Math Expands: Jeff Weeks
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
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 paperandscissors activities,
computer games,
and the awardwinning Shape of Space video
to introduce the same ideas to students in grades 610.
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 GoodmanStrauss's
Symmetry Unit
is especially good.



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.

