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Leonardo of Pisa (c. 1170 – c. 1250), also known as Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian
Italy

Italy , officially the Italian Republic , is a country located on the Italian Peninsula in Southern Europe and on the two largest islands in the Mediterranean Sea, Sicily and Sardinia....
 mathematician
Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
, considered by some "the most talented mathematician of the Middle Ages
Middle Ages

File:Karl 1 mit papst gelasius gregor1 sacramentar v karl d kahlen.jpgThe Middle Ages of European history are a period in history which lasted for roughly a millennium, commonly dated from the fall of the Roman Empire in the 5th century to the beginning of the Early Modern Period in the 16th century, marked by the division of Western Christi...
".

Fibonacci is best known to the modern world for:

ardo was born in Pisa, Italy in about 1170. His father Guglielmo was nicknamed Bonaccio ("good natured" or "simple").






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Leonardo of Pisa (c. 1170 – c. 1250), also known as Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian
Italy

Italy , officially the Italian Republic , is a country located on the Italian Peninsula in Southern Europe and on the two largest islands in the Mediterranean Sea, Sicily and Sardinia....
 mathematician
Mathematician

A mathematician is a person whose primary area of study and/or research is the field of mathematics....
, considered by some "the most talented mathematician of the Middle Ages
Middle Ages

File:Karl 1 mit papst gelasius gregor1 sacramentar v karl d kahlen.jpgThe Middle Ages of European history are a period in history which lasted for roughly a millennium, commonly dated from the fall of the Roman Empire in the 5th century to the beginning of the Early Modern Period in the 16th century, marked by the division of Western Christi...
".

Fibonacci is best known to the modern world for:
  • The spreading of the Hindu-Arabic numeral system
    Hindu-Arabic numeral system

    The Hindu-Arabic numeral system is a positional decimal numeral system first documented in ancient India no later than the ninth century, and later spread to the western world through Mathematics in medieval Islam....
     in Europe
    Europe

    Europe is, conventionally, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally divided from Asia to its east by the water divide of the Ural Mountains, the Ural , the Caspian Sea, and by the Caucasus Mountains to the southeast....
    , primarily through the publication in the early 13th century of his Book of Calculation, the Liber Abaci
    Liber Abaci

    Liber Abaci is a historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci. Its title has two common translations, The Book of the Abacus or The Book of Calculation....
    .
  • A number sequence
    Sequence

    In mathematics, a sequence is an ordered list of objects . Like a Set , it contains Element , and the number of terms is called the length of the sequence....
     named after him known as the Fibonacci number
    Fibonacci number

    In mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci . Fibonacci's 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been previously described in Indian mathematics....
    s, which he did not discover but used as an example in the Liber Abaci.


Biography

Leonardo was born in Pisa, Italy in about 1170. His father Guglielmo was nicknamed Bonaccio ("good natured" or "simple"). Leonardo's mother, Alessandra, died when he was nine years old. Leonardo was posthumously
Posthumous name

A posthumous name is an honorary name given to royalty, nobles, and sometimes others, in some cultures after the person's death. The posthumous name is commonly used when naming royalty of Table of Chinese monarchs, List of Korean monarchs, Vietnam and emperors of Japan....
 given the nickname Fibonacci (derived from filius Bonacci, meaning son of Bonaccio).

Guglielmo directed a trading post (by some accounts he was the consultant for Pisa) in Bugia
Bugia

Bugia is either:*A Spanish and Italian name of the presently Algerian port city of Bejaia*The Italian word for a candle, especially used as the name for an additional candle carried by a server standing beside a bishop at some Christian liturgical celebrations carried It is counted among the pontificalia....
, a port east of Algiers in the Almohad dynasty's sultanate in North Africa
North Africa

North Africa or Northern Africa is the northernmost region of the African continent, separated by the Sahara from Sub-Saharan Africa.Geopolitically, the United Nations subregion of Northern Africa includes the following seven countries or territories:...
 (now Bejaia
Béjaïa

B?ja?a or Bougie in Algerian Arabic) is a Mediterranean seaport on the Gulf of B?ja?a, capital of B?ja?a Province, northern Algeria. Under French colonial empires, it was formerly known under various European names, such as Budschaja in German, Bugia in Italian, and Bougie // ....
, Algeria
Algeria

Algeria , officially the People's Democratic Republic of Algeria, is a country located in North Africa. It is the largest country of the Mediterranean sea, second largest in the Arab World, and the second largest on the African continent and the eleventh-largest country in the world in terms of land area....
). As a young boy, Leonardo traveled there to help him. This is where he learned about the Hindu-Arabic numeral system.

