Introduction
Euclidean Geometry
The Five Axioms of Euclidean Geometry
Ruler and Compass Constructions
The Golden Ratio
Fibonacci Numbers
Plane Transformations
Plane Symmetries
Plane Symmetries, Vectors, and Matrices
Groups of Symmetries of Planar Objects
Frieze Patterns
Wallpaper Designs and Tiling of the Plane
Tilings and Art
Similarities, Fractals, and Cellular Automata
Similarities and Some Other Planar Transformations
Complex Numbers
Fractals: Definition and Some Examples
Julia Sets
Cellular Automata
Hyperbolic Geometry
Non-Euclidean Geometries: Background and Some History
Inversion
Hyperbolic Geometry
Some Basic Constructions in the Poincaré Model
Tilings of the Hyperbolic Plane
Perspective and Some Three-Dimensional Objects
Perspective
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
Topology
Homotopy of Spaces: An Informal Introduction
Two-Manifolds and the Euler Characteristic
Nonorientable Two-Manifolds and Three-Manifolds
Index
"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
 |
Ask a Question About this Product More... |
|
