This famous sequence reflects the Golden Ratio 1.618 (or .618), a proportion one can observe in the shape of galaxies, ocean waves, the human body and face, molecules, and throughout the natural world.
Among the many examples of Fibonacci in nature is the world's fastest animal, the Peregrine Falcon.
This bird does not comprehend the Fibonacci sequence, but it instinctively applies the Golden Ratio as it approaches its prey at over 200 miles per hour.
You see, the Peregrine Falcon doesn't dive straight down when aiming for prey. It approaches its meal in a logarithmic spiral.
You might think that descending in a spiral would take longer than plummeting straight down. Not so, because a straight-diving Peregrine would have to shift its head to the side to constantly keep the prey in its field of vision. Duke University's Professor Vance A. Tucker observed:
Although the spiral path is longer than the straight path, a mathematical model...shows that the falcon could reach the prey more quickly along the spiral path because the speed advantage of a straight head more than compensates for the longer path.
The Peregrine Falcon descends in a logarithmic spiral that is similar to the one imposed over this idealized stock market price pattern below (note how the spiral demarcates the market's trend changes):
Can we both theorize and observe that the stock market operates on the same mathematical basis as so many natural phenomena? The answer is yes...The Fibonacci sequence governs the numbers of waves that form in the movement of aggregate stock prices . . .
. . . Does the Fibonacci-based behavior of the stock market reflect spiral growth? Once again, the answer is yes. The idealized Elliott concept of the progression of the stock market, as presented in [the figure above], is an excellent base from which to construct a logarithmic spiral...In this construction, the top of each successive wave of higher degree is the touch point of the exponential expansion... Elliott Wave Principle, pp. 122 and 125
Co-authors A.J. Frost and Robert Prechter continue this line of thought a few pages later:
. . . market action is governed by the Golden Ratio. Even Fibonacci numbers appear in market statistics more often than mere chance would allow.
. . . the Wave Principle suggests the idea that the same law that shapes living creatures and galaxies is inherent in the spirit and activities of men en masse. Elliott Wave Principle, pp. 127-129
Yes, Fibonacci-based patterns appear in market prices time and again -- and even in the time spans between major market junctures. In other words, Fibonacci math can be useful in stock market timing.
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