Origin of the Fibonacci Number Sequence

• Fibonacci numbers are based upon the Fibonacci sequence discovered by Leonardo de Fibonacci de Pisa (b.1170-d.1240). His most famous work, the Liber Abaci (Book of the Abacus), was one of the earliest Latin accounts of the Hindu-Arabic number system. In this work, he developed the Fibonacci number sequence, which is historically the earliest recursive series known to date.

• The series was devised as the solution to a problem about rabbits. The problem is: If a newborn pair of rabbits requires one month to mature and at the end of the second month and every month thereafter reproduce itself, how many pairs will one have at the end of n months? The answer is: un. This answer is based upon the equation: un+1 = un+un-1.

• Although this equation might seem complex, it is actually quite simple. The sequence of the Fibonacci numbers is as follows:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144, 233, 377 ......  up to infinity 

• Starting with zero and adding one begins the series. The calculation takes the sum of the two numbers and adds it to the second number in the addition. The sequence requires a minimum of eight calculations.

• After the eighth sequence of calculations, there are constant relationships that can be derived from the series. For example, if you divide the former number by the latter, it yields .618.

And, if you divide the latter number by the former, it yields 1.618.

• The 0.618 and the 1.618 are two of the four Fibonacci-related numbers that I use to consider price action harmonic. The other two numbers that are derived from the series, the 0.786 and 1.27, are the square root of the 0.618 and the 1.618, respectively.

• These four numbers have been found to exist in many natural and man-made phenomena. The .618 and the 1.618 constants from the series are found in the Great Pyramids. Comparing the height to 1/2 its base derives these relationships.

• Fibonacci’s additive series is based upon the equation:

• Not only do these constant numeric relationships occur in the Fibonacci series, there are also universal examples that exhibit this phenomenon. For example, Venus takes 225 days to complete a revolution around the sun. As we all know, the Earth requires 365 days to complete one revolution. If you divide 225 by 365, the result is approximately .618 of a year. (225/365 = .6164 ~ .618) That's amazing!

"The Harmonic Trader," Copyright 1999.