Math 5: Pattern
The mathematics and art of repeated designs.

Time: 10A
Professor Dorothy Wallace, 204 Kemeny Hall, office hours TBA
Text: Shibori for Geometers, Morris&Wallace, available in the Math Department office.  \$30
Prerequisites: None except a willingness to work.

This course focuses on the interplay between the art of regularly repeated patterns and the abstract mathematics that results from close study of these patterns.  Student work displayed on this page shows some of the artistic results of previous classes, but not the mathematical side (which will only make sense if you take the course).

Grades will be based on 6 assignments incorporating both mathematics and art.  There are no exams but there may be some written pieces that accompany your math/art.  These will have equal weight and shall be graded through a combination of peer and instructor review.  One assignment may be re-done at the end of the course.  Students will submit a portfolio of all their work (math and art both) on the last day of class.

Honor principle: All assignments done with your own hands.  Consulting on math questions is ok, consulting on art is ok.  But you must create your own work.

Syllabus (subject to change):

Week 1: The mandala.  Finding, counting & naming symmetries. Positive/negative space.

Week 2: Color theory and mixing of paint.  Additive versus subtractive color.  Composition of symmetries, Cayley tables, some useful definitions.

Week 3:  Color interactions, Albers, LeWitt.introduction to block prints using Safety-cut.  The abstract group and identification of subgroups and their properties.

Week 4: Frieze patterns.  Classification according to mathematical concepts.  Various relations to finite patterns.  Subgroups of these patterns.

Week 5: Islamic tiles and other 2-way repeated patterns.  Motif versus pattern.  The "wallpaper groups".  Finding and labeling their symmetries and classification.  Illusions of symmetry.  Keeping repetition interesting. Kali software.

Week 6: Subgroup relationships among wallpaper patterns and artistic consequences of these.  Establishing and breaking patterns. Pattern as function.  Orbifolds.

Week 7: Shibori.  An art form and a math problem.

Week 8:  Escher, the circle limit and the illusion of motion.  Symmetries of dilation and of color.  Fractals.

Week 9: Patterns on surfaces.  Hyperbolic space, the illusion of curvature and depth. Vasarely. Op art.  Penrose.

Week 10: Other approaches.  Hundertwasser and cellular automata. Klimt. Open exhibit of best work on last day.