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Bubble clusters in front of a Gothic window
This computer illustration created by John M. Sullivan, shows bubble clusters in front of a Gothic window. Soap bubbles provide a multidimensional window for scientists and mathematicians working to solve the world's optimization questions.
More about this Image
This illustration was created as part of an optimal geometry research grant awarded by the National Science Foundation's Division of Mathematical Sciences to Frank Morgan, a leading researcher in optimal geometry from Williams College. Optimal geometry is concerned with geometric figures and their properties, and specifically: What shape or configuration of shapes best meets a situation's given constraints.
[Research supported by National Science Foundation grants DMS 0203434 and DMS 9876471.]
To learn more about optimal geometry involving soap bubbles, see the NSF Discovery story "Double Soap Bubbles: Proof Positive of Optimal Geometry." (Year of image: 1995)
Credit: ©John M. Sullivan, University of Illinois and Technical University of Berlin.
Special Restrictions: This image is copyright. The owner of this image, Prof. John M. Sullivan, has granted permission to use the image free of charge, for nonprofit use only. Any other use of this image is strictly prohibited without explicit permission from Prof. Sullivan, who can be reached via e-mail at Sullivan@math.tu-berlin.de; or by telephone at the Institut fur Mathematick in Berlin, Germany, at +49-30-314-29260.
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Images credited to the National Science Foundation, a federal agency, are in the public domain. The images were created by employees of the United States Government as part of their official duties or prepared by contractors as "works for hire" for NSF. You may freely use NSF-credited images and, at your discretion, credit NSF with a "Courtesy: National Science Foundation" notation.
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