Math and Art: An Introduction to Visual Mathematics

✍ Scribed by Sasho Kalajdzievski

• Publisher: Chapman and Hall/CRC
• Year: 2021
• Tongue: English
• Leaves: 399
• Edition: 2
• Category: Library

✦ Synopsis

Math and Art: An Introduction to Visual Mathematics explores the potential of mathematics to generate visually appealing objects and reveals some of the beauty of mathematics. It includes numerous illustrations, computer-generated graphics, photographs, and art reproductions to demonstrate how mathematics can inspire or generate art.

Focusing on accessible, visually interesting, and mathematically relevant topics, the text unifies mathematics subjects through their visual and conceptual beauty. Sequentially organized according to mathematical maturity level, each chapter covers a cross section of mathematics, from fundamental Euclidean geometry, tilings, and fractals to hyperbolic geometry, platonic solids, and topology. For art students, the book stresses an understanding of the mathematical background of relatively complicated yet intriguing visual objects. For science students, it presents various elegant mathematical theories and notions.

Features

• Provides an accessible introduction to mathematics in art

• Supports the narrative with a self-contained mathematical theory, with complete proofs of the main results (including the classification theorem for similarities)

• Presents hundreds of figures, illustrations, computer-generated graphics, designs, photographs, and art reproductions, mainly presented in full color

• Includes 21 projects and approximately 280 exercises, about half of which are fully solved

• Covers Euclidean geometry, golden section, Fibonacci numbers, symmetries, tilings, similarities, fractals, cellular automata, inversion, hyperbolic geometry, perspective drawing, Platonic and Archimedean solids, and topology

New to the Second Edition

• New exercises, projects and artworks

• Revised, reorganized and expanded chapters

• More use of color throughout

✦ Table of Contents

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 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