Kepler's Sphere Packing Problem Solved
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Keith Devlin (Devlin's Angle)  
Mathematician Thomas Hales of the University of Michigan announced in 1998 that — after six years effort — he had proved that a guess Kepler made back in 1611 was correct. The problem asks what is the most efficient way to pack equalsized spheres together in a large crate: in identical layers, one on top of the other, with each sphere in one layer sitting right on top of the sphere directly beneath it, or staggering the layers so that the oranges in each higher layer sit in the hollows made by the four oranges beneath them? (The formal term for this orangepile arrangement is a facecentered cubic lattice.) More generally, what is the most efficient packing of all?  


Levels:  High School (912), College, Research 
Languages:  English 
Resource Types:  Articles 
Math Topics:  Convex/Discrete Geometry, History and Biography 
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