¶ Omnidirectional Closest Packing of Spheres: Synergetics Principle Of (1)
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Now I am going to take an inventory of those balls in the different layers. There are 12 balls in this layer and if we count these up we find that there are 42 balls in the next layers. In this top layer there are 92 balls. If I put on another layer you will find that there are 162-- and another layer will be 252. The number of layers always comes out with the number two as a suffix. We know that this system is a decimal system of notation. Therefore we are counting in what the mathematician calls congruence in modulo ten-- a modulus of 10 units-- and there is a constant excess of two.
We find in algebraic work if you use a constant suffix (where you always have, say, 33 and 53, you could treat it as 50 and come out with the same algebraic conditions.) Therefore if all these come out with the number two, I can drop off the number two and not affect the algebraic relationships.
If I drop off the number two in that column they will all be zeros; so this would read, 10, 40, 90, 160, 250, and if I had another one it would be 360. I see each one of these are 10’s,
