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FIBONACCI RATIOS AND CLUSTERS

Every financial instrument traded on one of the stock or futures exchanges worldwide moves in trends, big and small. These trend movements have one underlying pattern in common: the Fibonacci summation series.

The Fibonacci summation series is considered the most important mathematical representation of natural phenomena ever discovered. The series can be found in nature, geometry, medicine, music, and so on. Generally speaking, the Fibonacci summation series is a natural law, and it is part of the aesthetic found in any kind of perfect shape or curve.

Fibonacci (Leonardo of Pisa; 1170–1240) lived and worked as a merchant and mathematician in Pisa, Italy. He was one of the most illustrious European scientists of his time. Among his greatest achievements was the introduction of Arabic numerals to supersede Roman numerals.

He developed the Fibonacci summation series:

The mathematical series trends asymptotically (that is, approaching slower and slower) toward a constant ratio. However, this ratio is irrational; it has a never-ending, unpredictable sequence of decimal values stringing after it. It can never be expressed exactly. Dividing any number in the series by its preceding value (e.g., 13/8 or 21/13) results in a ratio that oscillates around the irrational number 1.61803398875 … , being higher than the ratio one time and lower the next. The precise ...