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Algorism is the technique of performing basic
arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...
by writing numbers in place value form and applying a set of memorized rules and
facts A flexible alternating current transmission system (FACTS) is a system composed of static equipment used for the alternating current (AC) transmission of electrical energy. It is meant to enhance controllability and increase power transfer capabi ...
to the digits. One who practices algorism is known as an algorist. This
positional notation 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 th ...
system has largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude, such as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, ...
, and in some cases required a device such as 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 ...
.


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, structure, space, models, and change. History On ...
,
astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...
,
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 A scholar is a person who pursues academic and intellectual activities, particularly academics who apply their intellectualism into expertise in an area of study. A scholar can also be an academic, who works as a professor, teacher, or researche ...
in the
House of Wisdom The House of Wisdom ( ar, بيت الحكمة, Bayt al-Ḥikmah), also known as the Grand Library of Baghdad, refers to either a major Abbasid public academy and intellectual center in Baghdad or to a large private library belonging to the Abba ...
in
Baghdad Baghdad (; ar, بَغْدَاد , ) is the capital of Iraq and the second-largest city in the Arab world after Cairo. It is located on the Tigris near the ruins of the ancient city of Babylon and the Sassanid Persian capital of Ctesiphon ...
, whose name means "the native of
Khwarezm Khwarazm (; Old Persian: ''Hwârazmiya''; fa, خوارزم, ''Xwârazm'' or ''Xârazm'') or Chorasmia () is a large oasis region on the Amu Darya river delta in western Central Asia, bordered on the north by the (former) Aral Sea, on the ...
", which is now in modern-day
Uzbekistan Uzbekistan (, ; uz, Ozbekiston, italic=yes / , ; russian: Узбекистан), officially the Republic of Uzbekistan ( uz, Ozbekiston Respublikasi, italic=yes / ; russian: Республика Узбекистан), is a doubly landlocked co ...
. 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 a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...
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 one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...
. 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 rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
'', following the model of the word ''
logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number  to the base  is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 ...
'', 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 ''
algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
'' 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 (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...
arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...
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 of the Hindu–Arabic numer ...
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 A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The choi ...
. This system was popularized in Europe by Leonardo of Pisa, now known as
Fibonacci Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Wester ...
.


See also

*
Algorithmic art Algorithmic art or algorithm art is art, mostly visual art, in which the design is generated by an algorithm. Algorithmic artists are sometimes called ''algorists''. Overview Algorithmic art, also known as computer-generated art, is a subset o ...
*
Positional notation 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 th ...
*
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 ...
*
History of the Hindu–Arabic numeral system The Hindu–Arabic numeral system is a decimal place-value numeral system that uses a zero glyph as in "205". Its glyphs are descended from the Indian Brahmi numerals. The full system emerged by the 8th to 9th centuries, and is first described ...
*
Johannes de Sacrobosco Johannes de Sacrobosco, also written Ioannes de Sacro Bosco, later called John of Holywood or John of Holybush ( 1195 – 1256), was a scholar, monk, and astronomer who taught at the University of Paris. He wrote a short introduction to the Hi ...


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 The University of Indianapolis (UIndy) is a private United Methodist Church-affiliated university in Indianapolis, Indiana. It offers Associate, Bachelor's, Master's, and Doctoral degrees. It was founded in 1902 as Indiana Central University and ...
, 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 Gillispie, from Princeton University. It consi ...
, 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