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Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"Rounding Out Solutions to Three Conjectures", by Barry Cipra, Dana Mackenzie,and Charles Seife. Science, 17 March 2000, pages 1910-1912.

This article consists of three pieces by different authors reporting on thesolution of three mathematical problems. The first piece is about the"double-bubble conjecture", which confirmed that the familiar double-bubbleshape one finds when blowing soap bubbles is the most efficient possible way toenclose two volumes. The second describes a result in celestial mechanics,which shows that a configuration of three stars could settle into stable orbitsin which they all travel in a figure-eight pattern. The third piece discussesthe question of how efficiently one can pack spheres into a box if the spheresare not arranged, but simply dumped into the box so that they assume a randomconfiguration. Researchers found that, as the spheres are packed more densely,and hence more efficiently, more and more order is introduced into theconfiguration.

--- Allyn Jackson

American Mathematical Society