digplanet beta 1: Athena
Share digplanet:


Applied sciences






















For the number sequence, see Fibonacci number. For the Prison Break character, see Otto Fibonacci.
Portrait by unknown artist
Born c. 1170-75 in Pisa[1]
Died c. 1240 (aged around 70)
Most likely Pisa
Nationality Italian
Known for The Liber Abaci
Fibonacci number
The introduction of digital notation to Europe
Religion Catholic
Parents Guglielmo Bonacci

Leonardo Pisano Bigollo (c. 1170 – c. 1250)[2]—known as Fibonacci (Italian: [fiboˈnattʃi]), and also Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci—was an Italian mathematician, considered by some "the most talented Western mathematician of the Middle Ages."[3]

Fibonacci is best known to the modern world for[4] the spreading of the Hindu–Arabic numeral system in Europe, primarily through his composition in 1202 of Liber Abaci (Book of Calculation), and for a number sequence named the Fibonacci numbers after him, which he did not discover but used as an example in the Liber Abaci.[5]


Fibonacci was born around 1170 to Guglielmo Bonacci, a wealthy Italian merchant and, by some accounts, the consul for Pisa. Guglielmo directed a trading post in Bugia, a port in the Almohad dynasty's sultanate in North Africa. Fibonacci traveled with him as a young boy, and it was in Bugia (now Béjaïa, Algeria) that he learned about the Hindu–Arabic numeral system.[6]

Alternatively, according to a history text by mathematician Tobias Dantzig, his father was "a lowly shipping clerk nicknamed Bonaccio, which, in the idiom of the period, meant 'simpleton' ... hence 'Fibonacci,' the 'son of a simpleton.'"[7]

Recognizing that arithmetic with Hindu–Arabic numerals is simpler and more efficient than with Roman numerals, Fibonacci travelled throughout the Mediterranean world to study under the leading Arab mathematicians of the time. He returned from his travels in around 1200, and in 1202, the 32-year-old recorded what he had learned in Liber Abaci (Book of Abacus or Book of Calculation), and thereby popularized Hindu–Arabic numerals in Europe.

Fibonacci became a guest of Emperor Frederick II, who enjoyed mathematics and science. In 1240 the Republic of Pisa honored Fibonacci (referred to as Leonardo Bigollo)[8] by granting him a salary.

The date of Fibonacci's death is not known, but it has been estimated to be between 1240[9] and 1250,[10] most likely in Pisa.

Liber Abaci (1202)[edit]

A page of Fibonacci's Liber Abaci from the Biblioteca Nazionale di Firenze showing (in box on right) the Fibonacci sequence with the position in the sequence labeled in Roman numerals and the value in Hindu-Arabic numerals.
Main article: Liber Abaci

In the Liber Abaci (1202), Fibonacci introduced the so-called modus Indorum (method of the Indians), today known as Arabic numerals (Sigler 2003; Grimm 1973). The book advocated numeration with the digits 0–9 and place value. The book showed the practical importance of the new numeral system by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interest, money-changing, and other applications. The book was well received throughout educated Europe and had a profound impact on European thought.

Fibonacci sequence[edit]

Main article: Fibonacci number
19th century statue of Fibonacci in Camposanto, Pisa.

Liber Abaci also posed, and solved, a problem involving the growth of a population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. The number sequence was known to Indian mathematicians as early as the 6th century,[11][12][13] but it was Fibonacci's Liber Abaci that introduced it to the West.

In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers. Fibonacci began the sequence not with 0, 1, 1, 2, as modern mathematicians do but with 1,1, 2, etc. He carried the calculation up to the thirteenth place (fourteenth in modern counting), that is 233, though another manuscript carries it to the next place: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377.[14][15] Fibonacci did not speak about the golden ratio as the limit of the ratio of consecutive numbers in this sequence.


In the 19th century, a statue of Fibonacci was constructed and erected in Pisa. Today it is located in the western gallery of the Camposanto, historical cemetery on the Piazza dei Miracoli.[16]

There are many mathematical concepts named after Fibonacci, for instance because of a connection to the Fibonacci numbers. Examples include the Brahmagupta–Fibonacci identity, the Fibonacci search technique, and the Pisano period. Beyond mathematics, namesakes of Fibonacci include the asteroid 6765 Fibonacci and the art rock band The Fibonaccis.


