Snowflakes: Hexagonal Symmetry and the Golden Rectangle.
Successive Golden Rectangles dividing a Golden
Rectangle into squares (Snowflakes: Hexagonal Symmetry. Photo credit:
golden ratio and Snowflakes: Hexagonal Symmetry.
are snow crystals form when tiny supercooled
cloud droplets (about 10 μm in diameter) freeze. These
droplets are able to remain liquid at temperatures lower
than −18 °C (0 °F) because, to freeze, a few molecules in
the liquid droplet need to get together by chance to form an
arrangement close to that in an ice lattice; then the
droplet freezes around this 'nucleus'.
The individual ice crystals often have hexagonal symmetry. Although the ice is clear, scattering of light by the crystal facets and hollows/imperfections mean that the crystals often appear white in colour due to diffuse reflection of all spectrum of light by the small ice particles.
The 6-fold symmetry arises from the hexagonal crystal structure of ordinary ice, the branch formation is produced by unstable growth, with deposition occurring preferentially near the tips of branches.
Wilson "Snowflake" Bentley (1865
- 1931), born in Jericho, Vermont, is the first known photographer of snowflakes.
A golden rectangle
is a rectangle whose side lengths are in the golden ratio,
one-to-phi, that is, approximately 1:1.618. A distinctive
feature of this shape is that when a square section is
removed, the remainder is another golden rectangle, that is,
with the same proportions as the first. Square removal can
be repeated infinitely, which leads to an approximation of
the golden or Fibonacci spiral.