Mathematics: Bubble Problem's Practical Potential

From Washington Post
October 5, 1992
The problem sounds simple: If you bend a piece of wire into an irregular loop and dip it into soapy water, what will be the shape of the bubble formed by the loop?

It's a question that has teased mathematicians for 150 years. Figuring the shape of a bubble within a flat ring is easy - but try finding the area of a bubble in a slightly twisted metal loop.

Now researchers say they have found a solution that also will solve many practical problems of science and industry.

The bubble problem, first proposed by Belgium physicist Joseph Antoine Ferdinand Plateau, stumped many of the great minds of math. That's because mathematical equations describe a world where a line or a surface has no weight or thickness. But in the real world of bubbles, even the thinnest soap film has dimensions.

To come up with a solution, researchers at the University of California campuses at San Diego and Los Angeles created an imaginary soap bubble with an assigned thickness. They reduced the thickness until it approached zero and this, they say, is extremely close to the answer to Plateau's mathematical problem. Their methods are described in the current Proceedings of the National Academy of Sciences.

UCSD computer science professor T.C. Hu hopes the work will lead to a new branch of mathematics - dimensional geometry. "By putting size and weight into it, you get more realistic answer," said Hu, who wrote the article with UCLA professor Andrew Kahng and professor Gabriel Robins of the University of Virginia.

The method could be used to construct smaller, faster computer chips and to map paths to fit odd-shaped spaces using the least amount of material possible, said UCLA math professor Russel Caflisch.

"Not too many people really want to find the shape of a soap film, but it could be used to make parts for cars, for example," Caflisch said.

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