Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an

Italian Italian(s) may refer to: * Anything of, from, or related to the people of Italy over the centuries ** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom ** Italian language, a Romance language *** Regional Ita ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

from the

Republic of Pisa The Republic of Pisa ( it, Repubblica di Pisa) was an independent state centered on the Tuscan city of Pisa, which existed from the 11th to the 15th century. It rose to become an economic powerhouse, a commercial center whose merchants dominated ...

, considered to be "the most talented Western mathematician of the

Middle Ages In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire ...

". The name he is commonly called, ''Fibonacci'', was made up in 1838 by the Franco-Italian historian Guillaume Libri and is short for ('son of Bonacci'). However, even earlier in 1506 a notary of the Holy Roman Empire, Perizolo mentions Leonardo as "Lionardo Fibonacci". Fibonacci popularized the Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of ''

Liber Abaci ''Liber Abaci'' (also spelled as ''Liber Abbaci''; "The Book of Calculation") is a historic 1202 Latin manuscript on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci. ''Liber Abaci'' was among the first Western books to describe ...

'' (''Book of Calculation''). He also introduced Europe to the sequence of

Fibonacci number In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...

s, which he used as an example in ''Liber Abaci''.

Biography

Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official. Guglielmo directed a trading post in Bugia (Béjaïa) in modern-day Algeria), the capital of the

Hammadid empire The Hammadid dynasty () was a branch of the Sanhaja Berber dynasty that ruled an area roughly corresponding to north-eastern modern Algeria between 1008 and 1152. The state reached its peak under Nasir ibn Alnas during which it was briefly the m ...

. Fibonacci travelled with him as a young boy, and it was in Bugia (Algeria) where he was educated that he learned about the

Hindu–Arabic numeral system The Hindu–Arabic numeral system or Indo-Arabic numeral system Audun HolmeGeometry: Our Cultural Heritage 2000 (also called the Hindu numeral system or Arabic numeral system) is a positional decimal numeral system, and is the most common syste ...

. Fibonacci travelled around the

Mediterranean The Mediterranean Sea is a sea connected to the Atlantic Ocean, surrounded by the Mediterranean Basin and almost completely enclosed by land: on the north by Western Europe, Western and Southern Europe and Anatolia, on the south by North Africa ...

coast, meeting with many merchants and learning about their systems of doing arithmetic. He soon realised the many advantages of the Hindu-Arabic system, which, unlike the Roman numerals used at the time, allowed easy calculation using a

place-value system Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the ...

. In 1202, he completed the ''

'' (''Book of Abacus'' or ''The Book of Calculation''), which popularized Hindu–Arabic numerals in Europe. Fibonacci was a guest of Emperor Frederick II, who enjoyed mathematics and science. A member of Frederick II's court,

John of Palermo John of Palermo () was a translator of mathematical works from Arabic to Latin who lived in Palermo, Sicily. He worked in the court of Emperor Frederick II. It is not known if he was an Arab or a Sicilian. John had been introduced into the court of ...

, posed several questions based on Arab mathematical works for Fibonacci to solve. In 1240, the

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. Fibonacci is thought to have died between 1240 and 1250, in Pisa.

''Liber Abaci''

In the ''Liber Abaci'' (1202), Fibonacci introduced the so-called ''modus Indorum'' (method of the

India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...

ns), today known as the

, with ten digits including a

zero 0 (zero) is a number representing an empty quantity. In place-value notation such as the Hindu–Arabic numeral system, 0 also serves as a placeholder numerical digit, which works by multiplying digits to the left of 0 by the radix, usual ...

and positional notation. The book showed the practical use and value of this 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. Replacing Roman numerals, its

ancient Egyptian multiplication In mathematics, ancient Egyptian multiplication (also known as Egyptian multiplication, Ethiopian multiplication, Russian multiplication, or peasant multiplication), one of two multiplication methods used by scribes, is a systematic method for mul ...

method, and using an

abacus The abacus (''plural'' abaci or abacuses), also called a counting frame, is a calculating tool which has been used since ancient times. It was used in the ancient Near East, Europe, China, and Russia, centuries before the adoption of the Hi ...

for calculations, was an advance in making business calculations easier and faster, which assisted the growth of

banking A bank is a financial institution that accepts deposits from the public and creates a demand deposit while simultaneously making loans. Lending activities can be directly performed by the bank or indirectly through capital markets. Becau ...

and accounting in Europe. The original 1202 manuscript is not known to exist. In a 1228 copy of the manuscript, the first section introduces the numeral system and compares it with others, such as Roman numerals, and methods to convert numbers to it. The second section explains uses 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 In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two inte ...

and prime numbers.

