FIBONACCI (c. 1175 – c. 1250) was an Italian mathematician from
the Republic of
**Pisa**

Pisa , considered to be "the most talented Western
mathematician of the
**Middle Ages** ". The name he is commonly called,
"Fibonacci" (Italian: ), was made up in 1838 by the French historian
Guillaume Libri and is short for "filius Bonacci" ("son of (the)
Bonacci") and he is also known as LEONARDO BONACCI, LEONARDO OF PISA,
LEONARDO PISANO BIGOLLO, or LEONARDO FIBONACCI.

**Fibonacci**

Fibonacci popularized the
**Hindu–Arabic numeral system**

Hindu–Arabic numeral system in the
Western World primarily through his composition in 1202 of Liber
Abaci (Book of Calculation). He also introduced Europe to the
sequence of
**Fibonacci**

Fibonacci numbers , which he used as an example in Liber
Abaci.

CONTENTS

* 1 History
* 2
**Liber Abaci**

Liber Abaci (1202)
* 3
**Fibonacci**

Fibonacci sequence
* 4 Legacy
* 5 Works
* 6 See also
* 7 References
* 8 Further reading
* 9 External links

HISTORY

**Fibonacci**

Fibonacci was born around 1175 to Guglielmo, 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**

Almohad dynasty 's
sultanate in
**North Africa** .
**Fibonacci**

Fibonacci travelled with him as a young
boy, and it was in Bugia (now
**Béjaïa**

Béjaïa ,
**Algeria**

Algeria ) that he learned
about the
**Hindu–Arabic numeral system**

Hindu–Arabic numeral system .

**Fibonacci**

Fibonacci travelled extensively around the
**Mediterranean**

Mediterranean coast,
meeting with many merchants and learning about their systems of doing
arithmetic. He soon realised the many advantages of the Hindu-Arabic
system. In 1202, he completed the
**Liber Abaci**

Liber Abaci (Book of
**Abacus**

Abacus or Book
of Calculation) which popularized Hindu–Arabic numerals in Europe.

**Fibonacci**

Fibonacci became a guest of Emperor Frederick II , who enjoyed
mathematics and science. In 1240, the Republic of
**Pisa**

Pisa honored
**Fibonacci**

Fibonacci (referred to as Leonardo Bigollo) by granting him a salary
in a decree that recognized him for the services that he had given to
the city as an advisor on matters of accounting and instruction to
citizens.

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

LIBER ABACI (1202)

A page of Fibonacci's
**Liber Abaci**

Liber Abaci from the Biblioteca Nazionale
di Firenze showing (in box on right) the
**Fibonacci**

Fibonacci sequence with the
position in the sequence labeled in Roman numerals and the value in
Hindu-Arabic numerals. Main article:
**Liber Abaci**

Liber Abaci

In the
**Liber Abaci**

Liber Abaci (1202),
**Fibonacci**

Fibonacci introduced the so-called modus
Indorum (method of the Indians), today known as the Hindu–Arabic
numeral system . The book advocated numeration with the digits
0–9 and place value . The book showed the practical use and value of
the new Hindu-Arabic numeral system by applying the numerals to
commercial bookkeeping , converting weights and measures, calculation
of interest, money-changing, and other applications. The book was
well-received throughout educated Europe and had a profound impact on
European thought. No copies of the 1202 edition are known to exist.

The 1228 edition, first section introduces the Hindu-Arabic numeral
system and compares the system with other systems, such as Roman
numerals, and methods to convert the other numeral systems into
Hindu-Arabic numerals. Replacing the Roman numeral system, its ancient
Egyptian multiplication method, and using an abacus for calculations,
with a Hindu-Arabic numeral system was an advance in making business
calculations easier and faster, which led to the growth of banking and
accounting in Europe.

The second section explains the uses of Hindu-Arabic numerals in
business, for example converting different currencies, and calculating
profit and interest, which were important to the growing banking
industry. The book also discusses irrational numbers and prime numbers
.

FIBONACCI SEQUENCE

Main article:
**Fibonacci number**

Fibonacci number

**Liber Abaci**

Liber Abaci 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**

Fibonacci numbers . Although Fibonacci's
**Liber Abaci**

Liber Abaci contains the
earliest known description of the sequence outside of India, the
sequence had been noted by Indian mathematicians as early as the sixth
century.

In the
**Fibonacci**

Fibonacci sequence of numbers, each number is the sum of the
previous two numbers.
**Fibonacci**

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.
**Fibonacci**

Fibonacci did not speak about the golden ratio as the limit of the
ratio of consecutive numbers in this sequence.

LEGACY

Monument of Leonardo da
**Pisa**

Pisa (Fibonacci), by Giovanni Paganucci,
completed in 1863, in the Camposanto di
**Pisa**

Pisa .

In the 19th century, a statue of
**Fibonacci**

Fibonacci was constructed and raised
in Pisa. Today it is located in the western gallery of the Camposanto
, historical cemetery on the
**Piazza dei Miracoli**

Piazza dei Miracoli .

In 1877, Éduouard Lucas paid tribute to
**Fibonacci**

Fibonacci by naming the
**Fibonacci**

Fibonacci Sequence in his honor.

There are many mathematical concepts named after
**Fibonacci**

Fibonacci because of
a connection to the
**Fibonacci**

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 .

