Geometry

by Brannan, david A.; Esplen, Matthew F.; Gray, Jeremy J.

• ISBN13: 9781107647831
• ISBN10: 1107647835
• Edition: 2nd
• Format: Paperback
• Copyright: 2012-02-29
• Publisher: Cambridge Univ Pr

Summary

This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from www.cambridge.org/9781107647831.

Table of Contents

Preface

Introduction: geometry and geometries

Conics

Affine geometry

Projective geometry: lines

Projective geometry: conics

Inversive geometry

Hyperbolic geometry: the disc model

Elliptic geometry: the spherical model

The Kleinian view of geometry

Special symbols

Further reading

A primer of group theory

A primer of vectors and vector spaces

Solutions to the problems

Index

Table of Contents provided by Publisher. All Rights Reserved.