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Tuesday, 21 March, 2000, 12:24 GMT
Double bubble is no trouble

Bubble John M Sullivan
Nature will allow bubbles like this...
By BBC News Online science editor Dr David Whitehouse

Four mathematicians have announced a proof of the so-called Double Bubble Conjecture - that the familiar double soap bubble is the optimal shape for enclosing and separating two chambers of air.

In an address to the Undergraduate Mathematics Conference at the Rose-Hulman Institute of Technology in Indiana, Frank Morgan of Williams College, Massachusetts, announced that he, Michael Hutchings of Stanford, and Manuel Ritori and Antonio Ros of Granada, had finally proved what the double soap bubble had known all along.

When two round soap bubbles come together, they form a double bubble. Unless the two bubbles are the same size, the surface between them bows a bit into the larger bubble. The separating surface meets each of the two bubbles at 120 degrees.

Mathematicians have expressed surprise that when two bubbles are joined in this way that the interior surface that separates them is not bowed all that much.

Minimal energy

Explaining why this is so has been a puzzle for a long time. Scientists speculate that the bubble surface conforms to a "minimal energy" state that is stable - but proving it is another thing.

Bubble John M Sullivan
...but not like this
This shape is now known to have less area than any other way to enclose and separate the same two volumes of air. Other shapes have now been shown to be unstable by a new argument that involves rotating different portions of the bubble around a carefully chosen axis at different rates.

The breakthrough came while Morgan was visiting Ritori and Ros at the University of Granada last spring.

In 1995, the explanation of the special case of two equal bubbles was heralded as a major breakthrough when it was proved with the help of a computer. The new general case involves more possibilities than computers can now handle.

The new proof uses only ideas, pencil, and paper. What is more, a group of students has extended the theorem to 4-dimensional bubbles and in some cases five.

Graphics by John Sullivan

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