Geometry and Billiards pdf epub mobi txt 电子书 下载 2024


Geometry and Billiards

简体网页||繁体网页
Tabachnikov, Serge
American Mathematical Society
2005
176
0
Student Mathematical Library
9780821839195

图书标签: 数学  微分几何7  geometry  DS   


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发表于2024-12-24

Geometry and Billiards epub 下载 mobi 下载 pdf 下载 txt 电子书 下载 2024

Geometry and Billiards epub 下载 mobi 下载 pdf 下载 txt 电子书 下载 2024

Geometry and Billiards pdf epub mobi txt 电子书 下载 2024



图书描述

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.

Geometry and Billiards 下载 mobi epub pdf txt 电子书

著者简介

Serge Tabachnikov: Penn State, University Park, PA


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Geometry and Billiards pdf epub mobi txt 电子书 下载
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非常精彩的数学小册子,从普通的台球运动出发,依次让我们见识圆上的弹子系统与Benford定律的关系,共焦曲线,彩虹成因,周期轨道的存在,及其与Riemann面理论的关系,中间穿插讲了Hamilton力学,积分几何,遍历理论,山路引理等引人入胜的定理和结论,别开生面,令人迷醉啊。

评分

非常精彩的数学小册子,从普通的台球运动出发,依次让我们见识圆上的弹子系统与Benford定律的关系,共焦曲线,彩虹成因,周期轨道的存在,及其与Riemann面理论的关系,中间穿插讲了Hamilton力学,积分几何,遍历理论,山路引理等引人入胜的定理和结论,别开生面,令人迷醉啊。

评分

非常精彩的数学小册子,从普通的台球运动出发,依次让我们见识圆上的弹子系统与Benford定律的关系,共焦曲线,彩虹成因,周期轨道的存在,及其与Riemann面理论的关系,中间穿插讲了Hamilton力学,积分几何,遍历理论,山路引理等引人入胜的定理和结论,别开生面,令人迷醉啊。

评分

非常精彩的数学小册子,从普通的台球运动出发,依次让我们见识圆上的弹子系统与Benford定律的关系,共焦曲线,彩虹成因,周期轨道的存在,及其与Riemann面理论的关系,中间穿插讲了Hamilton力学,积分几何,遍历理论,山路引理等引人入胜的定理和结论,别开生面,令人迷醉啊。

评分

非常精彩的数学小册子,从普通的台球运动出发,依次让我们见识圆上的弹子系统与Benford定律的关系,共焦曲线,彩虹成因,周期轨道的存在,及其与Riemann面理论的关系,中间穿插讲了Hamilton力学,积分几何,遍历理论,山路引理等引人入胜的定理和结论,别开生面,令人迷醉啊。

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