Hmmmm. IIRC, the "close packing" problem is actually a somewhat non-trivial problem in mathematics. For two dimensions, it's been proved for a while that hexagonal close packing is optimal for identical diameter circles, but for three dimensions (and spheres), the proof of the Kepler Conjecture hasn't even been established with certainty (there is a proof that's been offered, but it's still under evalutation by other mathematicians, AFAIK...).

When circles or spheres of different diameters are involved, the problem of minimum area or volume for packing gets far more complicated.

Cheers,