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Geometry

David A. Brannan, Matthew F. Esplen, and Jeremy J. Grey
Publisher: 
Cambridge University Press
Publication Date: 
2012
Number of Pages: 
587
Format: 
Paperback
Edition: 
2
Price: 
55.00
ISBN: 
9781107647831
Category: 
Textbook
[Reviewed by
Fernando Q. Gouvêa
, on
05/28/2012
]

See J. I. Hall's review of the first edition (1999). In addition to many small changes and improvements, the authors have added some new material on conics as envelopes, barycentric coordinates,  Poncelet's Porism, planar maps, and Ptolemy's Theorem. They have also changed their approach to projective transformations, hyperbolic distance, and asymptotic d-triangles. Probably under pressure from American users, they have switched from "gradient" to "slope" and from ]0,1[ to (0,1) for open intervals.

This remains one of the best textbooks on elementary geometry.

 

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.

Dummy View - NOT TO BE DELETED