Perl: the Markov chain saw  
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RE: (tye)Re2: Packaging Algorithmby extremely (Priest) 
on Nov 08, 2000 at 07:18 UTC ( #40464=note: print w/ replies, xml )  Need Help?? 
Don't let someone's proof that some problem is impossible to solve prevent you from solving the problem well enough to get your work done! Well, again, "the sphere packing problem" is different than that. In fact, there have been some neat breakthru's in the field. We have 9600 baud and up modems thanks to a trelliscode based on packing spheres efficiently in 8 dimensions. Turns out a single sphere can be touched by 1024 spheres in a tightlypacked regular array. =) That result is basically cool in anyone's book. The original problem was that given a bunch of spheres that are the same size, how many can you get to touch a single sphere at the same time. In 2d, the answer is clearly 6. (try it with pennies.) In 3d, 12 is the answer but if you look at the spherical cone of impact that each outer sphere makes, it would seem that 13 COULD be possible. The deal is that no one has found a function that provably states for each dimension what the number is. Only a special case exists for multiples of 8. Highweirdness, plain and simple. 
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