02743nam 22005894a 450 991045072280332120200520144314.01-281-89922-49786611899226981-270-327-6(CKB)1000000000334247(EBL)296062(OCoLC)228171823(SSID)ssj0000103010(PQKBManifestationID)11120118(PQKBTitleCode)TC0000103010(PQKBWorkID)10060928(PQKB)11041999(MiAaPQ)EBC296062(WSP)00000043 (Au-PeEL)EBL296062(CaPaEBR)ebr10174094(CaONFJC)MIL189922(EXLCZ)99100000000033424720050728d2005 uy 0engur|n|---|||||txtccrAnalytic hyperbolic geometry[electronic resource] mathematical foundations and applications /Abraham A. UngarNew Jersey World Scientificc20051 online resource (482 p.)Description based upon print version of record.981-256-457-8 Includes bibliographical references (p. 445-456) and index.Preface; 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; IndexThis 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 segmeGeometry, HyperbolicTextbooksVector algebraTextbooksElectronic books.Geometry, HyperbolicVector algebra516.9Ungar Abraham A850286MiAaPQMiAaPQMiAaPQBOOK9910450722803321Analytic hyperbolic geometry1971628UNINA