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- ISBN:9787560391564
- 装帧:一般胶版纸
- 册数:暂无
- 重量:暂无
- 开本:24cm
- 页数:418页
- 出版时间:2021-02-01
- 条形码:9787560391564 ; 978-7-5603-9156-4
内容简介
本书共分为四部分, **部分介绍了陀螺组 ; 第二部分介绍了陀螺交换陀螺组 ; 第三部分介绍了陀螺矢量空间, 陀螺仪矢量是根据陀螺仪平行四边形法则添加的定向陀螺仪段的等价类, 正如矢量是根据平行四边形法则添加的定向段的等价类 ; 第四部分介绍了回转三角法。本书捕捉到的这些新奇的类比源于托马斯旋转, 这是相对论效应的数学抽象, 称为托马斯旋进。值得注意的是, 本书仅仅引入托马斯? 回转就把欧几里得几何变成了双曲几何, 并揭示了这两种几何所共有的神秘类比。
目录
Contents
Preface
1 Gyrogroups
1.1 From M6bius to Gyrogroups
1.2 Groupoids, Loops, Groups, and Gyrogroups
1.3 M6bius Gyrogroups: From the Disc To The Ball
1.4 First Gyrogroup Theorems
1.5 The Two Basic Equations of Gyrogroups
1.6 The Basic Cancellation Laws of Gyrogroups
1.7 Commuting Automorphisms with Gyroautomorphisms
1.8 The Gyrosemidirect Product
1.9 Basic Gyration Properties
1.10 An Advanced Gyrogroup Equation
1.11 Exercises
2 Gyrocommutative Gyrogroups
2.1 Gyrocommutative Gyrogroups
2.2 Mobius Gyrogroups
2.3 Einstein Gyrogroups
2.4 Gyrogroup Isomorphism
2.5 Exercises
3 Gyrovector Spaces
3.1 Definition and First Gyrovector Space Theorems
3.2 Gyrolines
3.3 Gyromidpoints
3.4 Analogies Between Gyromidpoints and Midpoints
3.5 Gyrogeodesics
3.6 Mobius Gyrovector Spaces
3.7 Mobius Gyrolines
3.8 Einstein Gyrovector Spaces
3.9 Einstein Gyrolines
3.10 Einstein Gyromidpoints and Gyrotriangle Gyrocentroids
3.11 Mobius Gyrotriangle Gyromedians and Gyrocentroids
3.12 The Gyroparallelogram
3.13 Points, Vectors, and Gyrovectors
3.14 The Gyroparallelogram Addition Law of Gyrovectors
3.15 Gyrovector Gyrotranslation
3.16 Gyrovector Gyrotranslation Composition
3.17 Gyrovector Gyrotranslation and the GyroparaUelogram Law
3.18 The Mobius Gyrotriangle Gyroangles
3.19 Exercises
4 Gyrotrigonometry
4.1 The Gyroangle
4.2 The Gyrotriangle
4.3 The Gyrotriangle Addition Law
4.4 Cogyrolines, Cogyrotriangles, and Cogyroangles
4.5 The Law of Gyrocosines
4.6 The SSS to AAA Conversion Law
4.7 Inequalities for Gyrotriangles
4.8 The AAA to S8S Conversion Law
4.9 The Law of Gyrosines
4.10 TheASA to 8AS Conversion Law
4.11 The Gyrotriangle Defect
4.12 The Right Gyrotriangle
4.13 Gyrotrigonometry
4.14 Gyrodistance Between a Point and a Gyroline
4.15 The Gyrotriangle Gyroaltitude
4.16 The Gyrotriangle Gyroarea
4.17 Gyrotriangle Similarity
4.18 The Gyroangle Bisector Theorem
4.19 The Hyperbolic Steiner-Lehmus Theorem
4.20 The Urquhart theorem
4.21 The Hyperbolic Urquhart theorem
4.22 The Gyroparallelogram Gyroangles
4.23 Relativistic Mechanical Interpretation
4.24 Gyro-Analogies that May Reveal the Origin of Dark Matter
4.24.1 Newtonian Systems of Particles
4.24.2 Einsteinian Systems of Particles
4.24.3 The Relativistic Invariant Mass Paradox
4.25 Exercises
Bibliography
Index
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