Hyperbolic Triangle Centers : The Special Relativistic Approach
After A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einstein's special theory of relativity, the purpose of his new book is to introduce hyperbolic barycentric coordinates, another important conce...
Gardado en:
| Autor Principal: | |
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| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado: |
Dordrecht :
Springer Netherlands
[20..].
Cham : Springer Nature |
| Edición: | 1st ed. 2010. |
| Series: | Fundamental Theories of Physics
166 |
| Acceso en liña: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Hyperbolic Triangle Centers, Texte imprimé, 9789048186389 • Hyperbolic triangle centers, the special relativistic approach, A. A. Ungar, Dordrecht, Springer, 2010, 1 vol. (xvi-319 p.), Fundamental theories of physics, 978-90-481-8636-5 • Hyperbolic triangle centers, the special relativistic approach, A. A. Ungar, Dordrecht, Springer, 2010, 1 vol. (xvi-319 p.), Fundamental theories of physics, 978-90-481-8636-5 |
| Résumé: | After A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einstein's special theory of relativity, the purpose of his new book is to introduce hyperbolic barycentric coordinates, another important concept to embed Euclidean geometry into hyperbolic geometry. It will be demonstrated that, in full analogy to classical mechanics where barycentric coordinates are related to the Newtonian mass, barycentric coordinates are related to the Einsteinian relativistic mass in hyperbolic geometry. Contrary to general belief, Einstein's relativistic mass hence meshes up extraordinarily well with Minkowski's four-vector formalism of special relativity. In Euclidean geometry, barycentric coordinates can be used to determine various triangle centers. While there are many known Euclidean triangle centers, only few hyperbolic triangle centers are known, and none of the known hyperbolic triangle centers has been determined analytically with respect to its hyperbolic triangle vertices. In his recent research, the author set the ground for investigating hyperbolic triangle centers via hyperbolic barycentric coordinates, and one of the purposes of this book is to initiate a study of hyperbolic triangle centers in full analogy with the rich study of Euclidean triangle centers. Owing to its novelty, the book is aimed at a large audience: it can be enjoyed equally by upper-level undergraduates, graduate students, researchers and academics in geometry, abstract algebra, theoretical physics and astronomy. For a fruitful reading of this book, familiarity with Euclidean geometry is assumed. Mathematical-physicists and theoretical physicists are likely to enjoy the study of Einstein's special relativity in terms of its underlying hyperbolic geometry. Geometers may enjoy the hunt for new hyperbolic triangle centers and, finally, astronomers may use hyperbolic barycentric coordinates in the velocity space of cosmology. |
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| descrición da copia: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9789048186372 |
| ISSN: | 2365-6425 |
| Acceso: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |