LEADER 05499nam 2200661Ia 450 001 9910453536303321 005 20200520144314.0 010 $a1-281-91199-2 010 $a9786611911997 010 $a981-277-230-8 035 $a(CKB)1000000000538154 035 $a(EBL)1681504 035 $a(OCoLC)815748131 035 $a(SSID)ssj0000103011 035 $a(PQKBManifestationID)11138340 035 $a(PQKBTitleCode)TC0000103011 035 $a(PQKBWorkID)10061338 035 $a(PQKB)10788639 035 $a(MiAaPQ)EBC1681504 035 $a(WSP)00002047 035 $a(PPN)168148110 035 $a(Au-PeEL)EBL1681504 035 $a(CaPaEBR)ebr10255619 035 $a(CaONFJC)MIL191199 035 $a(EXLCZ)991000000000538154 100 $a20071223d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAnalytic hyperbolic geometry and Albert Einstein's special theory of relativity$b[electronic resource] /$fAbraham Albert Ungar 210 $aSingapore ;$aHackensack, NJ $cWorld Scientific$dc2008 215 $a1 online resource (649 p.) 300 $aDescription based upon print version of record. 311 $a981-277-229-4 320 $aIncludes bibliographical references (p. 605-620) and index. 327 $aContents; Preface; Acknowledgements; 1. Introduction; 1.1 A Vector Space Approach to Euclidean Geometry and A Gyrovector Space Approach to Hyperbolic Geometry; 1.2 Gyrolanguage; 1.3 Analytic Hyperbolic Geometry; 1.4 The Three Models; 1.5 Applications in Quantum and Special Relativity Theory; 2. Gyrogroups; 2.1 Definitions; 2.2 First Gyrogroup Theorems; 2.3 The Associative Gyropolygonal Gyroaddition; 2.4 Two Basic Gyrogroup Equations and Cancellation Laws; 2.5 Commuting Automorphisms with Gyroautomorphisms; 2.6 The Gyrosemidirect Product Group; 2.7 Basic Gyration Properties 327 $a3. Gyrocommutative Gyrogroups3.1 Gyrocommutative Gyrogroups; 3.2 Nested Gyroautomorphism Identities; 3.3 Two-Divisible Two-Torsion Free Gyrocommutative Gyrogroups; 3.4 From M obius to Gyrogroups; 3.5 Higher Dimensional M obius Gyrogroups; 3.6 M obius gyrations; 3.7 Three-Dimensional M obius gyrations; 3.8 Einstein Gyrogroups; 3.9 Einstein Coaddition; 3.10 PV Gyrogroups; 3.11 Points and Vectors in a Real Inner Product Space; 3.12 Exercises; 4. Gyrogroup Extension; 4.1 Gyrogroup Extension; 4.2 The Gyroinner Product, the Gyronorm, and the Gyroboost; 4.3 The Extended Automorphisms 327 $a4.4 Gyrotransformation Groups4.5 Einstein Gyrotransformation Groups; 4.6 PV (Proper Velocity) Gyrotransformation Groups; 4.7 Galilei Transformation Groups; 4.8 From Gyroboosts to Boosts; 4.9 The Lorentz Boost; 4.10 The (p :q)-Gyromidpoint; 4.11 The (p1 :p2 :...: pn)-Gyromidpoint; 5. Gyrovectors and Cogyrovectors; 5.1 Equivalence Classes; 5.2 Gyrovectors; 5.3 Gyrovector Translation; 5.4 Gyrovector Translation Composition; 5.5 Points and Gyrovectors; 5.6 The Gyroparallelogram Addition Law; 5.7 Cogyrovectors; 5.8 Cogyrovector Translation; 5.9 Cogyrovector Translation Composition 327 $a5.10 Points and Cogyrovectors5.11 Exercises; 6. Gyrovector Spaces; 6.1 Definition and First Gyrovector Space Theorems; 6.2 Solving a System of Two Equations in a Gyrovector Space; 6.3 Gyrolines and Cogyrolines; 6.4 Gyrolines; 6.5 Gyromidpoints; 6.6 Gyrocovariance; 6.7 Gyroparallelograms; 6.8 Gyrogeodesics; 6.9 Cogyrolines; 6.10 Carrier Cogyrolines of Cogyrovectors; 6.11 Cogyromidpoints; 6.12 Cogyrogeodesics; 6.13 Various Gyrolines and Cancellation Laws; 6.14 M obius Gyrovector Spaces; 6.15 M obius Cogyroline Parallelism; 6.16 Illustrating the Gyroline Gyration Transitive Law 327 $a6.17 Turning the M obius Gyrometric into the Poincar e Metric6.18 Einstein Gyrovector Spaces; 6.19 Turning Einstein Gyrometric into a Metric; 6.20 PV(ProperVelocity) Gyrovector Spaces; 6.21 Gyrovector Space Isomorphisms; 6.22 Gyrotriangle Gyromedians and Gyrocentroids; 6.22.1 In Einstein Gyrovector Spaces; 6.22.2 In M obius Gyrovector Spaces; 6.22.3 In PV Gyrovector Spaces; 6.23 Exercises; 7. Rudiments of Differential Geometry; 7.1 The Riemannian Line Element of Euclidean Metric; 7.2 The Gyroline and the Cogyroline Element; 7.3 The Gyroline Element of M obius Gyrovector Spaces 327 $a7.4 The Cogyroline Element of M obius Gyrovector Spaces 330 $a This 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 606 $aSpecial relativity (Physics) 606 $aGeometry, Hyperbolic 608 $aElectronic books. 615 0$aSpecial relativity (Physics) 615 0$aGeometry, Hyperbolic. 676 $a516.9 700 $aUngar$b Abraham A$0850286 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910453536303321 996 $aAnalytic hyperbolic geometry and Albert Einstein's special theory of relativity$92098350 997 $aUNINA