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. 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 Aspects
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.
Comprehensive Material for a Math in Art Course
Providing 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
The Five Axioms of Euclidean Geometry
Ruler and Compass Constructions
The Golden Ratio
Plane Symmetries, Vectors, and Matrices
Groups of Symmetries of Planar Objects
Wallpaper Designs and Tiling of the Plane
Tilings and Art
Similarities, Fractals, and Cellular Automata
Similarities and Some Other Planar Transformations
Fractals: Definition and Some Examples
Non-Euclidean Geometries: Background and Some History
Some Basic Constructions in the Poincaré Model
Tilings of the Hyperbolic Plane
Perspective and Some Three-Dimensional Objects
The Mathematics of Perspective Drawing: A Brief Overview
Regular and Other Polyhedra
Sphere, Cylinder, Cone, and Conic Sections
Geometry, Tilings, Fractals, and Cellular Automata in Three Dimensions
Homotopy of Spaces: An Informal Introduction
Two-Manifolds and the Euler Characteristic
Nonorientable Two-Manifolds and Three-Manifolds
"This delightful book grew out of set of teaching notes for an interdisciplinary course called Math in Art that was co-taught by a mathematician and an artist or architect. … The mathematical ideas are presented visually in a way that seems quite natural, and it engages the reader through explorations with lots of hands-on exercises. The mathematical presentation is solid, and the choice of topics puts the focus on the visual presentation of mathematical concepts. The illustrations are beautiful! … This text is very readable. The mathematics is accessible to those with little mathematical background, and yet the presentation is still engaging for those with more background."
—MAA Reviews, March 2009
"All in all, this work offers an excellent account of art inspired by mathematics and art generated by mathematics, and it should interest readers in both fields. Summing Up: Highly Recommended."
– R.M. Davis, emeritus, Albion College, in Choice: Current Review for Academic Libraries, February 2009, Vol. 46, No. 6