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Chapter 11

Fibonacci Retracements

Leonardo of Pisa lived from 1170 to 1250, and he is regarded as perhaps the greatest mathematician of the Middle Ages. His father William had the nickname “Bonaccio,” which means good-natured, so Leonardo was subsequently known by the nickname of “Fibonacci” (short for filius Bonacci, or the son of Bonaccio).

William worked in North Africa at a trading post, and even though his home country of Italy had used the Roman numeral system for centuries, he came into contact with traders who instead used the Arabic method of numbers (which is what we use today—1, 2, 3, 4, and so forth, as opposed to numbers such as XI and MMC). Leonardo helped his father with his work, and in the course of doing so, he became acquainted with and enamored by the Arabic style of numbering, which seemed far more sensible and efficient than the Roman style. The world owes Leonardo a debt of gratitude for helping to popularize this system of numbers, since it's doubtful anyone today would appreciate having to use Roman numerals in everyday life.

Another great contribution Leonardo made was with respect to his writings related to what we today call Fibonacci numbers. This is a sequence of numbers which begins like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597. Each number is the sum of the two preceding numbers. These numbers have a variety of interesting properties, including the fact that, as the sequence progresses, each number divided by ...

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