Hyperbolic Geometry - Brossura

Iversen, Birger

Brossura

ISBN 10: 0521435285 ISBN 13: 9780521435284

Casa editrice: Cambridge University Press, 2009

Riassunto

Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics. In this book, the rich geometry of the hyperbolic plane is studied in detail, leading to the focal point of the book, Poincare's polygon theorem and the relationship between hyperbolic geometries and discrete groups of isometries. Hyperbolic 3-space is also discussed, and the directions that current research in this field is taking are sketched. This will be an excellent introduction to hyperbolic geometry for students new to the subject, and for experts in other fields.

Su questo libro

Descrizione del libro:

Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics. In this book, the rich geometry of the hyperbolic plane is studied in detail, leading to the focal point of the book, Poincare's polygon theorem and the relationship between hyperbolic geometries and discrete groups of isometries.

Contenuti:

Introduction; 1. Quadratic Forms; 2. Geometries; 3. Hyperbolic Plane; 4. Fuchsian Groups; 5. Fundamental Domains; 6. Coverings; 7. Poincare's Theorem; 8. Hyperbolic 3-Space; Appendix: Axioms for Plane Geometry.

Su questa edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 2009
• ISBN 10: 0521435285
• ISBN 13: 9780521435284
• Rilegatura: Copertina flessibile
• Numero di pagine: 316