Реферат: Fibonacci Essay Research Paper Leonardo da Pisa
Fibonacci Essay, Research Paper
Leonardo da Pisa, or more commonly known as Fibonacci, was born in Pisa, Italy in 1175. He was the son of Guilielmo Bonacci, a secretary of the Republic of Pisa. His father was only a secretary, so he was often sent to do work in Pisan trading colonies. He did this for many years until 1192. In 1192, Bonacci got a permanent job as the director of the Pisan trading colony in Bugia, Algeria.
Sometime after 1192, Bonacci brought Fibonacci with him to Bugia. Bonnaci expected Fibbonacci to become a merchant and so arranged for him in instruction of calculational techniques. One of the major themes in this involved the Hindu-Arabic numerals which had not yet been introduced into Europe. Eventually, Bonacci enlisted his son’s help in carrying out business for the Pisan republic and sent him on trips to Egypt, Syria, Greece, Sicily, and Provence. Fibonacci took this grand opportunity offered by his father, to study and learn the mathematical techniques employed in these various regions.
Around 1200, Fibonacci returned to Pisa where, for at least the next twenty-five years, he worked on his own mathematical compositions. The five works produced by him in this period which have survived are: the Liber Abbaci; the Practica geometriae; an undated letter to Theodorus, the imperial philosopher to the court of the Hohenstaufen emperor Frederick II; Flos, a collection of solutions to problems posed in the presence of Frederick II; and the Liber quadratorum, a number-theoretic book concerned with the simultaneous solution of equations quadratic in two or more variables. The most famous of these works is Liber Abbaci.
The Liber Abbaci is Latin for ?The Book of Calculations?.. This book was designed for the Latin-speaking-European-world to accept the decimal number system. The first chapter of Part 1 begins:
These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. With these nine figures, and with this sign 0 which in Arabic is called zephirum, any number can be written, as will be demonstrated.
He also introduced a series in Liber Abacci. It is the Fibonacci sequence, named in his honor. The series begins with 0 and 1. After that, he added the last two numbers to get the next (1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987,…)
He discovered it as a solution to. In 1225 Fibonacci took part in a tournament at Pisa ordered by the emperor himself, Frederick II. It went as follows:
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?
After 1228, virtually nothing is known of Leonardo’s life, except that by decree the Republic of Pisa awarded the “’serious and learned Master Leonardo Bigollo’ (discretus et sapiens) a yearly salarium of ‘libre XX denariorem’ in addition to the usual allowances”. This stipend rewarded Fibonacci for his pro bono advising to the Republic on matters involving accounting and related mathematical matters. Fibonacci died some in 1250, presumably in Pisa.