"The most beautiful
thing we can experience is the mysterious. It is the source of all true art
Nautilus – Living fossil
The Nautilus (in Greek 'sailor') has survived relatively unchanged for 450 million
years and is one of the only shells to survive from the Dinosaurs era. This
is why the Nautilus is sometimes referred to as a "living fossil
". The Nautilus is a nocturnal
creature and spends most of its time in the great depths of the ocean. The Nautilus
shell, lined with mother-of-pearl, grows into increasingly larger chambers throughout
its life and so has become a symbol for expansion and renewal.
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Nautilus shell and Phi
Dating back to Hindu myth, the Nautilus Shell was mentioned as a symbol of many
things in the creation. It is also a symbol for the inner beauty of nature.
The Nautilus shell is one of the known shapes that represent the golden mean
number. The golden mean number is also known as PHI - 1.6180339... The PHI is
a number without an arithmetic solution, the digits simply continue for eternity
without repeating themselves. The uniqueness of the golden mean is that it can
be found in all living forms such as the human skeleton, the shell and the sunflowers
seeds order. Plato called this value - "The key for the universe physics".
The Golden Mean number is widely used in art, architecture and religious symbols.
Artists like Da Vinci and Kandinsky have used the golden mean in their paintings.
The Guggenheim museum, planned by Frank Lloyd Wright, is shaped like the shell.
Researchers found that humans will consider beautiful an art work, architecture
and even a face that have the golden mean proportions.
Phi (golden mean) - "The key to the physics of the cosmos" (plato)
Phi is a constant value which is even more mysterious and profound in its implications
than pi. Like pi, phi is a number with no arithmetical solution. The decimals
just keep on going into infinity without ever repeating themselves. The unique
thing about this number is that it can be found incorporated in all known organic
structures. From the bone structure of human beings to the seed pattern of a
sunflower to the spiral of a sea shell, the phi proportion is there, underlying
all biological structures, seeming to be a geometrical blueprint for life itself.
While it cannot be worked out arithmetically, Phi can be easily obtained with
a compass and straightedge.
Finding the golden mean
Two simple ways of finding the Golden Section geometrically are as follows:
If you take two equal squares, side by side, (a 1x2 rectangle), divide one of
the squares in half, and with a compass, swing the diagonal down to the base
of the other square, the point where the diagonal touches the base will be phi,
or 1.6180339+, in relation to the side of the square, which is 1 (This formula
also describes exactly the rectangular floor of the King's Chamber).
The other method of determining the Golden Section is by dividing a line segment,
AB, at a point C, in such a way that the whole line is longer than the first
part in the same proportion as the first part being longer than the remainder.
AB/AC = AC/CB = 1.6180339 (notice the fractal and holographic nature of this
Golden mean in architecture
The phi ratio is found in the architecture of the Great Pyramid in the triangle
formed by the height, half-base, and the apothem, or diagonal. In other words,
the basic cross - section of the structure demonstrates the Golden Section.
If the half - base is given a value of 1, this gives the value of phi for the
apothem, and the square root of phi for the height. The Golden Section shows
up again and again in Giza and in much more baffling and tedious ways (Entire
volumes have been written on the geometries involved in the pyramids construction).
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