Crystals between salt and snowflakes
- From: "oriel36" <geraldkelleher@xxxxxxxxx>
- Date: 19 Dec 2005 04:20:46 -0800
Begin with a line and add two lines to make a triangle,another to make
a square, another for a pentagon then another for a hexagon.Adding
more lines turns the original triangle into a circle.This way we know
that all shapes are contained between line and circle and it is the
basis for all that follows.
Crystals tend to organise themselves into specific facets such as
squares (salt) and hexagons (snowflakes) -
http://www.bigfoto.com/miscellaneous/photos-16/salt-crystals-94jf.jpg
http://news.nationalgeographic.com/news/2004/02/photogalleries/snowflakes/images/primary/second_normal.jpg
Between the square and the hexagon is the pentagon.Unlike squares and
hexagons which can tile the plane and generate crystal facets,pentagons
cannot either tile the plane (without leaving gaps) or are their any
pentagonal facets representing a five sided crystal.
There is however, a means to generate a geometry which displays the
traits of pentagonal symmetry with the understanding that the crystal
structure or rather the facets are bound together in an enviroment that
is balanced between order and randomness.The quasi-crystals and their
Penrose tiles antecedents have been known for a few decades and they
put paid to statistics involved in crystal growth.
http://www.scienceu.com/geometry/articles/tiling/penrose.html
http://www.jcrystal.com/steffenweber/qc.html
For a geometer involved in recognising the ubiquitous nature of the phi
proportion in nature in re-affirming what our ancestors stretching back
to antiquity knew,the four basis angles of Penrose tiles ; 36, 72, 108
and 144 degrees represent the geometric equivalent of dna code and a
point of departure for appreceating forms in terms of natural beauty
and efficiency.
This is no meant as a sleight to those who hold that crystal growth is
intrinsic to the constituents of the crystal for snowflakes form as a
consequence of external conditions likewise there is an external
condition which is explicitly present in the growth of crystals that
generate icosahedral symmetry (3 dimensional form of pentagonal
symmetry).
The point is so delicate that it would wither in a flash,for in
glimpsing a little gap in the door which Penrose tiles and
quasicrystals provide through those 4 angles,it shuts firmly on those
who are not prepared to allow nature dictate the direction,by nature I
mean that unknown underlying influence which conditions so many
planetary forms to the phi proportion.I have not nor would not seek the
underlying cause but there is a way to re-affirm that binding geometric
relationship between phi and natural forms in a 21st century setting.
.
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