4. Symmetries in Time and Space


Creating symmetry: spatial transformations. Matrix operations. Introduction to objects and classes.

Reading
Selection from Washburn & Crowe, Symmetries of Culture (on reserve, Flaxman Library).

Assignment
Contrapuntal or symmetry-based image or performance. Midterm project proposal.

Nature/Culture
The 17 Wallpaper Groups (planar symmetry groups) from Wikipedia.
The 7 Frieze Patterns from the excellent Math and the Art of M.C. Escher site.
Archimedean Tilings from Wikipedia
From the Geometry Center, Kali (17 planar symmetry groups) with source code.
New York Times music critic Anthony Tommasini on counterpoint (video).
Traversing the Mirror from Jean Cocteau's film Orphée (1950) (video).

Mathematics: Matrix Multiplication
See Matrix Multiplication at mathwarehouse.com for simple details and exercises.
Mathforum has good explanations and a handy interactive 2D Transformation Applet.
The Wikipedia entry for Matrix Multiplication has some non-technical explanations, too.

The Algorithm Thought Police by Marius Watz