Math 5: Pattern
The mathematics and art of repeated designs.
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.
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).
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.
2: Color theory and mixing of paint. Additive versus subtractive
color. Composition of symmetries, Cayley tables, some useful
Week 3: Color interactions, Albers,
LeWitt.introduction to block prints using Safety-cut. The
abstract group and identification of subgroups and their properties.
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.
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.