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The Hidden Structure and
The Fibonacci numbers are Nature's
numbering system. They appear everywhere in Nature, from the leaf
arrangement in plants, to the pattern of the florets of a flower,
the bracts of a pinecone, or the scales of a pineapple. The
Fibonacci numbers are therefore applicable to the growth of every
living thing, including a single cell, a grain of wheat, a hive of
bees, and even all of mankind.
The Fibonacci sequence is 1, 1, 2, 3, 5, 8,
13, 21, 34, 55, and so on. It begins with the number 1, and each new
term from there is the sum of the previous two. The limit ratio
between the terms is .618034..., an irrational number variously
called the "golden ratio" and /or the "divine
proportion," but in this century more succinctly "PHI"
after the architect Phidias, who
designed the Parthenon.
Harmonic analysis of
In other words, any two adjoining numbers
equal the next higher number. For example, 5 + 8 = 13. Any number
divided by the next higher number gives a ratio of .618. For
example, 8 / 13 = .618. Any number divided by the next lower number
gives a reciprocal of 1.618.
In the lower numbers the ratios are not
exact, but close enough for practical purposes. To keep things
simple, I normally refer to the numbers as .62 and 1.62.
Both the Fibonacci Sequence and the Golden
Ratio appear in natural forms ranging from the geometry of the DNA
molecule (and the human body) to the physiology of plants and
animals. In the past few years, science has taken a quantum leap in
knowledge concerning the universal appearance and fundamental
importance of Fibonacci mathematics. Some of history's greatest
minds, from Pythagoras to Isaac Newton, have held phi (f
) and the Fibonacci sequence in the highest esteem and reverence.
DNA fibonacci spiral
fibonacci spiral structure
structure of the shell with phi (f )
spiral structure of the human ear
senses, including hearing, touch, taste, vision and pain receptors,
have not only spiral physiology, but also response curves that are
logarithmic (having a fibonacci structure). Cellular action membrane
potentials, which are important for muscles and nervous system, have
a voltage equal to the log of the ratio of the ion concentration
outside the cell to that of inside the cell. The brain and nervous
systems are made from the same type of cellular building units and
look similar microscopically, so the response curve of the
central nervous system is probably also logarithmic."
- Frederick A Hottes
relationships of the human head
relationships of the human body
Much more information
about the thirteenth century Italian mathematician, Leonardo de Pisa
(Filius Bonacci or Fibonacci) can be found on the internet.
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