See also[edit]


  1. ^ The Hindu-Arabic Numerals. David Eugene Smith and Louis Charles Karpinski, 1911: p.128
  2. ^ "The Fibonacci Series – Biographies – Leonardo Fibonacci (ca.1175 – ca.1240)". Library.thinkquest.org. Retrieved 2010-08-02. 
  3. ^ Howard Eves. An Introduction to the History of Mathematics. Brooks Cole, 1990: ISBN 0-03-029558-0 (6th ed.), p 261.
  4. ^ Leonardo Pisano – page 3: "Contributions to number theory". Encyclopædia Britannica Online, 2006. Retrieved 18 September 2006.
  5. ^ Parmanand Singh. "Acharya Hemachandra and the (so called) Fibonacci Numbers". Math. Ed. Siwan , 20(1):28–30, 1986. ISSN 0047-6269]
  6. ^ Dr R Knott: fibandphi (AT) ronknott DOT com. "Who was Fibonacci?". Maths.surrey.ac.uk. Retrieved 2010-08-02. 
  7. ^ Dantzig, Tobias (1983), Mathematics in Ancient Greece, Dover Publications,Inc., p. 113, ISBN 0-486-45347-2 .
  8. ^ See the incipit of Flos: "Incipit flos Leonardi bigolli pisani..." (quoted in the MS Word document Sources in Recreational Mathematics: An Annotated Bibliography by David Singmaster, 18 March 2004 – emphasis added), in English: "Here starts 'the flower' by Leonardo the wanderer of Pisa..."
    The basic meanings of "bigollo" appear to be "good-for-nothing" and "traveller" (so it could be translated by "vagrant", "vagabond" or "tramp"). A. F. Horadam contends a connotation of "bigollo" is "absent-minded" (see first footnote of "Eight hundred years young"), which is also one of the connotations of the English word "wandering". The translation "the wanderer" in the quote above tries to combine the various connotations of the word "bigollo" in a single English word.
  9. ^ Koshy, Thomas (2011), Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, p. 3, ISBN 9781118031315 .
  10. ^ Tanton, James Stuart (2005), Encyclopédia of Mathematics, Infobase Publishing, p. 192, ISBN 9780816051243 .
  11. ^ Susantha Goonatilake (1998). Toward a Global Science. Indiana University Press. p. 126. ISBN 978-0-253-33388-9. 
  12. ^ Donald Knuth (2006). The Art of Computer Programming: Generating All Trees – History of Combinatorial Generation; Volume 4. Addison-Wesley. p. 50. ISBN 978-0-321-33570-8. 
  13. ^ Rachel W. Hall. Math for poets and drummers. Math Horizons 15 (2008) 10–11.
  14. ^ Fibonacci Numbers from The On-Line Encyclopedia of Integer Sequences.
  15. ^ Il Liber Abbaci, 1857 edition, p. 231. Online at
  16. ^ "Fibonacci's Statue in Pisa". Epsilones.com. Retrieved 2010-08-02. 


  • Goetzmann, William N. and Rouwenhorst, K.Geert, The Origins of Value: The Financial Innovations That Created Modern Capital Markets (2005, Oxford University Press Inc, USA), ISBN 0-19-517571-9.
  • 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.

External links[edit]

Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Fibonacci — Please support Wikipedia.
This page uses Creative Commons Licensed content from Wikipedia. A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia.
363798 videos foundNext > 

Arthur Benjamin: The magic of Fibonacci numbers

Math is logical, functional and just ... awesome. Mathemagician Arthur Benjamin explores hidden properties of that weird and wonderful set of numbers, the Fi...

Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3]

Part 2: http://youtu.be/lOIP_Z_-0Hs Part 3: http://youtu.be/14-NdQwKz9w Re: Pineapple under the Sea: http://youtu.be/gBxeju8dMho My personal website, which y...

Fibonacci and the Golden Mean

Fibonacci and the Golden Mean.

