26th Kieval Lecture

Title of Talk:

M. C. Escher's graphic works fascinate us with their imagry-the images not only make obvious use of geometry, but often provide visual metaphors for abstract mathematical concepts. The lecture will examine the mathematical concepts implicit in several of Escher's works, outline the transformation geometry that governs his interlocking figures, and reveal how this "math anxious" artist actually did pioneering mathematical research in order to accomplish his artistic goals.

About the speaker:

Doris Schattschneider received an M.A. and Ph.D. in mathematics from Yale University and is currently 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 coauthor 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, Visions of Symmetry: Notebooks, Periodic Drawings and Related Work of M.C. Escher, W. H. Freeman, 1990, was the result of a two-year research project that was supported by the National Endowment for the Humanities. Her article, "Escher's Metaphors" appeared in the November, 1994 Scientific American. [More about the speaker below,]

Math Colloquium: 4:00 pm GH 221

The Fascination of Tiling.

This lecture will review some of the long history of tiling-a subject that mathematicians have only recently addressed and in so doing, have discovered its riches and tantalizing unanswered questions. The legacy of unknown artisans, manufacturers, and builders in many cultures >from earliest times testify to an accumulated knowledge about the art and utility of tiling.

Mathematicians ask: What shapes tile? In what ways do they tile? In how many ways do they tile? J. Kepler, P.J. MacMahon, and M.C. Escher are some of the early pioneeers who explored these questions. Many mathematicians (notably, B. Grünbaum and G.C. Shephard) have contributed to the current state of knowledge in this active field. But many others are also contributors since tilings provide models for natural phenomena such as crystal structure and cellular structure of plants, they are encountered in coding theory and nearest neighbor problems, and they provide wonderful recreational problems.

More about The speaker: Doris Schattschneider, professor of mathematics at Moravian College, received her Ph.D. in mathematics from Yale University, and has taught mathematics for over 30 years. The opportunity to combine art and mathematics by offering a special course on the geometry of periodic patterns many years ago began her fascination with tiling. Over a long span of years she has written many articles on tiling problems, and also brought the work on tilings by amateurs (and particularly the symmetry work of M.C. Escher) to the attention of the mathematical world. She was the reciepient of the Carl B. Allendoerfer Award in 1979 (for an article on tiling in Mathematics Magazine), editor of Mathematics Magazine 1981-1985, and was one of the first recipients of the MAA award for distinguished teaching of college or university mathematics.