Math Expands: Jeff Weeks
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
Foundation page describes his career.
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,
games, and the award-winning Shape of Space video to
introduce the same ideas to students in grades 6-10. The
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
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.
Kali (based on
unix Kali by Nina Amenta) brings tilings and symmetry to any child old
enough to hold a mouse, while
(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
For teachers interested in symmetry, Chaim Goodman-Strauss's
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
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.