LEADER 03068oam 2200565I 450 001 9910820575903321 005 20240402103606.0 010 $a0-429-17474-8 010 $a1-4822-3668-0 024 7 $a10.1201/b17858 035 $a(CKB)3710000000303681 035 $a(EBL)1659311 035 $a(SSID)ssj0001380846 035 $a(PQKBManifestationID)11860357 035 $a(PQKBTitleCode)TC0001380846 035 $a(PQKBWorkID)11371346 035 $a(PQKB)11234152 035 $a(MiAaPQ)EBC1659311 035 $a(OCoLC)900602677 035 $a(EXLCZ)993710000000303681 100 $a20180331h20152015 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAnalytic hyperbolic geometry in N dimensions $ean introduction /$fAbraham A. Ungar, Mathematics Department, North Dakota State University, Fargo, North Dakota, USA 205 $a1st ed. 210 1$aBoca Raton :$cTaylor & Francis,$d[2015] 210 4$dİ2015 215 $a1 online resource (616 p.) 225 0 $aA Science Publishers Book 300 $aA CRC title. 300 $aA Science Publishers book. 311 $a1-322-63526-9 311 $a1-4822-3667-2 320 $aIncludes bibliographical references. 327 $aFront 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 Dimensions 327 $a10. 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; Bibliography 330 $aThe 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. Franc?oise Chatelin noted in her book, and elsewhere, that the computation la 606 $aGeometry, Hyperbolic 615 0$aGeometry, Hyperbolic. 676 $a516.9 700 $aUngar$b Abraham A.$0850286 801 0$bFlBoTFG 801 1$bFlBoTFG 906 $aBOOK 912 $a9910820575903321 996 $aAnalytic hyperbolic geometry in N dimensions$94104637 997 $aUNINA