Thursday, November 11, 2010

Essay on Leonardo Fibonacci

Essay on Leonardo Fibonacci

Leonardo Pisano, or better known as Leonardo Fibonacci, was born in Pisa, Italy around 1170. His father was Guilielmo Bonacci, a secretary of the Republic of Pisa and responsible for directing the trading colony in Bugia, Algeria. It was here that Fibonacci received most of his education.

Some time after 1192, Fibonacci moved to Bugia with his father. His father wanted Leonardo to become a merchant there and arranged for his instruction in calculation techniques, especially involving the Hindu-Arabic numerals. Soon, Leonardo was helping his father carry out business for the Pisan republic, and was sent on trips to Egypt, Syria, Greece, Sicily, and Provence. Leonardo took these trips as an opportunity to learn the different mathematical techniques used in these regions.

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Leonardo ended his travels around the year 1200 and returned to Pisa, where, for the next twenty-five years, he worked on his own mathematical compositions. The five main works of this period are the Liber abbaci (1202, 1228), Practica geometriae (1220-1221), Flos (1225), and the Liber quadratorum. (1225) After 1228, not much is known about his life, except he has awarded an honor in Pisa for his achievements. He presumably died after 1240 in Pisa. During a time when scholarship was not noticed, Fibonacci’s sophisticated mathematical achievements made him clearly recognized around the entire world.

Fibonacci’s first work, the Liber abbaci, means the book of calculations. In the Liber abbaci, Fibonacci presents an overview of basic arithmetic and algebra. It also examines root extraction (GCF) and a variety of word problems, some which are similar to Egyptian problems. The Liber abbaci also contains many practical problems for merchants, ranging from calculations of interest, to problems concerning currency exchange rates, and profit margins. Also it contained a number of puzzles, including the famous reproduction of rabbits, which led to the Fibonacci sequence. In Fibonacci’s second work, Practica geometriae, he drew heavily from the works of ancient Greek masters, including Euclid and Archimedes. Fibonacci focused mainly on quadratic equations, which is undoubtedly his best skill. Included are many instructions given for practical people. Simplified instructions and easily read tables take the place of complicated computations. The work Flos was sent to Emperor Fredrick II as a response to questions set forth by Johannes of Palermo, a member of his court. Fibonacci solved the problems, and concluded that the solution was not a whole number, fraction, or irrational number. But he does go on to provide an approximation for the solution. In the Liber quadatorum, Fibonacci obtain many achievements in the number theory. He finds methods to find Pythagorean triples, and defines a special class of numbers called a congruum.

Some interesting anecdotes Fibonacci were and are compiled in many textbooks. His most famous, the Fibonacci sequence 1,1,2,3,5,8,13…He found the set of equations: 1=1^ 2, 1+3=2^ 2, and suggested the formula 1+ (2n-1)= n2. Fibonacci showed there is no pair x and y such that x2+y2 and x2-y2 are both perfect squares. He also showed that x4-y4 cannot be square.

The best known of Fibonacci’s achievements is definitely the Fibonacci sequence. Fibonacci numbers have applications in modern mathematics, and are often used in modern computer science. Fibonacci was a master of algebra in the east, and scholar in the west. He has been called the first great mathematician of the Christian West. Fibonacci introduced a system of knowledge we still use today, and provided a foundation for the modern number theory and many other useful parts of mathematics.

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