Algorism is the technique of performing basic

arithmetic Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. ...

by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This

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 ...

system has largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude, such as

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 ...

, and in some cases required a device such as 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 ...

Etymology

The word ''algorism'' comes from the name Al-Khwārizmī (c. 780–850), a Persian

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 ...

astronomer An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...

geographer A geographer is a physical scientist, social scientist or humanist whose area of study is geography, the study of Earth's natural environment and human society, including how society and nature interacts. The Greek prefix "geo" means "earth" a ...

and scholar in the

House of Wisdom The House of Wisdom ( ), also known as the Grand Library of Baghdad, was believed to be a major Abbasid Caliphate, Abbasid-era public academy and intellectual center in Baghdad. In popular reference, it acted as one of the world's largest publ ...

Baghdad Baghdad ( or ; , ) is the capital and List of largest cities of Iraq, largest city of Iraq, located along the Tigris in the central part of the country. With a population exceeding 7 million, it ranks among the List of largest cities in the A ...

, whose name means "the native of Khwarezm", which is now in modern-day

Uzbekistan , image_flag = Flag of Uzbekistan.svg , image_coat = Emblem of Uzbekistan.svg , symbol_type = Emblem of Uzbekistan, Emblem , national_anthem = "State Anthem of Uzbekistan, State Anthem of the Republ ...

. He wrote a treatise in Arabic language in the 9th century, which was translated into

Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...

in the 12th century under the title ''Algoritmi de numero Indorum''. This title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name. Al-Khwarizmi was the most widely read mathematician in Europe in the late Middle Ages, primarily through his other book, the

Algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

. In late medieval Latin, ''algorismus'', the corruption of his name, simply meant the "decimal number system" that is still the meaning of modern English algorism. During the 17th century, the French form for the word – but not its meaning – was changed to ''

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

'', following the model of the word ''

logarithm In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...

'', this form alluding to the ancient Greek . English adopted the French very soon afterwards, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English. In English, it was first used about 1230 and then by Chaucer in 1391. Another early use of the word is from 1240, in a manual titled ''Carmen de Algorismo'' composed by Alexandre de Villedieu. It begins thus: which translates as: The word ''

'' also derives from ''algorism'', a generalization of the meaning to any set of rules specifying a computational procedure. Occasionally ''algorism'' is also used in this generalized meaning, especially in older texts.

History

Starting with the

integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...

developed in India using

base 10 The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of t ...

notation, Al-Khwārizmī along with other mathematicians in medieval Islam, documented new arithmetic methods and made many other contributions to decimal arithmetic (see the articles linked below). These included the concept of the decimal fractions as an extension of the notation, which in turn led to the notion of the

decimal point FIle:Decimal separators.svg, alt=Four types of separating decimals: a) 1,234.56. b) 1.234,56. c) 1'234,56. d) ١٬٢٣٤٫٥٦., Both a comma and a full stop (or period) are generally accepted decimal separators for international use. The apost ...

. This system was popularized in Europe by Leonardo of Pisa, now known as

Fibonacci Leonardo Bonacci ( – ), commonly known as Fibonacci, was an Italians, Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". The name he is commonly called, ''Fibonacci ...

References

{{reflist, refs= {{cite journal, first=Jan P. , last=Hogendijk , title=al-Khwarzimi , journal=Pythagoras , volume=38 , issue=2 , year=1998 , pages=4–5 , issn=0033-4766 , archive-url=https://web.archive.org/web/20080319024147/http://www.kennislink.nl/web/show?id=116543 , archive-date=March 19, 2008 , url-status=dead , url=http://www.kennislink.nl/web/show?id=116543 {{cite web , first=Jeffrey A. , last=Oaks , url=http://facstaff.uindy.edu/~oaks/MHMC.htm , title=Was al-Khwarizmi an applied algebraist? , publisher= University of Indianapolis , access-date=2008-05-30 , archive-url=https://web.archive.org/web/20110718094835/http://facstaff.uindy.edu/~oaks/MHMC.htm , archive-date=2011-07-18 , url-status=dead {{cite encyclopedia , last = Toomer , first = Gerald , author-link = Gerald Toomer , title = Al-Khwārizmī, Abu Ja'far Muḥammad ibn Mūsā , encyclopedia =

Dictionary of Scientific Biography The ''Dictionary of Scientific Biography'' is a scholarly reference work that was published from 1970 through 1980 by publisher Charles Scribner's Sons, with main editor the science historian Charles Coulston Gillispie, Charles Gillispie, from Pri ...

, volume = 7 , editor = Gillispie, Charles Coulston , publisher = Charles Scribner's Sons , location = New York , date = 1990 , isbn = 978-0-684-16962-0 , url=http://www.encyclopedia.com/doc/1G2-2830902300.html Numeral systems Algorithms Eponyms in mathematics

Etymology

History

See also

References