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

Chapter 3
Hard problems with hard
spheres
3.1 The greengrocer’s dilemma
Now we will exchange our coins for a heap of oranges or a bag of ball bearings.
It is much more difficult to see the possibilities that they present, in the mind’s
eye or in reality. But one thing becomes quite clear at an early stage: no amount
of shaking the bag will cause the balls to come together in an elegant ordered
structure. By the same token, the greengrocer must take time and care to stack
his oranges neatly. Is his stacking the densest possible Of course, this is not
his objective. For our greengrocer, considerations of stability and aesthetics are
paramount. If he is an amateur mathematician perhaps he might just wonder....
3.2 Balls in bags
Let us look more closely at the ball bearings in the bag. In order to fix their
positions, wax may be poured in and the contents then dissected. The first person
to undertake this experiment systematically was J D Bernal, or rather his student
John Finney, in the 1950s 1 . The random packing of balls became known as Bernal
packing. One might wonder why it was not done before. Certainly it is tedious,
but such tedium is often part of the price of a PhD.
The preceding century, in which the detailed atomic arrangements of crystals
were hypothesized and powerful theories of symmetry applied to them, was one
in which perfect order was the ideal (as one might expect in an imperial age).
½ Bernal J D 1959 A geometrical approach to the structure of liquids Nature 183 141–7.
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