Ilka Agricola: Humboldt-Universität zu Berlin, Berlin, Germany,
Thomas Friedrich: Humboldt-Universität zu Berlin, Berlin, Germany
+ Read more• Preface to the English Edition 6
• Preface to the German Edition 8
• Chapter 1. Introduction: Euclidean space 14
o Exercises 19
• Chapter 2. Elementary geometrical figures and their properties 22
o §2.1. The line 22
o §2.2. The triangle 32
o §2.3. The circle 58
o §2.4. The conic sections 76
o §2.5. Surfaces and bodies 90
o Exercises 102
• Chapter 3. Symmetries of the plane and of space 112
o §3.1. Affine mappings and centroids 112
o §3.2. Projections and their properties 118
o §3.3. Central dilations and translations 121
o §3.4. Plane isometries and similarity transforms 127
o §3.5. Complex description of plane transformations 140
o §3.6. Elementary transformations of the space E[sup(3)] 144
o §3.7. Discrete subgroups of the plane transformation group 152
o §3.8. Finite subgroups of the spatial transformation group
o Exercises 169
• Chapter 4. Hyperbolic geometry 180
o §4.1. The axiomatic development of elementary geometry 180
o §4.2. The Poincaré model 187
o §4.3. The disc model 196
o §4.4. Selected properties of the hyperbolic plane 198
o §4.5. Three types of hyperbolic isometries 202
o §4.6. Fuchsian groups 207
o Exercises 217
• Chapter 5. Spherical geometry 222
o §5.1. The space S[sup(2)] 222
o §5.2. Great circles in S[sup(2)] 224
o §5.3. The isometry group of [sup(2)] 228
o §5.4. The Möbius group of S[sup(2)] 229
o §5.5. Selected topics in spherical geometry 231
o Exercises 239
• Bibliography 242
• List of Symbols 248
• Index
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