Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Introduction and Acknowledgements
CHAPTER 1: Euclidean Geometry
1.0. INTRODUCTION
1.1. THE FIVE AXIOMS OF EUCLIDEAN GEOMETRY
1.2. RULER AND COMPASS CONSTRUCTIONS
1.3. THE GOLDEN RATIO
1.4. FIBONACCI NUMBERS
CHAPTER 2: Plane Transformations
2.1. PLANE SYMMETRIES
2.2. PLANE SYMMETRIES, VECTORS, AND MATRICES (OPTIONAL)
2.3. GROUPS OF SYMMETRIES OF PLANAR OBJECTS
2.4. FRIEZE PATTERNS
2.5. WALLPAPER DESIGNS AND TILINGS OF THE PLANE
2.6. TILINGS AND ART
CHAPTER 3: Similarities, Fractals, and Cellular Automata
3.1. SIMILARITIES AND SOME OTHER PLANAR TRANSFORMATIONS
3.2. COMPLEX NUMBERS AND TRANSFORMATIONS (OPTIONAL)
3.3. FRACTALS: DEFINITION AND SOME EXAMPLES
3.4. JULIA SETS
3.5. CELLULAR AUTOMATA
CHAPTER 4: Hyperbolic Geometry
4.1. NON-EUCLIDEAN GEOMETRIES: BACKGROUND AND SOME
HISTORY
4.2. INVERSION
4.3. HYPERBOLIC GEOMETRY
4.4. SOME BASIC CONSTRUCTIONS IN THE POINCARΓ MODEL
4.5. TILINGS OF THE HYPERBOLIC PLANE
CHAPTER 5: Perspective
5.1. PERSPECTIVE: A BRIEF OVERVIEW OF THE EVOLUTION OF THE RULES OF PERSPECTIVE
5.2. PERSPECTIVE DRAWING AND CONSTRUCTIONS OF SOME
TWO-DIMENSIONAL (PLANAR) OBJECTS
5.3. PERSPECTIVE IMAGES OF THREE-DIMENSIONAL OBJECTS
5.4. MATHEMATICS OF PERSPECTIVE DRAWING: A BRIEF
OVERVIEW (OPTIONAL)
CHAPTER 6: Some Three-Dimensional Objects
6.1. REGULAR AND OTHER POLYHEDRA
6.2. SPHERE, CYLINDER, CONE, AND CONIC SECTIONS
6.3. GEOMETRY, TILINGS, FRACTALS, AND CELLULAR
AUTOMATA IN THREE AND HIGHER DIMENSIONS
CHAPTER 7: Topology
7.1. HOMOTOPY OF SPACES: AN INFORMAL INTRODUCTION
7.2. TWO-MANIFOLDS AND THE EULER CHARACTERISTIC
7.3. NON-ORIENTABLE TWO-MANIFOLDS AND THREE-MANIFOLDS
APPENDIX: CLASSIFICATION THEOREM FOR SIMILARITIES
SOLUTIONS OF ODD-NUMBERED EXERCISES
INDEX