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Search: id:A084824
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| A084824 |
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Maximum number of spheres of diameter one that can be packed in a cube of volume n (i.e. with edge length n^(1/3)). |
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+0
4
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| 1, 1, 1, 2, 4, 4, 5, 8, 8, 8, 9, 9, 10, 10, 14, 14, 14, 15, 18, 18, 19
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Higher sequence terms are only conjectures found by numerical experimentation. The 17 sphere configuration shown on Erich Friedman's "Spheres in Cubes" web page is not the best possible arrangement.
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REFERENCES
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Goldberg, M., On the Densest Packing of Equal Spheres in a Cube. Math. Mag. 44, 199-208, 1971.
Schaer, J., On the Densest Packing of Spheres in a Cube. Can. Math. Bul. 9, 265-270, 1966.
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LINKS
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Dave Boll, Packing spheres in cubes.
Erich Friedman, Spheres in Cubes.
Hugo Pfoertner, Best packing of equal spheres in a cube. Numerical results.
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EXAMPLE
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a(5)=4 because a cube of edge length 5^(1/3)=1.7099759 is large enough to contain 4 spheres arranged as a tetrahedron, which requires a minimum enclosing cube of edge length 1+sqrt(2)/2=1.70710678.
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CROSSREFS
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Cf. A084825, A084826, A084827, A084616.
Sequence in context: A111138 A035625 A132128 this_sequence A121528 A049782 A091666
Adjacent sequences: A084821 A084822 A084823 this_sequence A084825 A084826 A084827
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KEYWORD
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hard,more,nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 12 2003
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