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.
- Electronic book text
- 05 Jun 2012
- CAMBRIDGE UNIVERSITY PRESS
- Cambridge University Press (Virtual Publishing)
- Cambridge, United Kingdom
- 2nd Revised edition
- 750 b/w illus. 200 exercises
'This is a textbook that demonstrates the excitement and beauty of geometry ... richly illustrated and clearly written.' L'Enseignement Mathematique '... this is a remarkable and nicely written introduction to classical geometry.' Zentralblatt MATH '... could form the basis of courses in geometry for mathematics undergraduates. It will also appeal to the general mathematical reader.' John Stone, The Times Higher Education Supplement 'It conveys the beauty and excitement of the subject, avoiding the dryness of many geometry texts.' J. I. Hall, Mathematical Association of America 'To my mind, this is the best introductory book ever written on introductory university geometry ... readers are introduced to the notions of Euclidean congruence, affine congruence, projective congruence and certain versions of non-Euclidean geometry (hyperbolic, spherical and inversive). Not only are students introduced to a wide range of algebraic methods, but they will encounter a most pleasing combination of process and product.' P. N. Ruane, MAA Focus '... an excellent and precisely written textbook that should be studied in depth by all would-be mathematicians.' Hans Sachs, American Mathematical Society
Table of contents
Preface; Introduction: geometry and geometries; 1. Conics; 2. Affine geometry; 3. Projective geometry: lines; 4. Projective geometry: conics; 5. Inversive geometry; 6. Hyperbolic geometry: the disc model; 7. Elliptic geometry: the spherical model; 8. The Kleinian view of geometry; Special symbols; Further reading; Appendix 1. A primer of group theory; Appendix 2. A primer of vectors and vector spaces; Appendix 3. Solutions to the problems; Index.