NEWS RELEASE

4/24/00

Dawn Levy, News Service (650) 725-1944; e-mail: dawnlevy@stanford.edu

Editors: This release was written by Stanford science writing intern Catherine Zandonella. A photo of the double bubble is available. Photo credit: John Sullivan, University of Illinois.

### Double bubble no trouble for Stanford professor, undergraduate

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.

Over the past 10 years, substantial parts of the problem have been solved by Stanford's Jeff Brock, also a Szegö Assistant Professor of Mathematics, and by mathematics Professor Brian White. Together with Hutchings' previous work, the mathematicians narrowed the choices for the optimal shape down to just two, the double bubble and the belted bubble.

The new proof, done with pencil and paper rather than with a computer, is based on the idea of using an "axis of instability" for the belted bubble. If one twists the shape around this axis in a motion similar to wringing out a washcloth, the bubble surface area scrunches up and becomes smaller, while the volume stays the same. This decreased surface area debunks the assumption that the belted bubble configuration is the optimal one. Since all other possible configurations were ruled out by other proofs, says Hutchings, "if there is a best shape, it has to be the double bubble."

Last summer students from an undergraduate research program at Williams College in Massachusetts extended the results. Stanford undergraduate Ben Reichardt was one of a team of four students to prove the double bubble is the optimal shape for two bubbles in 4-dimensional and in some cases 5-dimensional universes.

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By Catherine Zandonella