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Balls in Space (Posted on 2005-12-09) Difficulty: 4 of 5
What is the maximum proportion of space that can be filled with an infinite number of identical spheres?

No Solution Yet Submitted by Andre    
Rating: 4.4000 (5 votes)

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Some Thoughts re(2): Idea | Comment 9 of 12 |
(In reply to re: Idea by Sir Percivale)

Filling a space with infinite points would theoretically work (I believe), except for the fact that points cannot be spheres.

If the spheres were of diameter P, they would fill the same proportion of space as any other spheres, so that is irrelevant.

I have not actually solved this problem yet, but I do have an idea: first of all, to fill a maximum percentage of area, the spheres should be stacked in layers so that each sphere is sitting in the gap formed by the three spheres below it (This may have already been mentioned). Then, all you need is to find a shape that will tesselate in this three-dimentional pattern, which can be circumscribed around a sphere. Find the ratio of the volume of the sphere to that of this mystery shape, and you've got yourself a solution.

  Posted by hal on 2005-12-11 23:16:56
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