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