Hyperbolic Geometry (Springer Undergraduate Mathematics Series)
Language: English
Published by Springer, 2005
- Softcover
- New
Seller: BennettBooksLtd, Los Angeles, CA, U.S.A.BennettBooksLtd
AbeBooks seller since April 17, 2008
Condition: New
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Seller Inventory # Q-1852339349
- Title
- Hyperbolic Geometry (Springer Undergraduate Mathematics Series)
- Author
- Anderson, James W.
- Publisher
- Springer
- Publication year
- 2005
- Condition
- New
- Binding
- paperback
- Language
- English
- ISBN 10
- 1852339349
- ISBN 13
- 9781852339340
- Edition
- 2nd Edition
- Item weight
- 18 ounces
- Dimensions
- 7x0x10
- Series
- Book 6 of 90: Springer Undergraduate Mathematics
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, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics. Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincaré disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon 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;
- a brief discussion of generalizations to higher dimensions;
- many newexercises.
"Synopsis" may belong to another edition of this title.
From the Back Cover
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, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré 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.
"About the title" may belong to another edition of this title.
BennettBooksLtd
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