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The University of Tennessee, Knoxville

Making Circles Behave

Ken Stephenson, ProfessorCollege of Arts and Sciences - Department of Mathematics

Imagine taking part in a protest march in which you are told ahead of time the names of the participants you must stand next to (and who, in turn, are required to stand next to you). Challenging? But it is proven that circles can accomplish exactly such a feat. Some circles have to get larger, others smaller, but as they jostle – be it a dozen or a hundred thousand circles – they succeed with wonderfully intricate and often stunning visual patterns. Just as the protesters get comfortably into place, however, comes the order to march while maintaining those designated neighbors. Impossible, you say? Au contraire. The circles manage this – no sweat. Like all good protesters, the circles come in a variety of colors with occasionally conflicting motivations. “Visualization…visualization!!” “Lattice formation, or die!” “Conformal, conformal, conformal maps!” (Aha, that would be the mathematicians.) “Energy minimization, save the planet!” Regardless, the march will certainly be a wonderful scene to contemplate. Stephenson’s presentation will be a brief visual tour of circle packings, both static and moving, and audience members may sit next to whomever they choose!​

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