Hmm, how does that apply to a sphere that touches the _outside_ of all the spheres?\n\nLets see...\n2d, instead of sqrt(2)-1 it'd be sqrt(2)+1\n3d, instead of sqrt(3)-1 it'd be sqrt(3)+1\n...oh.... I guess that makes sense.\nHow about a volume of the space between the inner circle and the outer circle?   Versus the volume of the unit spheres?  Or the surface area, for that matter.....