Fibonacci numbers

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Fibonacci numbers [1] were discovered by thirteenth-century Italian mathematician Leonardo Fibonacci (circa 1170-1250). Fibonacci, who introduced Arabic numbers to Europe, also introduced a theory in which the sum of any two consecutive numbers equals the next highest number (i.e., following this sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on.) According to Fibonacci, the ratio of any number to its next highest number approaches 0.618 after the first four numbers. Fibonacci numbers, and more significantly the ratio of those numbers to each other, can be found throughout nature and cycles, most popularly in the reproduction rates of rabbits.

Fibonacci ratios [2] are used in technical analysis to predict retracement areas during pullbacks, as well as targets, called “extensions,” for projected price moves.


  1. CFTC Glossary. Commodity Futures Trading Commission.
  2. Technical Analysis Terms. Lind-Waldock.