(Leonardo Bigollo, also known as Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci and Fibonacci; Pisa, Italy current,

Fibonacci

*c.*1175 -*id*.,*c.*1240) Italian mathematician who disseminated scientific knowledge of the Arab world, which collected in the*Liber Abaci*(*book of the abacus*) in the West. He popularized the use of the Arabic numerals and explained the principles of trigonometry in his*Practica Geometriae*(the*practice of geometry*).Fibonacci

Considered as the first discoursing of Europe (chronologically speaking) and as the introducer of the Arabic numeral system, he was educated child in Algeria, where his father was a customs officer, and where he learned "the abacus, the use of the Indians". He then had way, for commercial reasons, know everything what this science was taught in Egypt, in Syria, in Sicily and Provence. The material thus assembled gave him an order, a unit of method and clarity of teaching in the

*Liber Abaci*(*book of the abacus*), which, as a model of University text, served also by its flow of examples, for the compilation of textbooks of arithmetic for use by traders.Written in 1202 and expanded in a second editorial in 1228, the work contains fifteen chapters; the first presents the numbering of the nine figures that Fibonacci called "pigs" and that, indeed, they are ten, because it is necessary to add the zero "quod arabice zephirum apellatur"; in the following chapters Leonardo exposes notions on the digital calculation, addition and multiplication tables, showing its use to perform four operations with figures of considerable extent, and publicizing the criteria of divisibility by two, three and up to thirteen, gathering in tablitas apropos divisions results by these numbers of some integers not exceeding 200.

In the sixth and seventh chapters is fractions of the concept and the least common multiple and applications of a "tabula disgregationis", showing the breakdown of number of ordinary fractions in fundamentals, reveals the persistence of Egyptian logistics. The second part of the book, "Rule of Algebra", contains the formulas to recognize the second-degree equations, with demonstrations according to the old way, using geometric constructions, and numerous problems that can be solved with equations or systems of equations reducible to the second grade. This book, which should be considered as one of the most important of that time by the influence which took on the then resurgent Western scientific knowledge, procured him the author vast fame and drew upon him the attention of Emperor Federico II, who invited him to his court.

In 1220 he gave birth

*practice of geometry*, which contains an introduction that is linked to the fundamental propositions of Euclid, rules for measurement of lengths, areas and volumes and the division of the figures, and demonstrations of such standards, with specific applications and developments of calculation that constitute a useful complement to the earlier work. Following the example of the Greek masters, Leonardo Pisano modeled this work in the style of the*elements*of Euclid, and teaching procedures to follow when you want to measure a surface or volume or divide a figure given in parts subject to proposed conditions, always accompanied his teaching with demonstrations and calculations properly developed, in order to highlight that speaks carried out research similar to those contained in the*metric*of Heron of Alexandria.While this work of Fibonacci had a solely educational character, we must agree that it is one of the main geometric treaties of the middle ages. On the other hand is in the same work a middle part dedicated to an arithmetic theory of radicals square and cubic, apart from a method to square and cubic roots extraction from a given number. It is also noted in the book of Fibonacci the exposure of the procedures devised by Archytas and Plato and Heron of Alexandria to double cube problem along with the quadrature of the circle and the trisection of the angle, vainly seduced generations of scholars.

Among other known Fibonacci texts is a commentary on the book of the

*elements*of Euclid. It is also known that he composed a*Libro di merchatanti*. It is also famous for the discovery of the so-called series of Fibonacci, whose properties include its recurrence in numerous natural organic formations.