Exerpts from the famous book by Carolyn Boroden: For those who are not already familiar with the name Fibonacci, you may remember hearing something about it in 2006, when the movie The DaVinci Code appeared in theaters. When Jacques Saunière was found murdered at the Louvre Museum in Paris, the strange position that this deceased character was placed in mimicked the famous painting of the Vitruvian Man by Leonardo da Vinci. This painting has been known to illustrate how Fibonacci ratios appear in the human form. The film also piqued the curiosity of some people when the characters in the film started talking about Fibonacci numbers as part of a clue or code of some sort. For myself, I only chuckled and thought, “It’s about time someone is taking Fibonacci seriously.”
The Fibonacci number series and the properties of this series were made famous by the Italian mathematician Leonardo de Pisa. The Fibonacci number series starts with 0 and 1 and goes out to infinity, with the next
number in the series being derived by adding the prior two. For example, 55 + 89 = 144, 89 + 144 = 233, 144 + 233 = 377, and so on (see the following number series):
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 . . . out to infinity
What is most fascinating about this number series is that there is a constant found within the series as it progresses toward infinity. In the relationship between the numbers in the series, you will find that the ratio
is 1.618, or what is called the Golden Ratio, Golden Mean, or Golden or Divine Proportion. (For example, 55 x 1.618 = 89, and 144 is 1.618 times 89.)
Take any two consecutive numbers in the series after you get beyond the first few and you will find the Golden Ratio. Also note that the inverse or reciprocal of 1.618 is 0.618.
We will not use the Fibonacci number series to analyze the markets. Instead, we will use the ratios derived from this number series. We’ve already discussed 1.618 and 0.618 or the Golden Ratio and its inverse. The
main ratios I use in my everyday analysis are 0.382, 0.50, 0.618, 0.786, 1.00, 1.272, and 1.618.
We will sometimes also include 0.236, 2.618, and 4.236. You saw how we found the 0.618 and 1.618 ratios within the Fibonacci number series, but what about the rest of these ratios? Well, actually, they are all related mathematically.
For example:
- 1.0 - 0.618 = 0.382
- 0.618 x 0.618 = 0.382
- 1.0 / 2 = 0.50
- Square root of 0.618 = 0.786
- 0.618 is the reciprocal of 1.618
- Square root of 1.618 = 1.272
- 0.618 - 0.382 = 0.236
- 0.382 x 0.618 = 0.236
- 1.618 x 1.618 = 2.618
- 2.618 x 1.618 = 4.236
Now what do we do with these ratios and how do they help us trade? (To be continued.........)
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