Leonardo Bonacci ( – ), commonly known as Fibonacci, was an Italian

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, mathematical structure, structure, space, Mathematica ...

from the

Republic of Pisa The Republic of Pisa () was an independent state existing from the 11th to the 15th century centered on the Tuscan city of Pisa. It rose to become an economic powerhouse, a commercial center whose merchants dominated Mediterranean and Italian t ...

, 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 5th to the late 15th centuries, similarly to the post-classical period of global history. It began with the fall of the Western Roman Empire and ...

". The name he is commonly called, ''Fibonacci'', is first found in a modern source in a 1838 text by the Franco-Italian mathematician Guglielmo Libri and is short for ('son of Bonacci'). However, even as early as 1506, Perizolo, a notary of the

Holy Roman Empire The Holy Roman Empire, also known as the Holy Roman Empire of the German Nation after 1512, was a polity in Central and Western Europe, usually headed by the Holy Roman Emperor. It developed in the Early Middle Ages, and lasted for a millennium ...

, mentions him as "Lionardo Fibonacci". Fibonacci popularized the Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of (''Book of Calculation'') and also introduced Europe to the sequence of

Fibonacci number In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many w ...

s, which he used as an example in .

Biography

Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official who directed a trading post in Bugia, modern-day Béjaïa, Algeria. Fibonacci travelled with him as a young boy, and it was in Bugia where he was educated that he learned about the

Hindu–Arabic numeral system The Hindu–Arabic numeral system (also known as the Indo-Arabic numeral system, Hindu numeral system, and Arabic numeral system) is a positional notation, positional Decimal, base-ten numeral system for representing integers; its extension t ...

. 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 east by the Levant in West Asia, on the north by Anatolia in West Asia and Southern ...

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 Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...

used at the time, allowed easy calculation using a place-value system. 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 Frederick II (, , , ; 26 December 1194 – 13 December 1250) was King of Sicily from 1198, King of Germany from 1212, King of Italy and Holy Roman Emperor from 1220 and King of Jerusalem from 1225. He was the son of Emperor Henry VI of the Ho ...

, who enjoyed mathematics and science. A member of Frederick II's court, John of Palermo, 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 (1202), Fibonacci introduced the so-called ''modus Indorum'' (method of the

India India, officially the Republic of India, is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area; the List of countries by population (United Nations), most populous country since ...

ns), today known as the

, with ten digits including a

zero 0 (zero) is a number representing an empty quantity. Adding (or subtracting) 0 to any number leaves that number unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and compl ...

and

positional notation Positional notation, also known as place-value notation, positional numeral system, or simply place value, usually denotes the extension to any radix, base of the Hindu–Arabic numeral system (or decimal, decimal system). More generally, a posit ...

. The book showed the practical use and value of this by applying the numerals to commercial

bookkeeping Bookkeeping is the recording of financial transactions, and is part of the process of accounting in business and other organizations. It involves preparing source documents for all transactions, operations, and other events of a business. T ...

, 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 method, and using an

abacus An abacus ( abaci or abacuses), also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Hindu–Arabic numeral system. A ...

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 Deposit account, 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 m ...

and

accounting Accounting, also known as accountancy, is the process of recording and processing information about economic entity, economic entities, such as businesses and corporations. Accounting measures the results of an organization's economic activit ...

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

, 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 are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, ...

and

prime numbers A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

Fibonacci sequence

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 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 summation, sum to the larger of the two quantities. Expressed algebraically, for quantities and with , is in a golden ratio to if \fr ...

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, historical cemetery on the

Piazza dei Miracoli The Piazza dei Miracoli (; 'Square of Miracles'), formally known as Piazza del Duomo ('Cathedral Square'), is a walled compound in central Pisa, Tuscany, Italy, recognized as an important center of European medieval art and one of the finest ...

. 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

* (1202), a book on calculations (English translation by Laurence Sigler, 2002) * ''Practica Geometriae'' (1220), a compendium of techniques in

surveying Surveying or land surveying is the technique, profession, art, and science of determining the land, terrestrial Plane (mathematics), two-dimensional or Three-dimensional space#In Euclidean geometry, three-dimensional positions of Point (geom ...

, the

measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to ...

and partition of

area Area is the measure of a region's size on a 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 open surface or the boundary of a three-di ...

s and

volume Volume is a measure of regions in 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) ...

s, and other topics in practical

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

(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 equation ''Diophantine'' means pertaining to the ancient Greek mathematician Diophantus. A number of concepts bear this name: *Diophantine approximation In number theory, the study of Diophantine approximation deals with the approximation of real n ...

s, dedicated to

. See in particular congruum and the Brahmagupta–Fibonacci identity. * ''Di minor guisa'' (on commercial arithmetic; lost) * ''Commentary on Book X of

Euclid's Elements The ''Elements'' ( ) is a mathematics, mathematical treatise written 300 BC by the Ancient Greek mathematics, Ancient Greek mathematician Euclid. ''Elements'' is the oldest extant large-scale deductive treatment of mathematics. Drawing on the w ...

'' (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, on the grounds of a urban arboretum. It claims to be the "largest independently funded public library of sc ...

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