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THE FIBONACCI RATIO
This mathematical series develops when, beginning with 1,1, the next number is
formed from the sum of the previous two numbers. But what makes this series so
important?
The series tends
asymptotically (approaching slower and slower) toward a constant ratio. However,
this ratio is irrational, that is, it has a never-ending, unpredictable sequence
of decimal values stringing after it. It can never be expressed exactly. If each
number in the series is divided by its preceding value (e.g., 13 - 8), the
result is a ratio that oscillates around the irrational 1.61803398875 . . . ,
being higher one time and lower the next. But never in eternity can the precise
ratio be known to the last digit. For the sake of brevity, we will refer to it
as 1.618.
This ratio had
begun to gather special names even before Luca Pacioli (a medieval
mathematician) named it the Divine Proportion. Among its current day
names are the Golden Section, the Golden Mean, and the Ratio of
Whirling Squares. Kepler called the ratio "one of the jewels in geometry."
Algebraically it is generally designated by the Greek letter phi ($ = 1.618).
The asymptotic
tendency of the series, its ratio's ever-tightening oscillation around the
irrational phi, can be best understood by showing the ratios of the first few
entries in the series. This example takes the ratio of the second entry to the
first, the third to the second, the forth to the third, and so forth:
1:1= 1.0000, which is lower than phi by
0.6180 2:1= 2.0000, which is higher than phi by 0.3820 3:2 = 1.5000,
which is lower than phi by 0.1180 5:3 = 1.6667, which is higher than phi by
0.0486 8:5 = 1.6000, which is lower than phi by 0.0180
As we continue in the Fibonacci summation series, each member will divide into
the next one by a closer and closer approximation of phi which can never be
reached.
We will see
later that the individual numbers in the Fibonacci summation series can be seen
in commodity price movements. The swings of the ratios around the value 1.618 by
either higher or lower numbers will be found in the Elliot Wave Principle
described as the Rule of Alternation. Man subconsciously seeks the Divine
Proportion;
it satisfies his comfort level.
Dividing any
number of the Fibonacci sequence by the following number in the series
asymptotically approaches the ratio 0.618, which.
Forex Art Of Fibonacci (Forex 101)
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