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Record Nr. |
UNINA9910787261603321 |
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Autore |
Ungar Abraham A. |
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Titolo |
Analytic hyperbolic geometry in N dimensions : an introduction / / Abraham A. Ungar, Mathematics Department, North Dakota State University, Fargo, North Dakota, USA |
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Pubbl/distr/stampa |
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Boca Raton : , : Taylor & Francis, , [2015] |
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©2015 |
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ISBN |
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0-429-17474-8 |
1-4822-3668-0 |
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Descrizione fisica |
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1 online resource (616 p.) |
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Collana |
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A Science Publishers Book |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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A CRC title. |
A Science Publishers book. |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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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 Dimensions |
10. 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 |
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Sommario/riassunto |
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The 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 |
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