Cover 1
Title 2
Copyright 3
Contents 4
Preface to the English Edition 6
Preface to the German Edition 8
Chapter 1. Introduction: Euclidean space 14
Exercises 19
Chapter 2. Elementary geometrical figures and their properties 22
§2.1. The line 22
§2.2. The triangle 32
§2.3. The circle 58
§2.4. The conic sections 76
§2.5. Surfaces and bodies 90
Exercises 102
Chapter 3. Symmetries of the plane and of space 112
§3.1. Affine mappings and centroids 112
§3.2. Projections and their properties 118
§3.3. Central dilations and translations 121
§3.4. Plane isometries and similarity transforms 127
§3.5. Complex description of plane transformations 140
§3.6. Elementary transformations of the space E[sup(3)] 144
§3.7. Discrete subgroups of the plane transformation group 152
§3.8. Finite subgroups of the spatial transformation group 164
Exercises 169
Chapter 4. Hyperbolic geometry 180
§4.1. The axiomatic development of elementary geometry 180
§4.2. The Poincaré model 187
§4.3. The disc model 196
§4.4. Selected properties of the hyperbolic plane 198
§4.5. Three types of hyperbolic isometries 202
§4.6. Fuchsian groups 207
Exercises 217
Chapter 5. Spherical geometry 222
§5.1. The space S[sup(2)] 222
§5.2. Great circles in S[sup(2)] 224
§5.3. The isometry group of [sup(2)] 228
§5.4. The Möbius group of S[sup(2)] 229
§5.5. Selected topics in spherical geometry 231
Exercises 239
Bibliography 242
List of Symbols 248
Index 250
A 250
B 250
C 250
D 251
E 251
F 252
G 252
H 252
I 253
J 253
K 253
L 253
M 253
N 253
O 253
P 254
Q 254
R 254
S 255
T 255
V 256
W 256
Back Cover 257
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