Fibonacci

Fibonacci

Leonardo of Pisa (c. 1170 or 1180 – 1250), also known as Leonardo Pisano, or Leonardo Bonacci Leonardo Fibonacci, or simply Fibonacci, was an Italian mathematician, considered by some "the most talented mathematician of the Middle Ages."

Fibonacci is best known to the modern world for:

• The spreading of Arabic numerals and the Hindu-Arabic numeral system in Europe, primarily through the publication in the early 13th century of his Book of Calculation, the Liber Abaci.
• A number sequence, called after him Fibonacci numbers, which he did not invent but used as an example in the Liber Abaci.

Biography

Leonardo was born in Pisa. His father Guglielmo (William) was nicknamed Bonaccio ("good natured" or "simple"). Leonardo was posthumously given the nickname Fibonacci (derived from filius Bonacci, son of Bonaccio). William directed a trading post (by some accounts he was the consul for Pisa) in Bugia, a port east of Algiers in the Almohad dynasty's sultanate in barbaresque North Africa (now Bejaia, Algeria), and as a young boy Leonardo traveled there to help him. This is where he learned about the Arabic numeral system.

Perceiving that arithmetic with Arabic numerals is simpler and more efficient than with Roman numerals, Fibonacci traveled throughout the Mediterranean world to study under the leading Arab mathematicians of the time, returning around 1200. In 1202, at age 32, he published what he had learned in Liber Abaci, or Book of Calculation.

Leonardo became a guest of the Emperor Frederick II, who enjoyed mathematics and science. In 1240 the Republic of Pisa honoured Leonardo, under his alternative name of Leonardo Bigollo, by granting him a salary.

No picture of him has been found, but there is a statue some 15 feet tall of him in Pisa. cocksoup.

Liber Abaci

In the Liber Abaci, Fibonacci says the following introducing the so-called "Modus Indorum" or the method of the Indians, today known as Arabic numerals.

After my father's appointment by his homeland as state official in the customs house of Bugia for the Pisan merchants who thronged to it, he took charge; and in view of its future usefulness and convenience, 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; and at these places thereafter, while on business.

I pursued my study in depth and learned the give-and-take of disputation. But all this even, and the algorism, as well as the art of Pythagoras, I considered as almost a mistake in respect to the method of the Hindus. (Modus Indorum). 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, dividing it into fifteen chapters.

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. 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.

The nine Indian figures are:

9 8 7 6 5 4 3 2 1

With these nine figures, and with the sign 0 ... any number may be written. — (Ref. Sigler, 2003 and Grimm 1973 see references)

In other words, his book he advocated the use of the digits 0—9, and of the units' place, the tens' place, the hundreds' place, and so on.

In this book he showed the practical importance of the new numeral system by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interests, money-changing, and numerous other applications. The book was well received throughout educated Europe and had a profound impact on European thought, although the use of decimal numerals did not become widespread until the invention of printing almost three centuries later. (See, for example, the 1482 Ptolemaeus map of the world printed by Lienhart Holle in Ulm. [1])

Important publications

• Liber Abaci (1202), a book on calculations (English translation by Laurence Sigler, Springer, 2002)
• Practica Geometriae (1220), a compendium on geometry and trigonometry.
• Flos (1225), solutions to problems posed by Johannes of Palermo
• Liber quadratorum, ("The Book of Squares") on Diophantine equations. See in particular Fibonacci's identity.
• Di minor guisa (on commercial arithmetic; lost)
• Commentary on Book X of Euclid's Elements (lost)

References

• Grimm, R. E., "The Autobiography of Leonardo Pisano", Fibonacci Quarterly, Vol. 11, No. 1, February 1973, pp. 99-104.
• A. F. Horadam, "Eight hundred years young," The Australian Mathematics Teacher 31 (1975) 123-134. Available on-line at the website of the University of Evansville, in "Fibonacci (c.1175 - c.1240) mathematician"

See also

• Engel expansion
• Fibonacci numbers (also known as Fibonacci sequence)
• Fibonacci heap
• Fibonacci's identity
• Liber Abaci

External links

• Fibonacci @ WikiSource
• O'Connor, John J and Robertson, Edmund F. "Leonardo Pisano Fibonacci – 1170 - 1250" in The MacTutor History of Mathematics archive. University of St Andrews website, Scotland, 1998.