Aste T., Weaire D. Pursuit of perfect packing (IOP 2000)(147s).pdf

10 Loose change and tight packing
Figure 2.5. The area of regular polygons with a circle inscribed is a convex function of the
number of sides of the polygons (Ò).
Here we have a pattern which, were we not to construct it in the imagination,
presents itself to us in daily life, in the packing and stacking of drinking straws
and other cylindrical objects, or the layout of eggs in a carton. It would even form
spontaneously, at least locally, if we shuffled our coins together for long enough.
There is a research group in Northern France which does just this sort of
experiment, using a gigantic air table. This is a surface with small holes through
which air is pumped, so that flat objects can glide upon it without friction.
Later we will encounter other problems which look very similar to this one,
but few of them submit to such a straightforward argument. Indeed a false sense
of security may be induced by this example. It turns out that almost any variation
of the problem renders it more mysterious.
So what is so special about the packing of these discs It is the convenient
fact that there is a best local packing which can be extended without variation to
the whole structure. If we restore our handful of mixed change, or try to stack