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.

-30-

By Catherine Zandonella