Water Exercise Classes For Seniors
THE MEANING OF FORM
Kepler’s thoughts regarding form were: “Only that which forms a boundary in itself has a form, because the boundaries shape the forms.”
That is clear, but why a hexagon of all forms? Kepler continued:
It needed further consideration as to what was at work here. Was the form innate or produced from the outside? Was the hexagonal figure necessitated by the material out of which it was formed, or by its own nature, which was either the prototype of beauty which lies in a hexagon or due to the aim of this figure. So, inner or outer necessity a clear, beautiful train of thought! After this, Kepler developed the concept of the construction of “solid bodies” from minute units, which ideally should possess a spherical form That means that he had the first vision of what’s today called an atom. He also had an understanding of the order of the spheres. He assumed that the order was level, and there were layers over layers, which is what formed the crystal. This is still the current view. He concluded that at least two possibilities existed: that the order of the spheres formed a square (A) or a triangle (B). He even illustrated this:
In a second sketch, he showed the spatial construction: Layer A (with a sphere) is placed on layer
B, and this then on C, and so on. Finally, a pyramid is formed by four equilateral triangles therefore a tetrahedronwhich shows threefold symmetry, and that has to be the architectural basis for constructing “snow stars.”
Obviously, Kepler didn’t know the construction of water molecules at that point and so wasn’t able to foresee the necessity of the sixfold (not threefold) symmetry, but in any event it can be derived from the threefold symmetry.
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All in all, this was a stroke of genius! Kepler had described the construction of snow crystals in nearly the same way that it would be today. And all this 400 years ago, without the model of an atom, without developed crystallography, and without the help of technical instruments. Crystals are still described today as a three-dimensional spatial grid made up of spherical particles (atoms). And, as mentioned at the beginning, Max von Laue was able to confirm the structure of crystals through x-ray experiments in 1912.
In the case of water, the crystal structure is determined by the shape and form of the H2O molecule.
Contrary to what Kepler expected, the spherical density is less than he showed in his second sketch, but is formed of a looser group of molecules, which are ordered as a tetrahedron and combine to form little rings of six:
The sketch shows a small section of the crystal structure of ice and puts it in the context of the hexagon. It also explains why ice has a bigger volume than water and consequently is lighter and able to float on water: As ice, there’s relatively a lot of space between the individual components; in the fluid state, water is denser. Around two to four million water molecules of this structure are needed to be able to build around 0.039 inches (1 millimeter) of one edge of an ice crystal. The connection of the H2O molecules in the crystal grid is made through hydrogen bridges, which also play an important role in the formation of clusters.
