Number of Cannonballs in Piles of Different Shapes

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Find the number of cannonballs, assuming a solid packing.
Contributed by: Izidor Hafner (October 2012)
Open content licensed under CC BY-NC-SA
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Details
The idea for the Demonstration comes from [1], where some formulas are given.
[1] G. von Vega, Vorlesungen über die Mathematik, vol. 1, 7th ed., Vienna, 1835 pp. 240–243.
Permanent Citation
"Number of Cannonballs in Piles of Different Shapes"
http://demonstrations.wolfram.com/NumberOfCannonballsInPilesOfDifferentShapes/
Wolfram Demonstrations Project
Published: October 4 2012