This book is translated from Spanish, and therefore cheap. Occasionally you hit a word they forgot to translate, but it does not get in the way of reading. Written pretty tersely, so if you are not comfortable with taking classes open to graduates, you will have a hard time reading this book. On the other hand, if you are, you will find this book very concise, and not overburdened with meaningless examples.
Author(s): Ana Irene Ramírez Galarza, José Seade
Edition: 1
Publisher: Birkhäuser Basel
Year: 2007
Language: English
Pages: 225
Introduction to Classical Geometries......Page 0
Contents......Page 5
1 - Euclidean geometry......Page 11
1.1 Symmetries......Page 12
1.2 Rigid transformations......Page 25
1.3 Invariant under rigid transformations......Page 38
1.4 Cylinders and tori......Page 47
1.5 Finite subgroups of E(2) and E(3)......Page 56
1.6 Frieze patterns and tessellations......Page 68
2 - Affine geometry......Page 84
2.1 The line at infinity......Page 85
2.2 Affine transformations and their invariants......Page 92
3 - Projective geometry......Page 99
3.1 The real projective plane......Page 100
3.2 The Duality Principle......Page 107
3.3 The shape of P2(R)......Page 111
3.4 Coordinate charts for P2(R) (and for P1(C))......Page 117
3.5 The projective group......Page 121
3.6 Invariance of the cross ratio......Page 129
3.7 The space of conics......Page 134
3.8 Projective properties of the conics......Page 137
3.9 Poles and polars......Page 142
3.10 Elliptic geometry......Page 149
4 - Hyperbolic Geometry......Page 156
5.1 Differentiable functions......Page 206
5.2 Equivalence relations......Page 208
5.3 The symmetric group i four symbolic: S4......Page 209
5.4 Euclidean postulates......Page 212
5.5 Topology......Page 213
5.6 Some results on the circle......Page 215
Bibliography......Page 218
Index......Page 221
