Variations in the Forms of Snowflakes
from: Atlas der Krystalformen by Victor Goldschmidt (1853-1933)
his observations of geometric structures in nature, Johannes Kepler
also studied snowflakes and their six-pointed forms, and presented his
ideas on this in the small volume A New Year's Gift, or On Six-Cornered Snow.
Here, in addition to causal “scientific” considerations, he makes more
morphological observations, such as comparing the six-pointed form of
the snowflake and the six-petaled flowers of the lily family, and
contrasting these with the five-petaled blossoms of fruit trees-and
seeks to draw conclusions on the natural qualities of these plants thus
Image 4, however, is not from Kepler, but is much more recent: it is from Victor Goldschmidt's Atlas der Krystalformen.
Just as Kepler is famous as an astronomer, but hardly anyone knows that
the results of his studies emerged in the course of a search for the
musical harmony of the universe, so the Atlas der Krystalformen
is known as the standard work of this crystallographer, but it is
little known that Goldschmidt studied the connections between
crystallography and harmonics: in his book Über Harmonie und Complication,
he investigates analogous phenomena in music, colors, and various
domains of nature, on the basis of a fundamental law he developed from
It was above all the works of Victor Goldschmidt, along with those of
Kepler and Thimus, that inspired Hans Kayser's work-Kayser
reestablished harmonics as we know it today and presented it in a new
form for our times.
The commentary on Images 17 and 18 also relates to Goldschmidt's system of “complication.”