Gods Fingerprint→ The Fibonacci Sequence - Golden Ratio and The Fractal Nature of Reality

Gods Fingerprint→ The Fibonacci Sequence - Golden Ratio and The Fractal Nature of Reality "Fibonacci numbers are of interest to biologists and physicists bec...

Learn the SECRET to Trading Fibonacci

Learn the secret to trading fibonacci. Most people screw it up. Forex, Futures, Stock trading, it doesn't matter. You can use fibonacci retracements and exte...

Fibonacci Mystery - Numberphile

Brady's view on people who write: "FIRST" - http://youtu.be/CmRh9tFYC68 Dr James Grime on the Pisano Period - a seemingly strange property of the Fibonacci S...

2. The Golden Ratio & Fibonacci Numbers: Fact versus Fiction

(October 8, 2012) Professor Keith Devlin dives into the topics of the golden ratio and fibonacci numbers. Originally presented in the Stanford Continuing Stu...

The Fibonacci Sequence: Nature's Code

Hank introduces us to the most beautiful numbers in nature - the Fibonacci sequence. Like SciShow: http://www.facebook.com/scishow Follow SciShow: http://www...

How to Trade with Fibonacci Levels

This recording is from the Atlanta Meetup group where we discussed Trading with Fibonacci levels. In the meetup, we covered the following topics with Fibonac...

Ancient Knowledge Pt.2 Fibonacci Sequence, Golden Ratio, Phi in Nature, DNA, Fingerprint of God

Solving ancient mysteries Part 2. "The Ancients" knew much more than given credit for regarding Life, The Universe, Astronomy, Advanced Mathematics, Magnetis...

363798 videos foundNext > 

26983 news items

Mon, 28 Jul 2014 00:12:32 -0700

Markets that switch from bullish to bearish on a weekly basis at the highs, often eventually correct to the downside and this has been the case for the DAX, divergence on weekly momentum supporting this view. Two key downside targets were broken last ...
Elliott Wave
Mon, 21 Jul 2014 13:04:22 -0700

Fibonacci numbers follow a sequence that begins with 0 and 1, and each subsequent number is the sum of the previous two (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on). After the first several numbers in the sequence, the ratio of any number to the next ...
Action Forex
Mon, 21 Jul 2014 03:52:30 -0700

Gold's Love Affair With Fibonacci. Gold is one of the most difficult assets to analyse from a fundamental point of view. There are so many variables that affect its price that for some it becomes almost impossible to have a strong conviction about the ...
Thu, 17 Jul 2014 12:11:48 -0700

-“Crude has retraced all of June and is nearing the May low (98.73) and 200 DMA. Expect a rally attempt from nearby levels.” Crude has turned sharply higher and is nearing its Fibonacci resistance zone of 103.32-104.33. The underside of former ...
Tue, 01 Jul 2014 12:00:14 -0700

The New Zealand Dollar is often an overlooked currency that has been making some big moves lately. Last week, it nearly broke post-float record highs against the US Dollar. We saw another surge earlier this morning, but the Kiwi has yet to make a ...
Thu, 03 Jul 2014 20:00:00 -0700

Fibonacci Retracements are best used when we have a large primary move in one direction, followed by a move back in the opposite direction (called a retracement.) Drawing Fibs from the GBPJPY high in July 2007 to the low in September 2011 creates 3 ...
Thu, 24 Jul 2014 04:03:45 -0700

Euro reached its target levels and take profit on my orders worked. However, considering that Franc may yet continue moving upwards (see charts below), then Euro also may reach several new minimums. In this case I decided to keep two sell order with ...
Tue, 22 Jul 2014 04:03:38 -0700

Euro is slowly getting closer to the group of lower fibo-levels at 1.3465 – 1.3455. It looks like price is going to reach its targets in the nearest future. If pair rebounds from them, Euro may start new and more serious correction. As we can see at H1 ...

Oops, we seem to be having trouble contacting Twitter

Talk About Fibonacci

You can talk about Fibonacci with people all over the world in our discussions.

Support Wikipedia

A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia. Please add your support for Wikipedia!