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).

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