The hypercube and hypersphere: breaking them down and building them up
September 24, 2013
Bailey Hall 207
Refreshments will be served in Bailey Hall 204 at 4:45
A sphere in three-dimensional space can be broken into two congruent connected pieces in essentially only one way (two hemispheres). In four dimensions, the object that corresponds to the sphere can also be broken into two hemispheres, but can it be formed from two congruent connected pieces in any other way? In this talk, we investigate this question through an analysis of the four-dimensional cube, and use that to develop an interesting decomposition of the four-dimensional sphere that has no analog in three dimensions. Along the way, we learn some techniques for visualizing objects in four dimensions, and view computer images of objects from the fourth dimension. No prior experience with four dimensions is required.
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