WORKS

*
**Liber Abaci**

Liber Abaci (1202), a book on calculations (English translation
by Laurence Sigler, 2002)
* Practica Geometriae (1220), a compendium of techniques in
surveying , the measurement and partition of areas and volumes , and
other topics in practical geometry (English translation by Barnabas
Hughes, Springer, 2008).
* Flos (1225), solutions to problems posed by Johannes of Palermo
* Liber Quadratorum ("
**The Book of Squares** ") on Diophantine
equations , dedicated to Emperor Frederick II . See in particular
congruum and the
**Brahmagupta–Fibonacci identity** .
* Di minor guisa (on commercial arithmetic; lost)
* Commentary on Book X of Euclid\'s Elements (lost)

SEE ALSO

*
**Adelard of Bath**

Adelard of Bath
*
**Fibonacci numbers in popular culture**
* Republic of
**Pisa**

Pisa

REFERENCES

* ^ Smith, David Eugene; Karpinski, Louis Charles (1911), The
Hindu-Arabic Numerals, Boston and London: Ginn and Company, p. 128 .
* ^ A B C D E F G H "
**Fibonacci**

Fibonacci – Medieval Mathematics – The
Story of Mathematics". www.storyofmathematics.com. Retrieved
2017-11-18.
* ^ A B C Knott, R. "Who was Fibonacci?". Maths.surrey.ac.uk.
Retrieved 2010-08-02.
* ^ Eves, Howard . An Introduction to the History of Mathematics.
Brooks Cole, 1990: ISBN 0-03-029558-0 (6th ed.), p 261.
* ^ "Fibonacci." Collins English Dictionary – Complete and
Unabridged, 12th Edition 2014. 1991, 1994, 1998, 2000, 2003, 2006,
2007, 2009, 2011, 2014. HarperCollins Publishers 23 Jun. 2017
http://www.thefreedictionary.com/Fibonacci
* ^ Kieth Devllin "Finding Fibonacci" Princeton Univertsity Press
2017 pg 24
* ^
**Keith Devlin**

Keith Devlin , The Man of Numbers: Fibonacci's Arithmetic
Revolution,A&C Black, 2012 p.13.
* ^ "
**Fibonacci**

Fibonacci Numbers". www.halexandria.org.
* ^ Leonardo Pisano – page 3: "Contributions to number theory".
**Encyclopædia Britannica**

Encyclopædia Britannica Online, 2006. Retrieved 18 September 2006.
* ^ Singh, Parmanand. "Acharya Hemachandra and the (so called)
**Fibonacci**

Fibonacci Numbers". Math. Ed. Siwan , 20(1):28–30, 1986. ISSN
0047-6269]

* ^ See the incipit of Flos: "Incipit flos Leonardi BIGOLLI
pisani..." (quoted in the
**MS Word**

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.
* ^
**Keith Devlin**

Keith Devlin (7 November 2002). "A man to count on". The
Guardian. Retrieved 7 June 2016.
* ^ Koshy, Thomas (2011),
**Fibonacci**

Fibonacci and Lucas Numbers with
Applications, John Wiley & Sons, p. 3, ISBN 9781118031315 .
* ^ Tanton, James Stuart (2005), Encyclopédia of Mathematics,
Infobase Publishing, p. 192, ISBN 9780816051243 .
* ^ A B Sigler, Laurence E. (trans.) (2002), Fibonacci's Liber
Abaci, Springer-Verlag, ISBN 0-387-95419-8
* ^ Grimm 1973
* ^ A B Gordon, John Steele . "The Man Behind Modern Math".
Retrieved 2015-08-28.
* ^ A B "Fibonacci: The Man Behind The Math". NPR.org. Retrieved
2015-08-29.
* ^ A B Devlin, Keith. "The Man of Numbers: Fibonacci\'s Arithmetic
Revolution ". Retrieved 2015-08-29.
* ^ Singh, Pamanand (1985). "The so-called fibonacci numbers in
ancient and medieval India". Historia Mathematica. 12: 229–244. doi
:10.1016/0315-0860(85)90021-7 .
* ^ Goonatilake, Susantha (1998). Toward a Global Science. Indiana
University Press. p. 126. ISBN 978-0-253-33388-9 .
* ^ Knuth, Donald (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 .
* ^ Hall, Rachel W. Math for poets and drummers. Math Horizons 15
(2008) 10–11.
* ^
**Fibonacci**

Fibonacci Numbers from The On-Line Encyclopedia of Integer
Sequences.
* ^ Pisanus, Leonardus; Boncompagni, Baldassarre (1 January 1857).
Scritti: Il Liber Abbaci. Tip. delle Scienze Fisiche e Matematiche. p.
231 – via Google Books.
* ^ "Fibonacci\'s Statue in Pisa". Epsilones.com. Retrieved
2010-08-02.

FURTHER READING

* Devlin, Keith (2012). The Man of Numbers: Fibonacci's Arithmetic
Revolution. Walker Books. ISBN 978-0802779083 .
* 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 .
* Goetzmann, William N.,
**Fibonacci**

Fibonacci and the Financial Revolution
(October 23, 2003),
**Yale School of Management**

Yale School of Management International Center for
Finance Working Paper No. 03–28
* Grimm, R. E., "The Autobiography of Leonardo Pisano", Fibonacci
Quarterly , Vol. 11, No. 1, February 1973, pp. 99–104.
* Horadam, A. F. "Eight hundred years young," The Australian
Mathematics Teacher 31 (1975) 123–134.
* Gavin, J., Schärlig, A., extracts of
**Liber Abaci**

Liber Abaci online and
analyzed on BibNum

EXTERNAL LINKS

**Wikisource**

Wikisource has the text of