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   Analytic Hyperbolic Geometry and Einetein's Special Theory of Relativity 


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                              General Information


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Type.................: Ebook


Part Size............: 4,623,447 bytes


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                               Post Information


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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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