Hyperbolic Geometry (Springer Undergraduate Mathematics Series)

Hyperbolic Geometry (Springer Undergraduate Mathematics Series)

By: James W. Anderson (author)Paperback

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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, Mobius transformations, the general Mobius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincare disc model, convex subsets of the hyperbolic plane, and 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, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics.

Contents

Preamble; The Basic Spaces; The General Mobius Group; Length and Distance in H; Other Models of the Hyperbolic Plane; Convexity, Area and Trigonometry; Groups acting on H; Solutions; Further Reading; References; Notation; Index

Product Details

  • ISBN13: 9781852331566
  • Format: Paperback
  • Number Of Pages: 239
  • ID: 9781852331566
  • ISBN10: 1852331569

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