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Preface | p. vii |
List of Symbols | p. x |
Euclidean geometry | p. 1 |
Symmetries | p. 2 |
Rigid transformations | p. 15 |
Invariants under rigid transformations | p. 28 |
Cylinders and tori | p. 37 |
Finite subgroups of E(2) and E(3) | p. 46 |
Frieze patterns and tessellations | p. 58 |
Affine geometry | p. 75 |
The line at infinity | p. 76 |
Affine transformations and their invariants | p. 83 |
Projective geometry | p. 91 |
The real projective plane | p. 92 |
The Duality Principle | p. 99 |
The shape of P[superscript 2](R) | p. 103 |
Coordinate charts for P[superscript 2](R) (and for P[superscript 1] (C)) | p. 109 |
The projective group | p. 113 |
Invariance of the cross ratio | p. 121 |
The space of conics | p. 126 |
Projective properties of the conics | p. 129 |
Poles and polars | p. 134 |
Elliptic geometry | p. 141 |
Hyperbolic geometry | p. 149 |
Models of the hyperbolic plane | p. 149 |
Transformations of the hyperbolic plane | p. 157 |
Steiner network | p. 164 |
The hyperbolic metric | p. 168 |
First results in hyperbolic geometry | p. 177 |
Surfaces with hyperbolic structure | p. 183 |
Tessellations | p. 192 |
Appendices | p. 199 |
Differentiable functions | p. 199 |
Equivalence relations | p. 201 |
The symmetric group in four symbols: S[subscript 4] | p. 202 |
Euclidean postulates | p. 205 |
Topology | p. 206 |
Some results on the circle | p. 208 |
Bibliography | p. 211 |
Index | p. 215 |
Table of Contents provided by Ingram. All Rights Reserved. |
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The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.