Recognizing that arithmetic with Hindu-Arabic numerals is simpler and more efficient than with Roman numerals
Roman numerals

Roman numerals are a numeral system of ancient Rome based on letters of the alphabet, which are combined to signify the sum of their values. The system is decimal but not directly Positional notation and does not include a zero....
, Fibonacci traveled throughout the Mediterranean world to study under the leading Arab mathematicians of the time. Leonardo returned from his travels around 1200. In 1202, at age 32, he published what he had learned in Liber Abaci
Liber Abaci

Liber Abaci is a historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci. Its title has two common translations, The Book of the Abacus or The Book of Calculation....
 (Book of Abacus or Book of Calculation), and thereby introduced Hindu-Arabic numerals to Europe.

Leonardo became an amicable guest of the Emperor Frederick II
Frederick II, Holy Roman Emperor

Frederick II , of the House of Hohenstaufen dynasty, was an Kingdom of Italy pretender to the title of King of the Romans from 1212 and unopposed holder of that monarchy from 1215....
, who enjoyed mathematics and science. In 1240 the Republic of Pisa honoured Leonardo, referred to as Leonardo Bigollo, by granting him a salary.

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
Camposanto Monumentale

The Campo Santo Monumentale lies at the northern edge of the Piazza del Duomo, Pisa in Pisa, Italy."Campo Santo" can be literally translated as "holy field", because it is said to have been built around a shipload of sacred soil from Golgotha, brought back to Pisa from the Fourth Crusade by Ubaldo de' Lanfranchi, archbishop of Pisa in t...
, historical cemetery on the Piazza dei Miracoli.

Liber Abaci

In the Liber Abaci (1202), Fibonacci introduces 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
Numeral system

A numeral system is a writing system for expressing numerals , and a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
, using lattice multiplication and Egyptian fractions, by applying it to commercial bookkeeping
Bookkeeping

Bookkeeping is the recording of the value of assets, liabilities, income, and expenses in the daybooks, journals, and ledgers, in which debit and credit entries are chronologically posted to record changes in value....
, 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.

Liber Abaci also posed, and solved, a problem involving the growth of a hypothetical population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci number
Fibonacci number

In mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci . Fibonacci's 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been previously described in Indian mathematics....
s. The number sequence was known to Indian mathematicians as early as the 6th century, but it was Fibonacci's Liber Abaci that introduced it to the West.

Fibonacci sequence

In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers, starting with 0 and 1. Thus the sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 etc.

The higher up in the sequence, the closer two consecutive "Fibonacci numbers" of the sequence divided by each other will approach the golden ratio
Golden ratio

In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller....
 (approximately 1 : 1.618 or 0.618 : 1).

The golden ratio was used widely in the Renaissance in paintings.

In popular culture

  • Fibonacci's name was adopted by a Los Angeles
    Los Ángeles

    Los ?ngeles is the Capital of the Biob?o Province, in the municipality of the same name, in Regions of Chile VIII , in the center-south of Chile....
    -based art rock
    Art rock

    Art rock is a term describing a subgenre of rock music that tends to have "experimental music or avant garde music influences" and emphasizes "novel sonic texture."...
     group, The Fibonaccis
    The Fibonaccis

    The Fibonaccis were an art rock group from Los Angeles, California. The members were Magie Song , Ron Stringer , John Dentino , Joe Berardi , and Tom Corey ....
    , that recorded from 1982-1987.
  • Fibonacci and the Fibonacci number
    Fibonacci number

    In mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci . Fibonacci's 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been previously described in Indian mathematics....
    s are mentioned as a code to unlock a vessel in Dan Brown
    Dan Brown

    Dan Brown is an United States author of thriller fiction, best known for the 2003 bestselling novel, The Da Vinci Code and the 2000 bestselling novel, Angels & Demons....
    's best selling novel, The Da Vinci Code
    The Da Vinci Code

    The Da Vinci Code is a 2003 in literature Mystery -detective fiction fiction novel written by United States author Dan Brown and published by the Doubleday in the United States and Bantam Books in the United Kingdom....
    , and its movie adaptation
    The Da Vinci Code (film)

