Table of Contents

Part I

Triangles 3

Regular Polygons 26

Isometry in the Euclidean Plane 39

Two-Dimensional Crystallography 50

Similarity in the Euclidean Plane 67

Circles and Spheres 77

Isometry and Similarity in Euclidean Space   96

Part II

Coordinates 107

Complex Numbers 135

The Five Platonic Solids 148

The Golden Section and Phyllotaxis 160

Part III
Ordered Geometry 175

Affine Geometry 191

Projective Geometry 229

Absolute Geometry 263

Hyperbolic Geometry  287

Part IV

Differential Geometry of Curves  307

The Tensor Notation  328

Differential Geometry of Surfaces  342

Geodesics  366

Topology of Surfaces  379

Four-Dimensional Geometry  396

Tables  413

References  415

Answers to Exercises  419

Index 459 

About the Author

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, CC was a British-born Canadian geometer. Coxeter is regarded as one of the greatest geometers of the 20th century. He was born in London, received his BA and PhD from Cambridge, but lived in Canada from age 29.