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Analytic Hyperbolic Geometry and Eineteins Special Theory of Relativity~tqw~ darksiderg

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Analytic Hyperbolic Geometry and Einetein's Special Theory of Relativity
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Type.................: Ebook
Part Size............: 4,623,447 bytes
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Posted by............: ~tqw~

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Release Notes
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his book presents a powerful way to study Einstein's special theory of
relativity and its underlying hyperbolic geometry in which analogies with
classical results form the right tool. It introduces the notion of vectors into
analytic hyperbolic geometry, where they are called gyrovectors.

Newtonian velocity addition is the common vector addition, which is both
commutative and associative. The resulting vector spaces, in turn, form the
algebraic setting for the standard model of Euclidean geometry. In full analogy,
Einsteinian velocity addition is a gyrovector addition, which is both
gyrocommutative and gyroassociative. The resulting gyrovector spaces, in turn,
form the algebraic setting for the Beltrami-Klein ball model of the hyperbolic
geometry of Bolyai and Lobachevsky. Similarly, Mobius addition gives rise to
gyrovector spaces that form the algebraic setting for the Poincare ball model of
hyperbolic geometry.

Table Of Contents

1 Introduction 1
2 Gyrogroups 15
3 Gyrocommutative Gyrogroups 51
4 Gyrogroup Extension 101
5 Gyrovectors and Cogyrovectors 131
6 Gyrovector Spaces 153
7 Rudiments of Differential Geometry 239
8 Gyrotrigonometry 261
9 Bloch Gyrovector of Quantum Information and Computation 375
10 Special Theory of Relativity: The Analytic Hyperbolic Gometric Viewpoint:
Part I: Einstein Velocity Addition and its Consequences 397
11 Special Theory of Relativity: The Analytic Hyperboli Geometric Viewpoint:
Part II: Lorentz Transformation and its Consequences 445
12 Relativistic Gyrotrigonometry 537
13 Stellar and Particle Aberration 577
Notation and Special Symbols 601
Bibliography 605
Index 621

Product Details

* ISBN: 9812772294
* ISBN-13: 9789812772299
* Format: Hardcover, 628pp
* Publisher: World Scientific Publishing Company, Incorporated
* Pub. Date: April 2008

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