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Decomposing the Four-Dimensional Hypersphere

by

Professor Davide P. Cervone
Union College

February 21, 2005
4:30 pm
Blue House

Tea and pastries will be served


Abstract:

Have you ever wondered what an object in four dimensions might be like? What shapes in four space correspond to the concept of spheres and cubes in three dimension? A sphere in three dimensions can be broken down into two hemispheres that are glued together along their boundaries, so can we do something similar to make a "hypersphere" in four dimensions? It turns out that we can, but there are some even more interesting ways to break apart a four-dimensional hypersphere into two congruent pieces. In this talk, we will explore these ideas more carefully by investigating first the three-dimensional cube and its four-dimensional analog, the "hypercube", and will develop an unusual decomposition of the hypersphere that has connections to a wide range of mathematical areas, from dynamical systems to complex analysis. No previous knowledge of four-dimensional geometry is necessary, just an open mind and a willingness to move beyond your three-dimensional preconceptions. Computer-generated animations will play a crucial role in visualizing these objects, so if nothing else, at least come and enjoy the pictures!


For additional information, send e-mail to math@union.edu or call (518) 388-6246.
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