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Stanford Report, April 26, 2000

Mathematicians achieve 'optimal' results with double bubble experiments

BY CATHERINE ZANDONELLA

Blowing bubbles isn't just child's play. Mathematicians like to study soap bubbles too. Now Stanford mathematician Michael Hutchings and an international team have proved something bubble-blowers have suspected for years: The optimal shape for enclosing two chambers of air is the "double bubble," where one volume is stacked atop the other. This arrangement yields the smallest bubble surface area that can fit around any two fixed volumes.

Why study soap bubbles? "This problem helps us develop techniques we can use for similar problems having to do with optimization, like building something that is as light as possible or costs the least amount of money," says Hutchings, the Szegö Assistant Professor of Mathematics.

With this proof, Hutchings and his colleagues ruled out far-fetched but plausible bubble configurations, like having one bubble circle the other like an inner tube, or even nuttier ones, like having a third belt clinging to the inner tube. The discovery stems from work done in spring and summer of 1999.