Introduction to Geometry

This classic work is now available in an unabridged paperback edition. The Second Edition retains all the characterisitcs that made the first edition so popular: brilliant exposition, the flexibility permitted by relatively self-contained chapters, and broad coverage ranging from topics in the Euclidean plane, to affine geometry, projective geometry, differential geometry, and topology. The Second Edition incorporates improvements in the text and in some proofs, takes note of the solution of the 4-color map problem, and provides answers to most of the exercises.

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

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.