Leonardo of Pisa (lat. Leonardus Pisanus, Italian. Leonardo Pisano, circa 1170, Pisa-circa 1250, ibid) was the first major medieval mathematician. Best known by the nickname Fibonacci.
Fibonacci's father in trade was often in Algeria, and Leonardo studied mathematics there with Arab teachers. Later Fibonacci visited Egypt, Syria, Byzantium, Sicily. He got acquainted with the achievements of ancient and Indian mathematicians in Arabic translation. On the basis of his acquired knowledge Fibonacci wrote a number of mathematical treatises, which are an outstanding phenomenon of medieval Western European science. Leonardo Fibonacci's Work "the book of abacus" contributed to the spread of the positional number system in Europe, more convenient for calculations than the Roman notation; in this book, the possibilities of using Indian figures, which previously remained unclear, were studied in detail, and examples of solving practical problems, in particular, related to the trade business, were given. The positional system gained popularity in Europe during the Renaissance.
Fibonacci was born in the Italian city of Pisa, presumably in the 1170s (in some sources is 1180). His father, Guillermo, was a merchant. In 1192, he was appointed to represent the Pisan trade colony in North Africa and frequently visited Bejai, Algeria. At the request of his father, who wanted Leonardo to become a good merchant, he moved to Algeria and studied mathematics (the art of computing) from Arab teachers. A significant part of the acquired knowledge he set out in his "Book of abacus" (Liber abaci, 1202; to this day preserved only an amended manuscript in 1228). This book consists of 15 chapters and contains almost all the arithmetic and algebraic information of the time, presented with exceptional completeness and depth. The first five chapters of the book are devoted to the arithmetic of integers based on decimal numbering. Another book by Fibonacci, "the practice of geometry" (Practica geometriae, 1220), consists of seven parts and contains a variety of theorems with proofs relating to measuring methods. Along with the classical results, Fibonacci cites his own — for example, the first proof that the three medians of a triangle intersect at one point (Archimedes knew this fact, but if his proof existed, it did not reach us). Among the surveying techniques, which is devoted to the last section of the book — the use of a certain way marked square to determine distances and heights.
To determine the number of Fibonacci uses the perimeters of the inscribed and described 96-gon, which leads to its value . The book was dedicated to Dominicus Hispanus. In 1915, R. S. Archibald was engaged in the restoration of the lost work of Euclid on the division of figures, based on the" practice of geometry " Fibonacci and the French translation of the Arabic version.
The Golden section is found not only in art and architecture, but also in nature. The proportions of the Fibonacci series are present in the arrangement of leaves on trees, various seeds, in the biorhythms and functioning of the brain and visual perception, musical tones, poetic sizes, in the gene structures of living organisms and the like.
Lifetime portraits of Fibonacci is not preserved, and existing are modern ideas about it. Leonardo pisansky left almost no autobiographical information; the only exception is the second paragraph of the "Book of abacus", where Fibonacci sets out the reasons that prompted him to write a book:
"When my father was appointed to the post of customs officer, in charge of the Affairs of Bejaya flocking to him Pisan traders, he in my adolescence called me to him and offered a few days to learn the art of counting, sulivshem many amenities and benefits for my future. Taught by the skill of teachers to the basics of Indian numeracy, I acquired a great love for this art and at the same time learned that something about this subject is known among the Egyptians, Syrians, Greeks, Sicilians and provençals, who developed their methods. Later, during my trading trips around these parts, I devoted a lot of work to the detailed study of their methods and, in addition, mastered the art of scientific dispute. However, in comparison with the Indian method, all the constructions of these people, including the approach of the algorismics and the teachings of Pythagoras, seem almost misleading, and therefore I decided, having studied the Indian method as closely as possible, to present it in fifteen chapters as clearly as I can, with additions from my own mind and with some useful notes from the geometry of Euclid inserted Leonardo of Pisa Fibonacci number
As the researchers note, "Liber abaci" not just stands out, but rises sharply above the medieval literature on arithmetic and algebra. First of all, due to the fundamental nature of the presentation and the variety of methods and tasks considered in it. The level of the work was so high that it was mainly mathematicians, partly contemporaries of Leonardo, and to an even greater extent-representatives of subsequent generations who were able to master and use the information contained in it.
In fact, it was only three centuries after the publication of "Liber abaci" that its influence on the works of other authors became noticeable. With the advent of the work of Fibonacci European scientists of the middle Ages, who were often philosophers, scholastics or clerics, for whom mathematics was not the main occupation, began to pay more attention to algebra and to address its new issues in their research. However, the first serious results were achieved only in the Renaissance, by the beginning of the XVI century, when a group of Italian mathematicians (Scipio del ferro, Niccolo Tartaglia, Jerome Cardano, Ludovico Ferrari) received a General solution of cubic equations, thereby initiating higher algebra.
It turns out that as a scientist Leonardo pisansky not only surpassed, but also for many decades ahead of Western European mathematicians of his time. Like Pythagoras, who brought to Greek science the knowledge once received from the Egyptian and Babylonian priests, Fibonacci greatly contributed to the transfer of acquired in his youth mathematical knowledge of Indians and Arabs in Western European science and laid the Foundation for its further development.