Hyperbolic Geometry (Springer Undergraduate Mathematics Series) [ILLUSTRATED] (Paperback)

by James W Anderson (Author) "We begin our investigation by describing a model of the hyperbolic plane..." (more)
Key Phrases: hyperbolic line passing, hyperbolic line segment, parallel hyperbolic lines, Groups Acting (more...)

Editorial Reviews

Product Description
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, taking the approach that hyperbolic geometry consists of the study of those quantities invariant under the action of a natural group of transformations. Topics covered include the upper half-space model of the hyperbolic plane, Mbius transformations, the general Mbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincar disc model, convex subsets of the hyperbolic plane, the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications. 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 area of mathematics.

Product Details

• Paperback: 230 pages
• Publisher: Springer; 1 edition (October 18, 1999)
• Language: English
• ISBN-10: 1852331569
• ISBN-13: 978-1852331566
• Product Dimensions: 9.2 x 6.7 x 0.6 inches
• Shipping Weight: 12.8 ounces
• Average Customer Review: 5.0 out of 5 stars See all reviews (3 customer reviews)
• Amazon.com Sales Rank: #1,194,581 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

6 of 6 people found the following review helpful:

5.0 out of 5 stars Excellent book, August 22, 2007

By	mathematician (Tallahassee, FL USA) - See all my reviews

This review is from: Hyperbolic Geometry (Springer Undergraduate Mathematics Series) (Paperback)

This is an excellent introduction to hyperbolic geometry. It assumes knowledge of euclidean geometry, trigonometry, basic complex analysis, basic abstract algebra, and basic point set topology. That material is very well presented, and the exercises shed more light on what is being discussed. Plus, solutions to all the exercises are at the end of the book.

4 of 4 people found the following review helpful:

5.0 out of 5 stars Very good introduction, August 3, 2007

By	Justin Curry - See all my reviews (REAL NAME)

This review is from: Hyperbolic Geometry (Springer Undergraduate Mathematics Series) (Paperback)

I used this text along with Tristan Needham's "Visual Complex Analysis" to get a full dose of the geometric beauty inherent in studying complex variables. I found it to be a nice complement to the second year course in geometry at Cambridge University. Anderson does a wonderful job of working out in detail lots of examples so that you can get the algorithmic practice of solving problems. However this is not merely a cookbook. Rather, core elements of the theory are presented from the ground up, with plenty of time spent on understanding the group structure of Mobius transformations in various settings. Disc and upper-half plane models are treated as well as more general models. I recommend you buy both this book and Needham's if you want to appreciate the world of complex numbers.

7 of 10 people found the following review helpful:

5.0 out of 5 stars great book, January 28, 2004

By A Customer

this is a really great introduction to hyperbolic geometry. especially if you want to study gammas acting on the upper half plane. it starts at a much lower level then any other text.