MATC Mathematics Club
Lecture #115
Madison Area Technical College
Madison, Wisconsin
Abstract: Many cultures use repeating patterns and designs within their artwork and crafts. A tremendous amount of such artwork corresponds to classical mathematical formulations of design symmetries, and those mathematical ideas come up widely across cultures. But the exact way in which those ideas are expressed varies tremendously between cultures. Some cultures may use only a few of the available mathematical options, and which options they use are culture-specific, or specific to a particular art form. Other cultures introduce variations to their symmetries that violate mathematical symmetry definitions, and do so in consistent, formal, and culturally specific ways. These examples may be "mathematically rigorous," but are not well modeled by traditional mathematical approaches. In some cases, these variations may just be "tradition," but in other cases they appear to be based on specific artistic goals, cultural phenomena or values, or for known historical reasons. We will look at several examples of such art, identifying both the mathematical symmetries and the artistic variations within those symmetries.
Biography:
Associate Professor of Mathematics and Computer Science. B.A. University of Michigan–Flint, M.A. (mathematics), M.S. (computer science), and Ph.D. (geometry) University of Wisconsin–Madison. Darrah received a National Science Foundation grant to start the departmental Macintosh lab. He developed the lab exercises for CS 111 and has published a series of papers on the geometry of tilings. He is the author of Drawing Pictures with One Line: Exploring Graph Theory (1983). For many years he coached the College's teams in the annual ACM Computer Programming Competition, including two teams that went to the international finals. Special interests include the design and analysis of algorithms, software engineering, operating systems, parallel programming, geometry, and ethnomathematics. Web site: http://cs.beloit.edu/chavey
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