Fibonacci numbers are based upon the Fibonacci sequence discovered by Leonardo de Fibonacci de Pisa (b.1170- - d.1240). Although the numeric series was devised as the solution to a problem about rabbits, the concept generally relates to all natural cycles of growth and decline. 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 reproduces itself, how many pairs will one have at the end of n months? The answer is: u_n. This answer is based upon the equation: u_n+1+1 = u_n+u_n-1.

The sequence of the Fibonacci numbers is as follows:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.... 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.

(0+1=1)...(1+1=2)...(1+2=3)...(2+3=5)...(3+5=8)...(5+8=13)...(8+13=21)

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.

34/55 = .618181 ~ .618
55/89 = .617977 ~ .618
89/144 = .618055 ~ .618

Dividing the latter number by the former number derives another relationship from the sequence. This relationship yields approximately 1.618.

55/34 = 1.617647 ~ 1.618
89/55 = 1.618181 ~ 1.618
144/89 = 1.617977 ~ 1.618

Two other numbers often used when applying Fibonacci numbers to chart analysis, 0.786 and 1.27, are the square roots of 0.618 and 1.618.

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