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MATHEMATICS and art

Mathematics through Art....or is it Art through Mathematics? If you are not sure (but care), then this week's resource is for you.

Sasho Kalajdzievski's Math and Art: An Introduction to Visual Mathematics is a great resource to explore...and learn from. While exploring the potential of mathematics to generate interesting objects, the author uncovers the "beauty of mathematics."

The book is based on the course "Art and Math," offered at the University of Manitoba. Basically, a mathematician would present some mathematics, then an artist or architect tried to provide some "art" to "interprets" the mathematics.

The book presents ideas from a mathematical perspective, then integrates the discussion with relevant art. The topics included are:

  • Euclidean Geometry: Basic Axioms, Constructions, Golden Ratio, Fibonacci Numbers
  • Plane Transformations: Symmetries, Frieze Patterns, Tilings
  • Similarities and Fractals: Planer Transformations, Complex Numbers, Fractals, Julia Sets, Cellular Automata
  • Hyperbolic Geometry: Inversions, Poincare Constructions, Tilings
  • Perspective: 2D & 3D, Polyhedra, Conics, Tilings
  • Topology: 2-Manifolds & 3-Manifolds, Euler Characteristic
The content is organized sequentially according to mathematical maturity, but gets complex...especially since the mathematics overviews, by necessity, are brief. Though some mathematical sections are "optional," they are necessary if you are to understand what is going on...other than just browse through the pretty pictures!

For example, Look at the art on the cover of the book, a work by artist Jos Leys called Indra 461. Does it become more meaningful when told it illustrates an infinite iteration of circular inversions? To fully understand the art, you need to understand the mathematics of circular inversions...and the interation aspect will follow.

The text also includes a CD-ROM that provides color versions of the mathematical art, as well as six animations.