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As the new sequence
progresses, a third sequence begins in those numbers that are
added to the 4x multiple. This relationship is possible because
the ratio between second alternate Fibonacci numbers is
4.236, where .236 is both its inverse and its difference
from the number 4. This continuous series-building property is
reflected at other multiples for the same reasons.
1.618 (or .618) is known as the
Golden Ratio or Golden Mean. Its proportions are pleasing to the
eye and an important phenomenon in music, art, architecture and
biology. William Hoffer, writing for the December 1975 Smithsonian
Magazine, said:
...the proportion of
.618034 to 1 is the mathematical basis for the shape of
playing cards and the Parthenon, sunflowers and snail shells,
Greek vases and the spiral galaxies of outer space. The Greeks
based much of their art and architecture upon this proportion.
They called it "the golden mean."
Fibonacci's abracadabric rabbits
pop up in the most unexpected places. The numbers are
unquestionably part of a mystical natural harmony that feels
good, looks good and even sounds good. Music, for example, is
based on the 8-note octave. On the piano this is represented by
8 white keys, 5 black ones — 13 in all. It is no accident that
the musical harmony that seems to give the ear its greatest
satisfaction is the major sixth. The note A vibrates at a ratio
of .62500 to the note C. A mere .006966 away from the exact
golden mean, the proportions of the major sixth set off good
vibrations in the cochlea of the inner ear — an organ that
just happens to be shaped in a logarithmic spiral.
The continual occurrence of
Fibonacci numbers and the golden spiral in nature explains
precisely why the proportion of .618034 to 1 is so pleasing in
art. Man can see the image of life in art that is based on the
golden mean.
Nature uses the Golden Ratio in
its most intimate building blocks and in its most advanced
patterns, in forms as minuscule as atomic structure,
microtubules in the brain and DNA molecules to those as large as
planetary orbits and galaxies. It is involved in such diverse
phenomena as quasi crystal arrangements, planetary distances and
periods, reflections of light beams on glass, the brain and
nervous system, musical arrangement, and the structures of
plants and animals. Science is rapidly demonstrating that there
is indeed a basic proportional principle of nature. By the way,
you are holding your mouse with your five appendages, all
but one of which have three jointed parts, five
digits at the end, and three jointed sections to each
digit.
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