Math and Art: An Introduction to Visual Mathematics

by Kalajdzievski; Sasho

• ISBN13: 9781584889137
• ISBN10: 1584889136
• Edition: 1st
• Format: Nonspecific Binding
• Copyright: 2008-06-25
• Publisher: Chapman & Hall/

Summary

Reveals the Beauty of Math in ArtMath and Art: An Introduction to Visual Mathematicsexplores the potential of mathematics to generate visually appealing objects and reveals some of the beauty of mathematics. With a CD-ROM and a 16-page full-color insert, it includes numerous illustrations, computer-generated graphics, photographs, and art reproductions to demonstrate how mathematics can inspire art.Basic Math Topics and Their Visual AspectsFocusing 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 yetintriguing visual objects. For science students, it presents various elegant mathematical theories and notions.Comprehensive Material for a Math in Art CourseProviding all of the material for a complete one-semester course on mathematics in art, this self-contained text shows how artistic practice with mathematics and a comprehension of mathematical concepts are needed to logically and creatively appreciate the field of mathematics.

Table of Contents

Introduction	p. ix
Euclidean Geometry	p. 1
The Five Axioms of Euclidean Geometry	p. 4
Ruler and Compass Constructions	p. 6
The Golden Ratio	p. 14
Fibonacci Numbers	p. 24
Plane Transformations	p. 33
Plane Symmetries	p. 33
Plane Symmetries, Vectors, and Matrices (Optional)	p. 42
Groups of Symmetries of Planar Objects	p. 55
Frieze Patterns	p. 61
Wallpaper Designs and Tilings of the Plane	p. 72
Tilings and Art	p. 81
Similarities, Fractals, and Cellular Automata	p. 91
Similarities and Some Other Planar Transformations	p. 91
Complex Numbers (Optional)	p. 100
Fractals: Definition and Some Examples	p. 110
Julia Sets	p. 123
Cellular Automata	p. 131
Hyperbolic Geometry	p. 143
Non-Euclidean Geometries: Background and Some History	p. 143
Inversion	p. 146
Hyperbolic Geometry	p. 153
Some Basic Constructions in the Poincare Model	p. 158
Tilings of the Hyperbolic Plane	p. 163
Perspective and Some Three-Dimensional Objects	p. 169
Perspective	p. 169
Mathematics of Prespective Drawing: A Brief Overview (Optional)	p. 184
Regular and Other Polyhedra	p. 197
Sphere, Cylinder, Cone, and Conic Sections	p. 206
Geometry, Tilings, Fractals, and Cellular Automata in Three Dimensions	p. 216
Topology	p. 223
Homotopy of Spaces: An Informal Introduction	p. 223
Two-Manifolds and the Euler Characteristic	p. 230
Non-Orientable Two-Manifolds and Three-Manifolds	p. 237
Index	p. 249
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