Leonardo Pisano Fibonacci

Leonardo of Pisa, whose nicknames included Fibonacci and Bigolo (meaning "good-for-nothing"). lived c. 1170-1250.

The son of a Pisan merchant, Leonardo was educated in northern Africa, where he became one of Europe's greatest mathemeticians. Surviving publications include Liber abbaci (1202), Practica geometriae (1220), Flos (1225), and Liber quadratorum.

Fibonacci's Liber abbaci was the earliest work to introduce Arabic Numerals (which were actually Hindu on origin) and the use of zero as more than a simple placeholder to Europe. Europe, of course, had little use for academics at the time, and Fibonacci's work was largely ignored until it caught the attention of then-Holy Roman Emperor Frederic II, who invited Fibonacci to his court in 1225.

Although Fibonacci is best known for the so-called Fibonacci Numbers, this is only a small component of the contribution he made to modern mathematics. His publications rescued Europe from the dubious legacy of Roman mathematics, and from the Greek dogmatism against the existence of zero, in effect opening the door for the invention of calculus.

All dates are Common Era(C.E.) unless otherwise noted.

Nickname of Leonardo Bonacci, born in 1170, died in 1250, in Pisa, Italy, although he sometimes used the name Bigollo, which might mean "good-for-nothing," or possibly "traveller." Son of Giulielmo Bonacci, a diplomat who represented the merchants of the Republic of Pisa who were trading in Bugia. (Bugia, a port in northeastern Algeria was later called Bougie and is now called Bejaia.)

Fibonacci learned mathematics in Bugia, as his father wished him to become a merchant. It was there that Fibonacci first fell in love with mathematics. As Fibonacci said in the introduction to his book Liber Abaci, he "had me in my boyhood come to him and there wanted me to devote myself to and be instructed in the study of calculation for some days. There, following my introduction, as a consequence of marvelous instruction in the art, to the nine digits of the Hindus, the knowledge of the art very much appealed to me before all others, and for it I realized that all its aspects were studied in Egypt, Syria, Greece, Sicily, and Provence, with their varying methods."

After his instruction was complete, he travelled with his father for a number of years, studying the mathematical systems of the people he visited. However, he was not satisfied simply learning current mathematical theory. Again, from Liber Abaci:

But all this even, and the algorism (the use of Arabic numerals for computation, rather than Roman), as well as the art of Pythagoras I considered as almost a mistake in respect to the method of the Hindus. Therefore, embracing more stringently that method of the Hindus, and taking stricter pains in its study, while adding certain things from my own understanding and inserting also certain things from the niceties of Euclid's geometric art, I have striven to compose this book in its entirety as understandably as I could...Almost everything which I have introduced I have displayed with exact proof, in order that those further seeking this knowledge, with its pre-eminent method, might be instructed, and further, in order that the Latin people might not be discovered to be without it, as they have been up to now.

Liber abaci was Fibonacci's first book, and was dedicated to Michael Scotus, court astrologer to the Holy Roman Emperor Frederick II. It was probably Fibonacci's most widely copied and imitated book. In it, Fibonacci introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals. The book also studied simultaneous linear equations, and provided a large collection of problems aimed at merchants. These related to the price of good, how to calculate profit on transactions, how to convert between the various currencies in use in Mediterranean countries, and some additonal problems which had originated in China. It also had the distinction of introducing his famous Fibonacci numbers, and the Fibonacci Sequence. He presented it as a problem:

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?

His second book, Practica geometriae, published in 1220, was dedicated to Dominicus Hispanus, another of Frederick II's scholars. It contained a large collection of geometry problems arranged into eight chapters, with theorems based on Euclid's Elements and On Divisions. It also provided practical information for surveyors, including a chapter on how to calculate the height of tall objects using similar triangles.

During Fibonacci's life, Europe was not terribly interested in scholarship, as a rule. Therefore it's quite surprising that there was widespread interest in his work, a fact which contributed a good deal to his importance. Although he was famous for his practical applications, rather than abstract theorems, his work caught the interest of several scholars at the court of Frederick II. They began to correspond with Fibonacci, and eventually brought him to the Emperor's attention.

Michael Scotus, court astrologer to Frederick II, Theororus, the court philosopher, and Dominicus Hispanus suggested to the Emperor that he meet with Fibonacci when the Emperor's court convened in Pisa, around 1225. There, Fibonacci displayed himself well, solving three problems that Johannes of Palermo, another scholar at the Emperor's court, presented to Fibonacci as challenges. Fibonacci later published those solutions in Flos, published in 1225.

In 1240, the Republic of Pisa presented a salary to Fibonacci, or, as he was named in the decree, "the serious and learned Master Leonardo Bigollo." The salary, in the sum of 20 Pisan pounds per year, plus expenses, was given in recognition of the services he had given the city, such as pro bono advice on matters of accounting.

As Fibonacci lived in the days before printing, his books were hand written. Thus, to obtain a copy of one of his books, the copy must be made by hand. Of his books, there remain copies of Liber abaci, Practica Geometriae, Flos, and Liber quadratorum. (Liber Quadratorum, not mentioned earlier, was published in 1225, and dealt with solving Diophantine problems, second degree equations with two or more unknowns whose solutions must be integers or rational numbers.) Unfortunately, other texts that he wrote have been lost, such as Di minor guisa, a book on commercial arithmetic, and a commentary on Book X of Euclid's Elements. That commentary contained a numerical treatment of irrational numbers, which Euclid had approached from a geometric point of view.

Sadly, much of Fibonacci's work in number theory was largely ignored. People were extremely interested in the practical aspects of Fibonacci's work, but they had no use for his abstract concepts. It was not until almost 300 years later, in the work of Maurolico, that Fibonacci's results appeared again.

Finally, let me close with another quote from Liber Abaci: "If I have perchance omitted anything more or less proper or necessary, I beg indulgence, since there is no one who is blameless and utterly provident in all things."

http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Fibonacci.html - Article on Fibonacci by J.J. O'Connor and E.F. Robertson at the School of Mathematics and Statistics of the University of St. Andrews, Scotland.
http://cedar.evansville.edu/~ck6/bstud/fibo.html - Article on Fibonacci by Clark Kimberling, professor of mathematics, University of Evansville

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