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Double Soap Bubbles: Proof Positive of Optimal Geometry

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Side-by-side images of double-bubbles of equal and unequal volume chambers.

Double bubbles: If the two bubbles that meet have equal volumes of air, the shared membrane between them is a flat disc. But in the case of unequal volumes, the smaller bubble, given its larger internal pressure, will bow slightly into the larger bubble. In either scenario, the two bubbles always meet at angles of 120 degrees.

Credit: John M. Sullivan, Technical University of Berlin and University of Illinois at Urbana-Champaign


Bubble cluster in front of a Gothic window

Soap bubbles provide a multi-dimensional window for scientists and mathematicians working to solve the world's optimization questions.

Credit: John M. Sullivan, Technical University of Berlin and University of Illinois at Urbana-Champaign


Frank Morgan holding stained glass reproduction

Frank Morgan of Williams College (shown) and three other mathematicians -- Michael Hutchings of University of California at Berkeley, and Manuel Ritoré and Antonio Ros of Universidad de Granada in Spain -- proved the Double Bubble Conjecture in 1999. The stained glass window, commissioned by Clay Mathematics Institute students whose paper Morgan advised, illustrates an aspect of the students' research regarding optimal double bubbles.

Credit: Frank Morgan, Williams College


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