News Release
A Mathematical Milestone:
Double Bubble Conjecture Proved
For further information, contact:
Professor Frank Morgan, Williams College
Telephone: (413) 597-2437
Email: Frank.Morgan@williams.edu
Professor Joel Hass
University of California at Davis
Telephone: (530) 752-1082
Email: hass@math.ucdavis.edu
March 18, 2000
PROVIDENCE, RI---Four mathematicians have proved the Double Bubble Conjecture,
which states that the familiar double soap bubble (shown on the right in the
figure below) is the optimal shape for enclosing and separating two chambers
of air.
In a lecture today at the Rose-Hulman Institute of Technology
in Indiana, Frank Morgan of Williams College will announce that he, Michael
Hutchings of Stanford University, and Manuel Ritori and Antonio Ros of the
University of Granada in Spain have proved this landmark conjecture.
When two round soap bubbles come together, they form a double bubble as on the
right in the figure. 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. This precise shape is now known to
have less area than any other shape that encloses and separates the same two
volumes of air, even wild possibilities like the one on the left in the figure,
in which the second bubble wraps around the first and a tiny separate part of
the first wraps around the second.
In 1995 the special case of two equal-sized bubbles was heralded as a major
breakthrough when proved with the help of a computer by Hass, Hutchings, and
Schlafly. The new proof, involving more possibilities than computers can
handle, uses only pencil, paper, and ideas.
In an amazing postscript, a group of undergraduates has extended the theorem to
4-dimensional bubbles. Ben Reichardt of Stanford, Yuan Lai of MIT, and Cory
Heilmann and Anita Spielman of Williams, working under Morgan's direction,
found a way to extend the proof to 4 dimensional space and to certain cases in
dimensions 5 and above.
Standard and Nonstandard Double Bubbles
Computer graphics copyright © 1999
by John M. Sullivan.
The familiar double soap bubble on the right is now known to be the optimal
shape for a double chamber. Wild competing bubbles with components wrapped
around each other as on the left are shown to be unstable by a novel
argument. Computer graphics by John M. Sullivan, University of Illinois,
www.math.uiuc.edu/~jms/Images/double/
Double Bubble Conjecture World Wide Web sources:
http://www.math.uiuc.edu/~jms/Images/double/:
Pictures of the double soap bubble
http://www.williams.edu/Mathematics/fmorgan/ann.html:
Research announcement of proof
http://www.ugr.es/~ritore/bubble/bubble.htm:
The complete mathematics paper
http://www.maa.org/news/columns.html: Frank Morgan's Math Chat column and TV show
Founded in 1888 to further mathematical research and scholarship, the 30,000-member American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.
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