Escher's Combinatorial Patterns

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It is a little-known fact that M.C. Escher posed and answered some combinatorial questions about patterns produced in an algorithmic way. We report on his explorations, indicate how close he came to the correct solutions, and pose an analogous problem in three dimensions.

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Biographical Information: Doris Schattschneider received an M.A. and Ph.D. in mathematics from Yale University and is Professor of Mathematics at Moravian College in Bethlehem, Pennsylvania. Her dual interest in geometry and art led naturally to the study of tiling problems and the work of the Dutch artist M. C. Escher. She has authored many scholarly articles on plane tiling and has acted as "Boswell" to reveal to the professional world the mathematical investigations of homemaker Marjorie Rice and M. C. Escher. She is co-author of a book and collection of geometry models: "M. C. Escher Kaleidocycles", Pomegranate Artbooks, 1987, that has been translated into 16 European languages. Her book on Escher, "Visions of Symmetry: Notebooks, Periodic Drawings and Related Work of M.C. Escher," W. H. Freeman, 1990, was supported by the National Endowment for the Humanities. Her articles about Escher's work include "Escher's Metaphors," in Scientific American, (November 1994) "Escher's Combinatorial Patterns," in The Electronic Journal of Combinatorics, v.4, no.2 (1997), #R17, and "Automating Escher's Combinatorial Patterns," (with Rick Mabry and Stan Wagon), in Mathematica in Education and Research, v. 5, no. 4 (1997).

This talk is given as part of the 1997 Big Sky Conference on Geometry, Discrete Mathematics, and Algorithms.

Friday, September 12, 1997
4:10 p.m. in MA 109
Coffee/Tea/Treats 3:30 p.m. in MA 104 (Lounge)

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