*bonacci*

*This nOde last updated December 30th, 2006 and is permanently morphing…*

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Fibonacci sequence noun

The sequence of numbers, 1, 1, 2, 3, 5, 8, 13, . . . , in which each successive number is equal to the sum of the two preceding numbers.

[After Leonardo Fibonacci (died c. 1250), Italian mathematician.]

Fibonacci, Leonardo (fêbonät´chê), ; b. c.1170, d. after 1240; Italian mathematician, known also as Leonardo da Pisa. The Fibonacci SEQUENCE 0, 1, 1, 2, 3, 5, 8, 13, 21, … , in which each term is the sum of the two preceding terms, occurs in higher mathematics in various connections.

Fibonacci numbers

Fibonacci numbers (fib-e-nä’chê num`berz) noun

In mathematics, an infinite series in which each successive integer is the sum of the two that precede it- for example, 1, 1, 2, 3, 5, 8, 13, 21, 34…. Fibonacci numbers are named for the thirteenth-century mathematician Leonardo Fibonacci. In computing, Fibonacci numbers are used to speed binary searches by repeatedly dividing a set of data into groups in accordance with successively smaller pairs of numbers in the Fibonacci sequence. For example, a data set of 34 items would be divided into one group of 21 and another of 13. If the item being sought were in the group of 13, the group of 21 would be discarded, and the group of 13 would be divided into 5 and 8; the search would continue until the item was located. The ratio of two successive terms in the Fibonacci sequence converges on the Golden Ratio, a “magic number” that seems to represent the proportions of an ideal rectangle. The number describes many things, from the curve of a nautilus shell to the proportions of playing cards or, intentionally, the Parthenon, in Athens, Greece.

Fibonacci, Leonardo

Fibonacci, Leonardo or Leonardo of Pisa (1170?-1240?), Italian mathematician, who compiled and supplemented the mathematical knowledge of classical, Arabic, and Indian cultures, and contributed to algebra and number theory. Born in Pisa, Fibonacci was about 20 when he went to Algeria, where he began to learn Indian numerals and Arabic calculating methods. Fibonacci used this experience to improve on the commercial computing techniques he knew and to extend the work of classical mathematical writers, such as Greek mathematicians Diophantus and Euclid. His writings on recreational mathematics became classic mental challenges and often involved the summation of recurrent series, such as the Fibonacci series.

Science, 1202

Liber Abaci by Italian traveler-mathematician Leonardo Fibonacci (Leonardo da Pisa) introduces Europe to Arabic numerals from North Africa and the zero from India, making calculation much easier than with Roman numerals.

First off, the system we use is not the Arabic system as many of us like to believe. It is the Hindu system. We refer to it as Arabic because Europe got the numerals from the Islamic world, which it sweepingly referred to as Arabic.

The switch took place in the Middle Ages, propelled by a book by the mathematician Leonardo Fibonacci in which

he discusses the merits of the Hindu numeral system. What you need to remember is that Islam was a more powerful culture, one that was more scientifically advanced than European civilizations after the fall of the Western Roman Empire. The Hindu numeral system promised the ability to understand Islamic mathematics.

The Hindus also invented the number zero. This was one of the greatest achievements in mathematical history.

Leonardo of Pisa or Leonardo Pisano (c. 1175 – 1250), also known as Fibonacci, was an Italian mathematician and is best known for the invention of the Fibonacci numbers and his role in the introduction of the modern positional base-10 system for writing numbers to Europe.

Leonardo’s father Guilielmo (William) was nicknamed Bonacci (‘good natured’ or ‘simple’). Leonardo was posthumously given the nickname Fibonacci (for filius Bonacci, son of Bonacci). William directed a trading post (by some accounts he was the consul for Pisa) in Bugia, North Africa (now Bejaia, Algeria), and as a young boy Leonardo traveled there to help him. There he learnt from the Arabic numeral system.

Perceiving the superiority of these Arabic numerals, Fibonacci travelled throughout the Mediterranean world to study under the leading Arab mathematicians of the time, returning around 1200. In 1202, at age 27, he published what he had learned in Liber Abaci, or Book of Calculation. This book showed the practical importance of the new number 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 enthusiastically received throughout educated Europe and had a profound impact on European thought.

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.

- King’s Chamber in the Great Pyramid in Egypt
- plants

- isolationist ambient track _Fibonacci Express_ MP3 (192k) by Pluramon off of _Render Bandits_ CD on Mille Plateaux #051 (1998)

- track _Fibonacci’s Curve_ MP3 (192k) by Passarani 2099 off of _Ancient Technology_ 12″ on Nature (1999)
- track _Fibonacci Sequence_ MP3 by BT
- nodes
- Golden Mean