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        Departments of Mathematical Sciences and Mathematics
                    The Johns Hopkins University
                                                                       
                           JOINT SEMINAR

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Professor Thomas C. Hales                         March 30, 2000
Department of Mathematics                         304 Whitehead Hall
University of Michigan                            NO PRESEMINAR
                                                  Refreshments: 3:30 p.m.
                                                  Seminar: 4:00 p.m.

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                 THE PROOF OF THE KEPLER CONJECTURE
                                                                        
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                             ABSTRACT

Over 400 years ago, Sir Walter Raleigh asked his mathematical assistant to
find formulas for the number of cannonballs in regularly stacked piles.
These investigations aroused the curiosity of the great astronomer,
Johannes Kepler, and led to a problem that has gone centuries without a
solution: Why is the familiar cannonball stack the most efficient
arrangement possible?  This talk will describe the history of this and
some related problems in geometry.  (The first special case of the Kepler
conjecture was established by Gauss in 1831.)  Various bounds on the
density of a sphere packing have been obtained in the 20th century.  This
talk will describe a recent computer-assisted proof of the Kepler
conjecture. 

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