FIBONACCI (c. 1175 – c. 1250) was a mathematician from the
Republic of
**Pisa** in what is now
**Italy** , 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** popularized the
**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** numbers , which he used as an example in _Liber
Abaci_.

CONTENTS

* 1 History
* 2 _Liber Abaci_ (1202)
* 3
**Fibonacci** sequence
* 4 Legacy
* 5 Works
* 6 See also
* 7 References
* 8 Further reading
* 9 External links

HISTORY

**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** 's
sultanate in
**North Africa** .
**Fibonacci** travelled with him as a young
boy, and it was in Bugia (now
**Béjaïa** ,
**Algeria** ) that he learned
about the
**Hindu–Arabic numeral system** .

**Fibonacci** travelled extensively around the
**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** _ (_Book of Abacus_ or
_Book of Calculation_) which 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) 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** _ 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 Hindu-Arabic
numerals. The book advocated numeration with the digits 0–9 and
place value . The book showed the practical use and value of the new
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 Arabic numeral system
and compares the system with other systems, such as Roman numerals,
and methods to convert the other numeral systems into Arabic numerals.
Replacing the Roman numeral system, its ancient Egyptian
multiplication method, and using an abacus for calculations, with an
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 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**

_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** numbers . Although Fibonacci's _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** 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.
**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** (Fibonacci), by Giovanni Paganucci,
completed in 1863, in the Camposanto di
**Pisa** .

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

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

WORKS

* _
**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

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

REFERENCES

* ^ Smith, David Eugene; Karpinski, Louis Charles (1911), _The
Hindu-Arabic Numerals_, Boston and London: Ginn and Company, p. 128 .
* ^ _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** , _The Man of Numbers: Fibonacci's Arithmetic
Revolution,_A&C Black, 2012 p