The sphere packing problem can be summarized in just a few words: how can we fill a large space with as many spheres as possible? Nearly 400 years ago, Kepler conjectured what grocers have known all along; the best way is the familiar "orange pile" or "cannon-ball" arrangement. Although this seems intuitively obvious, it wasn't proved until just recently -- if, in fact, the proof is correct. It's scheduled to be published this year, along with a very unusual editorial note about its correctness.
We'll discuss sphere packing and some related problems, such as the kissing problem and the n-dimensional sphere packing problem. Although there is some very complex mathematics lurking in the background, the talk will concentrate on the general ideas and concepts and should be accessible to most calculus students.
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