Primera línea
In this chapter, we set the stage for what is to come.
Descripción de contraportada
The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, suitable for third or fourth year undergraduates. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations.
Topics covered include the upper half-plane model of the hyperbolic plane, Mbius transformations, the general Mbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincar disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula and its applications.
This updated second edition also features:
an expanded discussion of planar models of the hyperbolic plane arising from complex analysis;
the hyperboloid model of the hyperbolic plane;
brief discussion of generalizations to higher dimensions;
many new exercises.
The style and level of the book, which assumes few mathematical prerequisites, make it an ideal introduction to this subject and provides the reader with a firm grasp of the concepts and techniques of this beautiful part of the mathematical landscape.
Detalles
- Título Hyperbolic Geometry
- Autor James W. Anderson
- Encuadernación Tapa blanda
- Edición 2nd
- Páginas 276
- Volúmenes 1
- Idioma ENG
- Editorial Springer
- Fecha de publicación 2005-08-23
- Ilustrado Sí
- Features Bibliography, Illustrated, Index
- ISBN 9781852339340 / 1852339349
- Peso 1.1 libras (0.50 kg)
- Dimensiones 9.9 x 6.9 x 0.7 pulgadas (25.15 x 17.53 x 1.78 cm)
- Número de catálogo de la Librería del Congreso de EEUU 2005923338
- Dewey Decimal Code 516.9
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Hyperbolic Geometry
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Hyperbolic Geometry
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Hyperbolic Geometry (Springer Undergraduate Mathematics Series)
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Hyperbolic Geometry (Springer Undergraduate Mathematics Series)
de Anderson, James W
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- 9781852339340 / 1852339349
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