LEADER 02709nam 22005774a 450 001 9910784043903321 005 20230617010100.0 010 $a1-281-89922-4 010 $a9786611899226 010 $a981-270-327-6 035 $a(CKB)1000000000334247 035 $a(EBL)296062 035 $a(OCoLC)228171823 035 $a(SSID)ssj0000103010 035 $a(PQKBManifestationID)11120118 035 $a(PQKBTitleCode)TC0000103010 035 $a(PQKBWorkID)10060928 035 $a(PQKB)11041999 035 $a(MiAaPQ)EBC296062 035 $a(WSP)00000043 035 $a(Au-PeEL)EBL296062 035 $a(CaPaEBR)ebr10174094 035 $a(CaONFJC)MIL189922 035 $a(EXLCZ)991000000000334247 100 $a20050728d2005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAnalytic hyperbolic geometry$b[electronic resource] $emathematical foundations and applications /$fAbraham A. Ungar 210 $aNew Jersey $cWorld Scientific$dc2005 215 $a1 online resource (482 p.) 300 $aDescription based upon print version of record. 311 $a981-256-457-8 320 $aIncludes bibliographical references (p. 445-456) and index. 327 $aPreface; Acknowledgements; Contents; 1. Introduction; 2. Gyrogroups; 3. Gyrocommutative Gyrogroups; 4. Gyrogroup Extension; 5. Gyrovectors and Cogyrovectors; 6. Gyrovector Spaces; 7. Rudiments of Differential Geometry; 8. Gyrotrigonometry; 9. Bloch Gyrovector of Quantum Computation; 10. Special Theory of Relativity: The Analytic Hyperbolic Geometric Viewpoint; Notation And Special Symbols; Bibliography; Index 330 $aThis is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geometry. Analytic hyperbolic geometry regulates relativistic mechanics just as analytic Euclidean geometry regulates classical mechanics. The book presents a novel gyrovector space approach to analytic hyperbolic geometry, fully analogous to the well-known vector space approach to Euclidean geometry. A gyrovector is a hyperbolic vector. Gyrovectors are equivalence classes of directed gyrosegments that add according to the gyroparallelogram law just as vectors are equivalence classes of directed segme 606 $aGeometry, Hyperbolic$vTextbooks 606 $aVector algebra$vTextbooks 615 0$aGeometry, Hyperbolic 615 0$aVector algebra 676 $a516.9 700 $aUngar$b Abraham A$0850286 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910784043903321 996 $aAnalytic hyperbolic geometry$93855060 997 $aUNINA