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Originally Posted by THILLIAR
The upper ball is always centered over the centroid of the equilateral triangle formed by the centers of the lower three balls THAT ARE TOUCHING?
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Yes
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How would one compensate for such a problem, mathamatically?
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I'm not sure what you mean by "compensate" in that question. wblipp already posted the math.
Perhaps what you need is a diagram. I did a brief search and found
http://www.chem.ox.ac.uk/icl/heyes/s...1.html#anchor4
Look under "CLOSE PACKING OF SPHERES".
And this:
http://www.math.binghamton.edu/zasla....20040406.html