Mathematical Digest

"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