right-hand side of your screen.

An Invitation to Alexandrov Geometry

Author : Stephanie Alexander
Publisher : Springer
ISBN 13 : 3030053121
Total Pages : 88 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis An Invitation to Alexandrov Geometry by : Stephanie Alexander

Download or read book An Invitation to Alexandrov Geometry written by Stephanie Alexander and published by Springer. This book was released on 2019-05-08 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.

Pool Techniques and Tricks

Author : Pierre Morin
Publisher :
ISBN 13 : 9781554079384
Total Pages : 0 pages
Book Rating : 4.0/5 (793 download)

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Book Synopsis Pool Techniques and Tricks by : Pierre Morin

Download or read book Pool Techniques and Tricks written by Pierre Morin and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: An estimated 49 million Americans participate in cue sports, the most popular being pool, also known as pocket billiards. But for those who want to improve their game -- whether for recreation or competition -- little guidance is available. Pool Techniques and Tricks fills that gap. It is a comprehensive illustrated guide on how to play pool like a champion. It reveals the secrets of the world's best players and describes how their knowledge of table geometry and physics, along with a few well-guarded "secrets," are key to their success. The reader is introduced to vocabulary, rules, equipment, basic techniques and various strategies to help master every aspect of this fascinating hobby. Using clear diagrams, photographs and concise explanations, more than 100 professional trick shots are demonstrated. Each trick is rated as to difficulty, and the point of cue-to-ball contact is shown. The book also contains: An introduction to the history of pool A survey of champions in men's and women's world competition Equipment and accessories Hand and finger positions and using the bridge Geometry of the table and working with ball motion How to analyze and play difficult shots Strategy and competition. A separate chapter includes rules for all of the cue sports: 8-ball, 9-ball, 10-ball, 14.1, snooker and carambola. With Pool Techniques and Tricks, anyone can be a pro pool player, recreational or competitive. AUTHOR: Pierre Morin was a trial lawyer for 35 years. He began to play pool at a very early age, has participated in many tournaments and has won roughly a hundred. He is the author of four books on the subject. colour throughout

Basic Pool

Author : Arthur "Babe" Cranfield
Publisher : Simon and Schuster
ISBN 13 : 1510712313
Total Pages : 232 pages
Book Rating : 4.5/5 (17 download)

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Book Synopsis Basic Pool by : Arthur "Babe" Cranfield

Download or read book Basic Pool written by Arthur "Babe" Cranfield and published by Simon and Schuster. This book was released on 2016-11-01 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn tips and tactics from the very best, in this newly revised and expanded edition. * Consumer reviews say it best: pool Hall of Famer Arthur “Babe” Cranfield wrote an "easy to read and understand" pool manual that will have "beginners and skilled players alike" play better. "Excellent guide", "helpful illustrations", "recommended to all". * Give it a try and "you cannot help but play better".

Pleasures of Small Motions

Author : Ph. D. Fancher
Publisher : Rowman & Littlefield
ISBN 13 : 1493072714
Total Pages : 160 pages
Book Rating : 4.4/5 (93 download)

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Book Synopsis Pleasures of Small Motions by : Ph. D. Fancher

Download or read book Pleasures of Small Motions written by Ph. D. Fancher and published by Rowman & Littlefield. This book was released on 2022-06-01 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: A psychotherapist and pool columnist breaks new ground by applying good science to the mental game of billiards and gives invaluable insight on competitive play.

Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts

Author : Valeriĭ Viktorovich Kozlov
Publisher : American Mathematical Soc.
ISBN 13 : 0821845500
Total Pages : 182 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts by : Valeriĭ Viktorovich Kozlov

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.

Outer Billiards on Kites (AM-171)

Author : Richard Evan Schwartz
Publisher : Princeton University Press
ISBN 13 : 1400831970
Total Pages : 320 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Outer Billiards on Kites (AM-171) by : Richard Evan Schwartz

Download or read book Outer Billiards on Kites (AM-171) written by Richard Evan Schwartz and published by Princeton University Press. This book was released on 2009-10-05 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B. H. Neumann introduced this system in the 1950s, and J. Moser popularized it as a toy model for celestial mechanics. All along, the so-called Moser-Neumann question has been one of the central problems in the field. This question asks whether or not one can have an outer billiards system with an unbounded orbit. The Moser-Neumann question is an idealized version of the question of whether, because of small disturbances in its orbit, the Earth can break out of its orbit and fly away from the Sun. In Outer Billiards on Kites, Richard Schwartz presents his affirmative solution to the Moser-Neumann problem. He shows that an outer billiards system can have an unbounded orbit when defined relative to any irrational kite. A kite is a quadrilateral having a diagonal that is a line of bilateral symmetry. The kite is irrational if the other diagonal divides the quadrilateral into two triangles whose areas are not rationally related. In addition to solving the basic problem, Schwartz relates outer billiards on kites to such topics as Diophantine approximation, the modular group, self-similar sets, polytope exchange maps, profinite completions of the integers, and solenoids--connections that together allow for a fairly complete analysis of the dynamical system.

The Universe of Conics

Author : Georg Glaeser
Publisher : Springer
ISBN 13 : 3662454505
Total Pages : 488 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis The Universe of Conics by : Georg Glaeser

Download or read book The Universe of Conics written by Georg Glaeser and published by Springer. This book was released on 2016-03-22 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries. With more than two thousand years of history, conic sections play a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics. This text will be invaluable to undergraduate mathematics students, those in adjacent fields of study, and anyone with an interest in classical geometry. Augmented with more than three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises.