03048oam 2200553I 450 991078726160332120230807212114.00-429-17474-81-4822-3668-010.1201/b17858 (CKB)3710000000303681(EBL)1659311(SSID)ssj0001380846(PQKBManifestationID)11860357(PQKBTitleCode)TC0001380846(PQKBWorkID)11371346(PQKB)11234152(MiAaPQ)EBC1659311(OCoLC)900602677(EXLCZ)99371000000030368120180331h20152015 uy 0engur|n|---|||||txtccrAnalytic hyperbolic geometry in N dimensions an introduction /Abraham A. Ungar, Mathematics Department, North Dakota State University, Fargo, North Dakota, USABoca Raton :Taylor & Francis,[2015]©20151 online resource (616 p.)A Science Publishers BookA CRC title.A Science Publishers book.1-322-63526-9 1-4822-3667-2 Includes bibliographical references.Front Cover; Preface; Contents; List of Figures; Author's Biography; 1. Introduction; Part I: Einstein Gyrogroups and Gyrovector Spaces; 2. Einstein Gyrogroups; 3. Einstein Gyrovector Spaces ; 4. Relativistic Mass Meets Hyperbolic Geometry; Part II: Mathematical Tools for Hyperbolic Geometry; 5. Barycentric and Gyrobarycentric Coordinates; 6. Gyroparallelograms and Gyroparallelotopes; 7. Gyrotrigonometry; Part III: Hyperbolic Triangles and Circles; 8. Gyrotriangles and Gyrocircles; 9. Gyrocircle Theorems; Part IV: Hyperbolic Simplices, Hyperplanes and Hyperspheres in N Dimensions10. Gyrosimplex Gyrogeometry11. Gyrotetrahedron Gyrogeometry; Part V: Hyperbolic Ellipses and Hyperbolas; 12. Gyroellipses and Gyrohyperbolas ; Part VI: Thomas Precession; 13. Thomas Precession; Notations and Special Symbols; BibliographyThe concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language that sheds natural light on hyperbolic geometry and special relativity. Several authors have successfully employed the author's gyroalgebra in their exploration for novel results. Françoise Chatelin noted in her book, and elsewhere, that the computation laGeometry, HyperbolicGeometry, Hyperbolic.516.9Ungar Abraham A.850286FlBoTFGFlBoTFGBOOK9910787261603321Analytic hyperbolic geometry in N dimensions3779054UNINA