    The Da Vinci Code is a 2006 in film feature film, which is based on the bestselling 2003 novel The Da Vinci Code by Dan Brown. It was one of the most anticipated films of 2006, and was previewed at the opening night of the Cannes Film Festival on May 17, 2006....
    .
  • A youthful Fibonacci is one of the main characters in the novel Crusade in Jeans
    Crusade in Jeans

    Crusade in Jeans is a children's novel written by Thea Beckman. It contains a fictional account of the children's crusade of 1212, as witnessed by Dolf Vega, a boy from the 20th century....
     (1973). He was left out of the 2006 movie version
    Crusade in Jeans (film)

    Crusade in Jeans is a 2006 Netherlands film, an adaptation of the book Crusade in Jeans by Thea Beckman. The film was directed by Ben Sombogaart....
    , however.


Books written by Fibonacci

  • Liber Abaci
    Liber Abaci

    Liber Abaci is a historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci. Its title has two common translations, The Book of the Abacus or The Book of Calculation....
     (1202), a book on calculations (English translation by Laurence Sigler, Springer, 2002)
  • Practica Geometriae (1220), a compendium on geometry
    Geometry

    Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
     and trigonometry
    Trigonometry

    Trigonometry is a branch of mathematics that deals with triangle s, particularly those plane triangles in which one angle has 90 degrees . Trigonometry deals with relationships between the sides and the angles of triangles and with the trigonometric functions, which describe those relationships....
    .
  • Flos
    Flos

    Flos is also the name of a mathematical work by Fibonacci.Flos is a genus of butterfly in the family Lycaenidae....
     (1225), solutions to problems posed by Johannes of Palermo
    Palermo

    Palermo is a historic city in southern Italy, the Capital of the autonomous region Sicily and the province of Palermo. The city is noted for its rich history, culture, architecture and gastronomy, playing an important role throughout much of its existence; it is over 2,700 years old....
  • Liber quadratorum, ("The Book of Squares
    The Book of Squares

    The Book of Squares is a book on algebra by Leonardo Fibonacci, published in 1225. Brahmagupta-Fibonacci identity, establishing that the set of all sums of two squares is closed under multiplication, appears in it....
    ") on Diophantine equation
    Diophantine equation

    In mathematics, a Diophantine equation is an indeterminate equation polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations....
    s, dedicated to Emperor Frederick II
    Frederick II, Holy Roman Emperor

    Frederick II , of the House of Hohenstaufen dynasty, was an Kingdom of Italy pretender to the title of King of the Romans from 1212 and unopposed holder of that monarchy from 1215....
    . See in particular Fibonacci's identity
    Fibonacci's identity

    In mathematics, the term Fibonacci's identity may refer either to* the Brahmagupta?Fibonacci identity in algebra, showing that the set of all sums of two squares is closed under multiplication; or to...
    .
  • Di minor guisa (on commercial arithmetic; lost)
  • Commentary on Book X of Euclid
    Euclid

    Euclid , floruit 300 BC, also known as Euclid of Alexandria, was a Greek mathematics and is often referred to as the Father of Geometry. He was active in Alexandria during the reign of Ptolemy I ....
    's Elements     (lost)


See also

  • Acharya Hemachandra
    Acharya Hemachandra

    Hemachandra Acharya was an Indian Jainism scholar, poet, and polymath who wrote on grammar, philosophy, prosody, and contemporary history. Noted as a prodigy by his contemporaries, he gained the title Kalikal Sarvagya, ....
  • Brahmagupta–Fibonacci identity
  • Carmichael's theorem
    Carmichael's theorem

    Carmichael's theorem, named after the USA mathematician Robert Daniel Carmichael, states that for n greater than 12, the nth Fibonacci number F has at least one prime number factor that is not a factor of any earlier Fibonacci number....
  • Casey Mongoven
    Casey Mongoven

    Casey Patrick Mongoven is an American composer who works with Fibonacci numbers and the golden ratio....
  • Egyptian fraction
    Egyptian fraction

    An Egyptian fraction is the sum of distinct unit fractions, such as . That is, each Fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other....
  • Elliott wave principle
    Elliott wave principle

    The Elliott wave principle is a form of technical analysis that attempts to forecast market trends in the financial markets and other collective activities....
  • Engel expansion
    Engel expansion

    The Engel expansion of a positive real number x is the unique non-decreasing sequence of natural numbers such thatRational numbers have a finite Engel expansion, while irrational numbers have an infinite Engel expansion....
  • Fibonacci coding
    Fibonacci coding

