J. Kepler,
De nive sexangula, 1611.
An English translation (by Colin Hardie) was published in 1966
by Oxford Press as
The six-cornered snowflake.
This pamphlet is impressive.
It is arguable that no one had worked so hard at three dimensional imaging
since
Democritus and Eudoxus (or their Chinese
equivalents) discovered the volume formula for tetrahedra.
One curious feature that makes it rather difficult to read
is that there are so few images in it and so many attempts to
describe complex 3D phenomena verbally.
I am greatly indebted to the staff at the Fisher Librray and especially
the librarian, Richard Landon, for their cooperation in producing the images
from Kepler's pamphlet that I have used.
E. Klarreich,
Foams and honeycombs,
American Scientist (March-April 2000).
A good popular account of Kepler's and other related conjectures.
R. Peikert,
Dichteste Packungen von gleichen Kreisen
in einem Quadrat,
Elemente der Mathematik 49 (1994), 15-26.
A survey of the much more difficult problem of packing
in small squares.
C. A. Rogers,
The packing of equal spheres,
Proceedings of the London Mathematical Society 8 (1958), 609-620.
Rogers proves an upper bound for packings in n dimensions which
reduces to Thue's result when n=2. In section 3 he presents the scaling argument
(without pictures!) that was used in the last section.
A. Thue,
Über die
dichteste Zuzammenstellung von kongruenten Kreisen
in der Ebene, Christiana Vid. Selsk. Skr. 1 (1910), 1-9.
