دانلود کتاب Math and Art: An Introduction to Visual Mathematics

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Cover Page Half-Title Page Title Page Copyright Page Dedication Page 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 POINCARÉ 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