From 1170 to 1250 Fibonacci was the name used by the Italian mathematician Leonardo Pisano. The son of Guilielmo and a member of the Bonacci family, Fibonacci himself sometimes used the name Bigollo, which may mean good-for-nothing traveller. A brilliant mathematician who wrote several books, Fibonacci was a genius ahead of his day. He is most well known today for the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc, which figures prominently in what is today known as Fibonaccian mathematics, and has a quarterly scholarly journal devoted to it. Fibonacci introduced the western world, which until that time had used the Roman numeral system, to the modern decimal system, imported from Babylonia. The Fibonacci number sequence are studied as part of number theory and have applications in the counting of mathematical objects such as sets, permutations and sequences as well as in computer science.

Fibonacci believed that Arabic numerals were simpler and more efficient than Roman numerals. He traveled throughout the Mediterranean world of his day and studied under the major Arab mathematicians of the day, and returned to Pisa around 1200. In the year 1202, when he was 32 years old, he published what he had learned in The Book of Calculation. In it he showed the practical importance of this new to Europeans number system by applying it to commercial accounting and to conversion of weights and measures. He also showed how to apply it to the calculation of interest, money-changing, and many other applications. The book was well received in educated Europe and it had a profound impact on European thought. Still the use of decimal numerals did not become widespread until the invention of printing almost three hundred years later. Fibonacci was honored to be a guest of the Holy Roman Emperor Frederick II who was a fan of mathematics and science. In the year 1240 his city, the Republic of Pisa honored him by paying him a salary from the city.

In practicality Fibonacci’s numbers are used in the run time analysis of Euclid’s algorithm determining he greatest common divisor of two integers. It was also used by Yuri Matiyasevich to solve Hilbert’s tenth problem. The numbers are also used in a formula about diagonals Pascal’s triangle. He said that every positive integer can be written uniquely in a way as the sum of one or more distinct Fibonacci numbers and inn that way the sum does not include any two consecutive numbers, which is called Zeckendorf’s theorem. A sum of Fibonacci numbers that satisfies these ideas is a Zeckendorf representation. They are also used for tuning of musical interments in art to determine the size of formal elements.

The numbers are also commonly found in nature. They have been found in the patterns of leaves, grass and flowers, and branching in bushes and trees. Fibonacci numbers can also be found in the arrangement of tines on a pine cone, in raspberry seeds and other natural areas. Commonly Fibonacci numbers are seen in fractal Fuchsian groups and Kleinian groups, and in the solutions to reaction diffusion differential equations. Genes too and enzymes often show Fibonacci patterns.

Known in his day and recognized as a genius, he was able to see patterns that escaped most others, and only in the modern age of computers are his numbers and patterns able to be utilized anywhere near what he envisioned them to be used for. His translation of Arabic numerals to replace the rather limited and bulky Roman system of numerals is a debt the entire modern world owes to him. And certainly serious forex traders also owe a debt to this man from Pisa.

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