Fibonacci in
Nature: The Golden Ratio and the Golden Spiral
The more you learn about Fibonacci, the more amazed you will be at its importance
The more you learn about Fibonacci, the more amazed you will be at its importance
By Elliott Wave International
If you've studied the financial markets, even for a short time,
you've probably heard the term "Fibonacci numbers." The ratios and
relationships derived from this mathematical sequence are applied to the
markets to help determine targets and retracement levels.
Did you know that Fibonacci numbers are found in nature as well?
In fact, we can see examples of the Fibonacci sequence all around us, from the
ebb and flow of ocean tides to the shape of a seashell. Even our human bodies
are examples of Fibonacci. Read more about the fascinating phenomenon of
Fibonacci in nature.
Let's start with a refresher on Fibonacci numbers. If we start
at 0 and then go to the next whole integer number, which is 1, and add 0 to 1,
that gives us the second 1. If we then take that number 1 and add it again to
the previous number, which is of course 1, we have 1 plus 1 equals 2. If we add
2 to its previous number of 1, then 1 plus 2 gives us 3, and so on. 2 plus 3
gives us 5, and we can do this all the way to infinity. This series of numbers,
and the way we arrive at these numbers, is called the Fibonacci sequence. We
refer to a series of numbers derived this way as Fibonacci numbers.
We can go back to the beginning and divide one number by its
adjacent number - so 1÷1 is 1.0, 1÷2 is .5, 2÷3 is .667, and so on. If we keep
doing that all the way to infinity, that ratio approaches the number .618. This
is called the Golden Ratio, represented by the Greek letter phi (pronounced "fie"). It is an
irrational number, which means that it cannot be represented by a fraction of
whole integers. The inverse of .618 is 1.618. So, in other words, if we carry
the series forward and take the inverse of each of these numbers, that ratio
also approaches 1.618. The Golden Ratio, .618, is the only number that will
also be equal to its inverse when added to 1. So, in other words, 1 plus .618
is 1.618, and the inverse of .618 is also 1.618.
This is a diagram of the Golden Spiral. The Golden Spiral is a
type of logarithmic spiral that is made up of a number of Fibonacci
relationships, or more specifically, a number of Golden Ratios. For example, if
we take a specific arc and divide it by its diameter, that will also give us
the Golden Ratio 1.618. We can take, for example, arc WY and divide it by its
diameter of WY. That produces the multiple 1.618. Certain arcs are also related
by the ratio of 1.618. If we take the arc XY and divide that by arc WX, we get
1.618. If we take radius 1 (r1), compare it with the next radius of
an arc that's at a 90° angle with r1, which is r2, and
divide r2 by r1, we also get 1.618.
Now here are some pictures of this Golden Spiral in various
aspects of nature. For example, on the left is a whirlpool that displays the
Golden Spiral and, therefore, these Fibonacci mathematical properties. We also
see the Golden Spiral in the formation of hurricanes (center) and in the
chambered nautilus shell (right), which also happens to be a common background
that Elliott Wave International uses for a number of its presentations and
graphics.
We can also see the Golden Ratio in the DNA molecule. Research
has shown that if you look at the height of the DNA molecule relative to its
length, it is in the proportion of .618:1. If we look at the components of the
DNA molecule, there is a major groove in the left section and a minor groove in
the right section. The major groove is equal to .618 of the entire length of
the DNA molecule, and the minor groove is equal to .382 of the entire length.
This graphic of the human body also shows how the Golden Ratio
exists in certain relationships of the human anatomy.
Learn How You Can Use Fibonacci to Improve
Your Trading
If you'd like to learn more about Fibonacci and how to apply
it to your trading strategy, download the entire 14-page free eBook, How You Can Use
Fibonacci to Improve Your Trading.
EWI Senior Tutorial Instructor Wayne Gorman explains:
See how easy it is to use Fibonacci in your trading. Download your free eBook today >>
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