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The Fibonacci Sequence, Defined -
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The Fibonacci Sequence comes to us originally not from a movie based on a book by Dan Brown, but rather, from the “Book of Calculation,” penned by Fibonacci himself, which, among other things also introduced Europe to the notions of the decimal point and that zero was the first number in the sequence: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Both of these concepts were as revolutionary in their time as the number sequence that bears his name.

As to the sequence itself, it was originally presented as a puzzle or question. The original question was this:

“How many pairs of rabbits placed in an enclosed area can be produced in a single year from one pair of rabbits if each pair gives birth to a new pair each month, starting with the second month?”

The solution to this puzzle/problem gives rise to the sequence of numbers we now call “The Fibonacci Sequence.”

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and continuing on indefinitely.

If you look at this number pattern, you’ll see a handy “trick” you can use to calculate the next number in the sequence, as far as you’d like to take it. Simply add any two numbers in the sequence and you’ll get the NEXT number in the sequence, every single time. Try it yourself and see.

Thus, as long as you know that the first two numbers in the sequence are 1, and 1, you can generate as many additional numbers in the Fibonacci sequence as you like.

1+1 = 2
2+1 = 3
2+3 = 5

And so on.

It gets better! Skipping over the first few numbers in the sequence so that we’re buried cozily in its midst, we can start examining the relationships of the numbers to each other. Here are a few critical ones to keep in mind:

• Pick any number in the chain (besides the first few). It is approximately 1.618 times the preceding number. (Example, if you look at the number 144 you’ll find that 144/89 (the number that precedes it) = 1.61797 (rounded to 1.618)
• Pick any number in the chain (besides the first few). You’ll find that the number you’ve selected is approximately 0.618 times the number that comes next in the sequence.
• Pick any number in the chain (again, besides the first few). You’ll find that the number is approximately 2.618 times the number that exists two positions to the left (lower in the series). Here, again we’ll take the number 144. Looking two positions to the left, we find the number 55. 144/55 = 2.61818 (rounding to 2.618).
• Pick any number in the chain (other than the first few, of course). That number is approximately 0.382 times the number that exists two places to the right.

Of all these ratios, far and away the most important one is the number 0.618, which is known as the Golden Mean (also known as the Golden Ratio).

This ratio is found virtually everywhere in nature. You can find it in the shape of a ram’s horns, seashells, the growth patterns of mold spores…almost anything, and of course, all our greatest artists make use of it to properly proportion the human form when drawing or painting it. It can be found in every great piece of music.

The ancient Greeks used the Golden Ratio when constructing the Parthenon, and the ancient Egyptians used it when constructing the pyramids. It’s probably the most pervasive number in the universe!

You even find Fibonacci relationships (and especially the Golden Mean) governing most human activities, so it’s not surprising that they also appear in our financial markets.