Math Club Presentation with Professor Biddle

Professor Biddle will be giving a lecture this week about the geometry of hypercubes and hyperspheres. Abstract below:

The n-cube and n-sphere are higher dimensional analogues of the square and circle respectively. In this talk we explore the geometry of these objects by finding their diameters and hypervolumes. We'll see the strange result that the hypervolume of an n-sphere has a maximum when n is about 7 and then decreases to zero as n goes to infinity. If time permits, we'll explore some other interesting properties of higher dimensional and infinite dimensional spheres, including an introduction to the homotopy groups of spheres.

Only a background in calculus is necessary for this talk.

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