Preface -- Introduction -- Axiomatic Geometry -- Rigidity and Architecture -- Computer Graphics -- Symmetries in Anthropology -- Robotics -- Molecular Shapes -- 1 The Axiomatic Method in Geometry -- 1.1 The Aims of Axiomatic Geometry -- Section 1.1 Exercises -- 1.2 Proofs in Axiomatic Geometry -- Section 1.2 Exercises -- 1.3 Axioms for Euclidean Geometry -- Section 1.3 Exercises -- 2 The Euclidean Heritage -- 2.1 Congruence -- Section 2.1 Exercises -- 2.2 Perpendicularity -- Section 2.2 Exercises -- 2.3 Parallelism -- Section 2.3 Exercises -- 2.4 Area and Similarity -- Section 2.4 Exercises -- 3 Non-Euclidean Geometry -- 3.1 Hyperbolic and Other Non-Euclidean Geometries -- Section 3.1 Exercises -- 3.2 Spherical Geometry: A Three-Dimensional View -- Section 3.2 Exercises -- 3.3 Spherical Geometry: An Axiomatic View -- Section 3.3 Exercises -- 4 Transformation Geometry I: Isometries and Symmetries -- 4.1 Isometries and Their Invariants -- Section 4.1 Exercises -- 4.2 Composing Isometries -- Section 4.2 Exercises -- 4.3 There Are Only Four Kinds of Isometries -- Section 4.3 Exercises -- 4.4 Symmetries of Patterns -- Section 4.4 Exercises -- 4.5 What Combinations of Symmetries Can Strip Patterns Have? -- Section 4.5 Exercises -- 5 Vectors in Geometry -- 5.1 Parametric Equations of Lines -- Section 5.1 Exercises -- 5.2 Scalar Products, Planes, and the Hidden Surface Problem -- Section 5.2 Exercises -- 5.3 Norms, Spheres, and the Global Positioning System -- Section 5.3 Exercises -- 5.4 Curve Fitting with Splines in Two Dimensions -- Section 5.4 Exercises -- 6 Transformation Geometry II: Isometries and Matrices -- 6.1 Equations and Matrices for Familiar Transformations -- Section 6.1 Exercises -- 6.2 Composition and Matrix Multiplication -- Section 6.2 Exercises -- 6.3 Frames and How to Represent Them -- Section 6.3 Exercises.

6.4 Properties of the Frame Matrix -- Section 6.4 Exercises -- 6.5 Forward Kinematics for a Simple Robot Arm -- Section 6.5 Exercises -- 7 Transformation Geometry III: Similarity, Inversion, and Projection -- 7.1 Central Similarity and Other Similarity Transformations in the Plane -- Section 7.1 Exercises -- 7.2 Inversion -- Section 7.2 Exercises -- 7.3 Perspective Projection and Image Formation -- Section 7.3 Exercises -- 7.4 Parallelism and Vanishing Points of a Perspective Projection -- Section 7.4 Exercises -- 7.5 Parallel Projection -- Section 7.5 Exercises -- 8 Graphs, Maps, and Polyhedra -- 8.1 Introduction to Graph Theory -- Section 8.1 Exercises -- 8.2 Euler's Formula and the Euler Number -- Section 8.2 Exercises -- 8.3 Polyhedra, Combinatorial Structure, and Planar Maps -- Section 8.3 Exercises -- 8.4 Special Kinds of Polyhedra: Regular Polyhedra and Fullerenes -- Section 8.4 Exercises -- 8.5 List Coloring and the Five-Color Theorem -- Section 8.5 Exercises -- Bibliography -- Chapters 1 and 2 -- Chapter 3 -- Chapter 4 -- Chapter 5 -- Chapter 6 -- Chapter 7 -- Chapter 8 -- Answers to Odd-Numbered Exercises -- Chapter 1 -- Chapter 2 -- Chapter 3 -- Chapter 4 -- Chapter 5 -- Chapter 6 -- Chapter 7 -- Chapter 8 -- Index.