Assorted links
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The Kepler Conjecture is about the most efficient packing of identical spheres [Wikipedia entry]. In introductory materials courses we learn that a face centered cubic (fcc) packing of identical spheres has a packing efficiency of 74%; but, is this the best we can do? While Kepler conjectured in 1611 that the answer is ‘yes’, the proof was announced in 1999; there was a twist, however: the proof made use of computers to systematically eliminate a bunch of possibilities. Checking this proof took some time, and when it was finally published, it received a lot of attention in mainstream media, two of which are noteworthy:
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American Scientist: The Proof is in the Packing.
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Theory of Grain Growth. In two dimensions, Mullins and von Neumann derived a simple result that showed that grains with less than six neighbours would shrink. A generalization of this result to three dimensions took a while; again, when the proof was published in 2007, it was covered by mainstream media. However, it was framed as a problem in the evolution of beer bubbles!
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Kenneth Chang in NYTimes: In Bubbles and Metal, the Art of Shape-Shifting. In the print edition, the headline was: Tiny Bubbles: In Beer, Metal, It’s All Math!
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Guru has a set of posts on this topic (with links to several other pieces): Grain growth: Beyond von Neumann-Mullins, Grain Growth: Beyond von Neumann-Mullins — Edition 2, and finally, Shapes of Crystallites and Their Evolution.
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