Fibonacci sequence

''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

s. Although Fibonacci's ''Liber Abaci'' contains the earliest known description of the sequence outside of India, the sequence had been described by Indian mathematicians as early as the sixth century. In the Fibonacci sequence, each number is the sum of the previous two numbers. Fibonacci omitted the "0" and first "1" included today and began the sequence with 1, 2, 3, ... . He carried the calculation up to the thirteenth place, the value 233, though another manuscript carries it to the next place, the value 377. Fibonacci did not speak about the

golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( ...

as the limit of the ratio of consecutive numbers in this sequence.

Legacy

In the 19th century, a statue of Fibonacci was set in Pisa. Today it is located in the western gallery of the

Camposanto Camposanto ( Modenese: ; Mirandolese: ) is a ''comune'' (municipality) in the Province of Modena in the Italian region Emilia-Romagna, located about northwest of Bologna and about northeast of Modena on the Panaro river. Although the name in ...

, historical cemetery on the

Piazza dei Miracoli The Piazza dei Miracoli (; en, Square of Miracles), formally known as Piazza del Duomo ( en, Cathedral Square), is a walled 8.87-hectare area located in Pisa, Tuscany, Italy, recognized as an important centre of European medieval art and one of ...

. There are many mathematical concepts named after Fibonacci because of a connection to the Fibonacci numbers. Examples include the

Brahmagupta–Fibonacci identity In algebra, the Brahmagupta–Fibonacci identity expresses the product of two sums of two squares as a sum of two squares in two different ways. Hence the set of all sums of two squares is closed under multiplication. Specifically, the identity say ...

, the

Fibonacci search technique In computer science, 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. Note that the running time analysis is this ...

, and the

Pisano period In number theory, the ''n''th Pisano period, written as '(''n''), is the period with which the sequence of Fibonacci numbers taken modulo ''n'' repeats. Pisano periods are named after Leonardo Pisano, better known as Fibonacci. The existence of ...

. Beyond mathematics, namesakes of Fibonacci include the asteroid 6765 Fibonacci and the art rock band

The Fibonaccis The Fibonaccis were an American art rock band formed in 1981 in Los Angeles. The band consisted of songwriters John Dentino ( keyboards) and Ron Stringer (guitar), Magie Song (vocals), Joe Berardi (drums) and later Tom Corey (bass). Formation Th ...

Works

* ''

'' (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

area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an ope ...

s and

volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). Th ...

s, and other topics in practical

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

(English translation by Barnabas Hughes, Springer, 2008). * ''Flos'' (1225), solutions to problems posed by Johannes of Palermo * '' Liber quadratorum'' ("

The Book of Squares ''The Book of Squares'', ''(Liber Quadratorum'' in the original Latin) is a book on algebra by Leonardo Fibonacci, published in 1225. It was dedicated to Frederick II, Holy Roman Emperor Frederick II (German: ''Friedrich''; Italian: ''Federi ...

") on Diophantine equations, dedicated to Emperor Frederick II. See in particular

congruum In number theory, a congruum (plural ''congrua'') is the difference between successive square numbers in an arithmetic progression of three squares. That is, if x^2, y^2, and z^2 (for integers x, y, and z) are three square numbers that are equally ...

and the

. * ''Di minor guisa'' (on commercial arithmetic; lost) * ''Commentary on Book X of

Euclid's Elements The ''Elements'' ( grc, Στοιχεῖα ''Stoikheîa'') is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt 300 BC. It is a collection of definitions, postulat ...

'' (lost)

Notes

References

External links

* "Fibonacci, Leonardo, or Leonardo of Pisa." Complete Dictionary of Scientific Biography. 2008. Encyclopedia.com. (April 20, 2015)
Fibonacci
at Convergence *
Fibonacci (2 vol., 1857 & 1862) ''Il liber abaci'' and ''Practica Geometriae''
– digital facsimile from the

Linda Hall Library The Linda Hall Library is a privately endowed American library of science, engineering and technology located in Kansas City, Missouri, sitting "majestically on a urban arboretum." It is the "largest independently funded public library of scien ...

Fibonacci, Liber abbaci

Bibliotheca Augustana Augsburg Technical University of Applied Sciences (german: Technische Hochschule Augsburg or simply ''THA'') is a German university located in Augsburg. It was founded in 1971, but its institutional roots as an art academy go back to 1670. With ...

{{DEFAULTSORT:Fibonacci 1250 deaths 1170s births 13th-century Latin writers 13th-century Italian mathematicians Fibonacci numbers Italian Roman Catholics Medieval European mathematics Number theorists People from Pisa Medieval geometers Italian expatriates in Algeria Court of Frederick II, Holy Roman Emperor