LEONARDO FIBONACCI
Fibonacci writes in his famous book Liber abaci (1202): When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else and I came to understand it, for whatever was studied by the art in Egypt, Syria, Greece, Sicily and Provence, in all its various forms Around 1200, Fibonacci returned to Pisa. Leonardo Fibonacci was the greatest European mathematician of the Middle Ages. He was the first to introduce the Hindu - Arabic number system into Europe. Leonardo wrote a book on how to do arithmetic in the decimal system, called "Liber abaci", completed in 1202. It describes the rules we are all now learn at elementary school for adding numbers, subtracting, multiplying and dividing. In his book Leonardo wrote the numerals in descending order and his fractions came before the numeral like 1/2 4 instead of 4 1/2. One result of his book attested to his mastery not only of the Hindy-Arabic techniques of practical calculation but also of the theory of quadratic equations. In his work, Fibonacci put forth not so much an original exposition as a compilation of the techniques of Arabic arithmetic and algebra. Leonardo`s mathematical environment encompassed more than this Arabic theory of algebra however. Within his sphere of commercial activities, there also a need for comprehensive catalogues of techniques for solving day-to-day problems. A problem in the third section of Liber abaci led to the introduction of the Fibonacci numbers : A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive? By charting the populations of rabbits Fibonacci discovered a number series from which one can derive the Golden Section. Here`s the beginning of the sequence : 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ..... Each number is the sum of the two preceding numbers as follows : 1 = 1 + 0 French mathematician Edouard Lucas (1842 - 1891) gave the name Fibonacci numbers to this series and found many other important applications of them.It also caused some of the people many years after Fibonacci made the discovery to create a society in his name. The Fibonacci Society was founded in 1962, and a journal, The Fibonacci Quarterly, first appeared in 1963, and was dedicated to unraveling its secrets. There were a lot of secrets to be found. Fibonacci ended his travels around the year 1200 and at that time he returned to Pisa. There he wrote a number of important texts which played an important role in reviving ancient mathematical skills and he made significant contributions of his own. Fibonacci lived in the days before printing, so his books were hand written and the only way to have a copy of one of his books was to have another hand-written copy made. Of his books we still have copies of Liber abaci (1202), Practica geometriae (1220), Flos (1225), and Liber quadratorum. We know that he wrote some other texts which, unfortunately, are lost. Fibonacci's influence was more limited than one might have hoped and apart from his role in spreading the use of the Hindu-Arabic numerals and his rabbit problem, Fibonacci's contribution to mathematics has been largely overlooked. Direct influence was exerted only by those portions of the Liber abaci and of the Practica that served to introduce Hindu-Arabic numerals and methods and contributed to the mastering of the problems of daily life. Here Fibonacci became the teacher of the masters of computation and of the surveyors, as one learns from the Summa of Luca Pacioli ... Fibonacci was also the teacher of the "Cossists", who took their name from the word 'causa' which was first used in the West by Fibonacci in place of 'res' or 'radix'. His alphabetic designation for the general number or coefficient was first improved by Viète.Fibonacci's work in number theory was almost wholly ignored and virtually unknown during the Middle ages. Leonardo Fibonacci died in Pisa, some time after 1240. Fibonacci sequenceFibonacci is perhaps best known for a simple series of numbers, introduced in Liber abaci and later named the Fibonacci numbers in his honour. The series begins with 0 and 1. After that, use the simple rule: Add the last two numbers to get the next. 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987,... You might ask where this came from? In Fibonacci's day, mathematical competitions and challenges were common. In 1225 Fibonacci took part in a tournament at Pisa ordered by the emperor himself, Frederick II. It was in just this type of competition that the following problem arose: Beginning with a single pair of rabbits, if every month each productive pair bears a new pair, which becomes productive when they are 1 month old, how many rabbits will there be after n months? The Golden SectionA special value, closely related to the Fibonacci series, is called the golden section. This value is obtained by taking the ratio of successive terms in the Fibonacci series: Ratio of successive Fibonacci terms. If you plot a graph of these values you'll see that they seem to be tending to a limit. This limit is actually the positive root of a quadratic equation and is called the golden section, golden ratio or sometimes the golden mean. The golden section is normally denoted by the Greek letter phi. In fact, the Greek mathematicians of Plato's time (400BC) recognized it as a significant value and Greek architects used the ratio 1:phi as an integral part of their designs, the most famous of which is the Parthenon in Athens.
Phi and geometryPhi also occurs surprisingly often in geometry. For example, it is the ratio of the side of a regular pentagon to its diagonal. If we draw in all the diagonals then they each cut each other with the golden ratio too (see picture). The resulting pentagram describes a star which forms part of many of the flags of the world.
The pentagram star features in many of the world's flags, including the European Union and the United States of America. Fibonacci in market tradingFibonacci ratios found they way into market trading with power and grace. Number of up-trend and down-trend moves characterized by Fibonacci ratios is unprecedented. While Fibonacci Retracement is still the most popular shape for the price analysis, visit the overview of Fibonacci Solution - software that takes Fibonacci trading to the new level.
Comprehensive list of Fibonacci Software benefits. Examples of Fibonacci Trading. Fibonacci in natureThe rabbit breeding problem that caused Fibonacci to write about the sequence in Liber abaci may be unrealistic but the Fibonacci numbers really do appear in nature. For example, some plants branch in such a way that they always have a Fibonacci number of growing points. Flowers often have a Fibonacci number of petals, daisies can have 34, 55 or even as many as 89 petals! Finally, next time you look at a sunflower, take the trouble to look at the arrangement of the seeds. They appear to be spiraling outwards both to the left and the right. There are a Fibonacci number of spirals! It seems that this arrangement keeps the seeds uniformly packed no matter how large the seed head.
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Leonardo Fibonacci was born in Pisa, Italy, around 1175. His father was Guilielmo Bonacci, a secretary of the Republic of Pisa.His father was also a customs officer for the North African city of Bugia. Some time after 1192. Bonacci brought his son with him to Bugia.Guilielmo wanted for Leonardo to become a merchant and so arranged for his instruction in calculational techniques, especially those involving the Hindu - Arabic numerals which had not yet been introduced into Europe .Since Fibonacci was the son of a merchant, he was able go travel freely all over the Byzantine Empire. Merchants at the time were immuned, so they were allowed to move about freely. This allowed him to visit many of the area's centers of trade. While he was there, he was able to learn both the mathematics of the scholars and the calculating schemes in popular use, at the time.
