Christmas Ornaments, Packed Like Sardines - ScienceNOW: Chan realized he could solve the problem by imagining his cylinder full of ball bearings as a stack of disks, with a single layer of ball bearings on each disk. He then wrote a computer simulation to model it that way. The computer would lay spheres in a disk, and when it ran out of room, it would move up until it found enough space to fit another sphere. It would then rotate around fitting spheres on that level until there was no more room, moving up again, and repeating. Not all the spheres on a certain disk needed to be level; if a sphere could nestle down a little into a space created by two spheres on the disk below to get the tightest fit, it would. If the spheres below pushed it up a little higher than the other spheres on its disk, that was okay, too.
Chan was pleased to see that the program, running just 15 minutes on a laptop, produced results very close to those of weeklong computer simulations run by his colleagues...
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