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MacArthur Fellow Jeff Weeks explores universes of two, three, and four dimensions, leading both students and researchers to experience the different shapes that could describe the universe in which we live. A master of exposition in topology and geometry, he is a versatile and productive designer of computer software for investigating knots, spaces, tessellations, and geometry across all dimensions. The MacArthur Foundation page describes his career.
His book The Shape of Space shows college and advanced high school students how our universe may be finite, yet have no boundary, and explores some of its possible shapes. His latest work Exploring the Shape of Space combines paper-and-scissors activities, computer games, and the award-winning Shape of Space video to introduce the same ideas to students in grades 6-10. The computer games are freely available online.
Dr. Weeks is currently collaborating with cosmologists hoping to use upcoming satellite data to determine whether the real universe is finite or infinite, and if it is finite, to determine its exact shape. An elementary account of this work appears in the article Is space finite? in the April 1999 issue of Scientific American. Math majors and graduate students will find a more complete exposition of the underlying mathematics in Measuring the shape of the universe in the December 1998 issue of the Notices of the American Mathematical Society.
His program Kali (based on unix Kali by Nina Amenta) brings tilings and symmetry to any child old enough to hold a mouse, while KaleidoTile (based on unix software developed at the Geometry Center) is intended for high school students. Both are freely available.
For additional geometry materials, the best source is the Math Forum. For teachers interested in symmetry, Chaim Goodman-Strauss's Symmetry Unit is especially good. Conway, Doyle, Gilman, and Thurston's Geometry and the Imagination notes provide an elementary and intuitive introduction to a variety of topics in topology and geometry, including symmetry and orbifolds.
On a research level, Dr. Weeks' program SnapPea lets the user create and study various possible shapes for space. It is used by pure mathematicians as well as by cosmologists applying the mathematics to model the real universe.