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

30 Hard problems with hard spheres
Figure 3.6. Thomas Harriot (1560–1621). Courtesy of Trinity College Oxford.
matter was composed of atoms. In a letter in 1607, he tried to persuade Kepler to
adopt an atomic theory in his study of optics. Kepler declined, but a few years later
in his De Nive Sexangula (1611) he adopted an atomistic approach to describe the
origin of the hexagonal shape of snowflakes. To do this he assumed that the
snowflakes are composed of tiny spheres 14 .
Kepler recognized the analogy with the bee’s honeycomb. He therefore studied
the shape resulting from compressing spheres arranged in the closest way. The
construction of the ‘most compact solid’ is described as follows:
For in general equal pellets, when collected in any vessel, come to a mutual
arrangement in two modes according to the two modes of arranging
them in a plane.
If equal pellets are loose in the same horizontal plane and you drive
them together so tightly that they touch each other, they come together
either in a three-cornered or in a four-cornered pattern. In the former
case six surround one; in the latter four. Throughout there is the same
pattern of contact between all the pellets except the outermost. With
a five-sided pattern uniformity cannot be maintained. A six-sided pattern
breaks up into three-sided. Thus there are only the two patterns as
described.
½ See Leppmeier M 1997 Kugelpackungen von Kepler bis heute (Wiesbaden: Vieweg).