    In mathematics, Fibonacci coding is a universal code which encodes positive integers into binary code words. All tokens end with "11" and have no "11" before the end....
  • Fibonacci heap
    Fibonacci heap

    In computer science, a Fibonacci heap is a Heap consisting of a forest of trees. It has a better amortized analysis running time than a binomial heap....
  • Fibonacci prime
    Fibonacci prime

    A Fibonacci prime is a Fibonacci number that is prime number.The first Fibonacci primes are :...
  • Fibonacci search technique
    Fibonacci search technique

    The Fibonacci search technique is a method of searching a sorted array using a divide and conquer algorithm that narrows down possible locations with the aid of Fibonacci numbers....
  • Golden ratio
    Golden ratio

    In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller....
  • Hylomorphism (computer science)
    Hylomorphism (computer science)

    In computer science, and in particular functional programming, a hylomorphism is a recursive function, corresponding to the function composition of an anamorphism and a catamorphism ....
  • Lagged Fibonacci generator
    Lagged Fibonacci generator

    A Lagged Fibonacci generator is an example of a pseudorandom number generator. This class of random number generator is aimed at being an improvement on the 'standard' linear congruential generator....
  • Lucas number
    Lucas number

    The Lucas numbers are an integer sequence named after the mathematician Fran?ois ?douard Anatole Lucas , who studied both that sequence and the closely related Fibonacci numbers ....
  • Negafibonacci
    Negafibonacci

    DefinitionIn mathematics, negaFibonacci numbers are the negatively indexed elements of the Fibonacci sequence.The negaFibonacci numbers are defined inductively by the recurrence relation:...
  • NegaFibonacci coding
    NegaFibonacci coding

    In mathematics, negaFibonacci coding is a universal code which encodes integers into binary code words. It is similar to Fibonacci coding, except that it allows both positive and negative integers to be represented....
  • Pisano period
    Pisano period

    In mathematics, the nth Pisano period, written p, is the periodic function with which the sequence of Fibonacci numbers, modular arithmetic n repeats....
  • Practical number
    Practical number

    In mathematics, and in particular number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n....
  • Primefree sequence
    Primefree sequence

    In mathematics, a primefree sequence is a sequence of integers that does not contain any prime numbers. More specifically, it generally means a Fibonacci number-like sequence with composite number but coprime initial terms that is infinite but contains no primes....
  • Reciprocal Fibonacci constant
    Reciprocal Fibonacci constant

    The reciprocal Fibonacci constant, or ?, is defined as the sum of the Reciprocal s of the Fibonacci numbers:The ratio of successive terms in this sum tends to the reciprocal of the golden ratio....
  • Verner Emil Hoggatt, Jr.
    Verner Emil Hoggatt, Jr.

    Verner Emil Hoggatt, Jr. was an United States mathematician, known mostly for his work in Fibonacci numbers and number theory.Hogatt received a Ph.D....
  • Virahanka
    Virahanka

    Virahanka was an Indian prosody who is also known for his work on mathematics. He possibly lived in the 6th century AD, but it is also possible that this date may be as late as 8th century....
  • Viswanath's constant
    Viswanath's constant

    A random Fibonacci sequence is a variant of the Fibonacci sequence, defined by the recurrence relation fn = ±fn-1 ± fn-2 with the signs chosen randomly....
  • Zeckendorf's theorem
    Zeckendorf's theorem

    Zeckendorf's theorem, named after Belgium mathematician Edouard Zeckendorf, is a theorem about the representation of integers as sums of Fibonacci numbers....


Bibliography

  • 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 0195175719.
  • 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

  • by Ron Knott.
  • Goetzmann, William N., Fibonacci and the Financial Revolution (October 23, 2003), Yale School of Management
    Yale School of Management

    The Yale School of Management is the graduate business school of Yale University and is located on Hillhouse Avenue in New Haven, Connecticut, Connecticut, United States....
     International Center for Finance Working Paper No. 03-28
  • Charles Burnett, - the Medieval background to Fibonacci's work
  • at
  • wallstreetcosmos.com, , (2008).
  • and . in . University of St Andrews
    University of St Andrews

    The University of St Andrews is the List of oldest universities in continuous operation university in Scotland and third oldest in the English-speaking world, having been founded between 1410 and 1413....
     website, Scotland, 1998.