Algorism
Encyclopedia
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Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...
by writing numbers in place value form and applying a set of memorized rules and facts
Mathematical table
Before calculators were cheap and plentiful, people would use mathematical tables —lists of numbers showing the results of calculation with varying arguments— to simplify and drastically speed up computation...
to the digits. One who practices algorism is known as an algorist. This system largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude
Magnitude (mathematics)
The magnitude of an object in mathematics is its size: a property by which it can be compared as larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs....
and in some cases required a device such as an abacus
Abacus
The abacus, also called a counting frame, is a calculating tool used primarily in parts of Asia for performing arithmetic processes. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of...
.
Etymology
The word "Algorism", comes from the name Al-Khwārizmī (c. 780-850), a PersianPersian people
The Persian people are part of the Iranian peoples who speak the modern Persian language and closely akin Iranian dialects and languages. The origin of the ethnic Iranian/Persian peoples are traced to the Ancient Iranian peoples, who were part of the ancient Indo-Iranians and themselves part of...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...
, a geographer
Geographer
A geographer is a scholar whose area of study is geography, the study of Earth's natural environment and human society.Although geographers are historically known as people who make maps, map making is actually the field of study of cartography, a subset of geography...
and a scholar in the House of Wisdom
House of Wisdom
The House of Wisdom was a library and translation institute established in Abbassid-era Baghdad, Iraq. It was a key institution in the Translation Movement and considered to have been a major intellectual centre during the Islamic Golden Age...
in Baghdad
Baghdad
Baghdad is the capital of Iraq, as well as the coterminous Baghdad Governorate. The population of Baghdad in 2011 is approximately 7,216,040...
, whose name means "the native of Kharazm
Khwarezm
Khwarezm, or Chorasmia, is a large oasis region on the Amu Darya river delta in western Central Asia, which borders to the north the Aral Sea, to the east the Kyzylkum desert, to the south the Karakum desert and to the west the Ustyurt Plateau...
", a city that was part of the Greater Iran
Greater Iran
Greater Iran refers to the regions that have significant Iranian cultural influence. It roughly corresponds to the territory on the Iranian plateau and its bordering plains, stretching from Iraq, the Caucasus, and Turkey in the west to the Indus River in the east...
during his era and now is in modern day Uzbekistan
Uzbekistan
Uzbekistan , officially the Republic of Uzbekistan is a doubly landlocked country in Central Asia and one of the six independent Turkic states. It shares borders with Kazakhstan to the west and to the north, Kyrgyzstan and Tajikistan to the east, and Afghanistan and Turkmenistan to the south....
He wrote a treatise in Arabic language in the 9th century, which was translated into Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
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. 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. In 17th century French the word's form, but not its meaning, changed to algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
, following the model of the word logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
, this form alluding to the ancient Greek arithmos = number. 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:
"Haec algorismus ars praesens dicitur, in qua Talibus Indorum fruimar bis quinque figuris."
"Algorism is the art by which at present we use those Indian figures, which number two times five."
The word Algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
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 arithmetic developed in India using base 10 notation, Al-Khwārizmī along with other mathematicians in medieval Islam, both IranIran
Iran , officially the Islamic Republic of Iran , is a country in Southern and Western Asia. The name "Iran" has been in use natively since the Sassanian era and came into use internationally in 1935, before which the country was known to the Western world as Persia...
ian and Arabic, 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.
See also
- Positional notationPositional notationPositional notation or place-value notation is a method of representing or encoding numbers. Positional notation is distinguished from other notations for its use of the same symbol for the different orders of magnitude...
- Hindu-Arabic numeral systemHindu-Arabic numeral systemThe Hindu–Arabic numeral system or Hindu numeral system is a positional decimal numeral system developed between the 1st and 5th centuries by Indian mathematicians, adopted by Persian and Arab mathematicians , and spread to the western world...
- History of the Hindu-Arabic numeral systemHistory of the Hindu-Arabic numeral systemThe Hindu-Arabic numeral system is a decimal place-value numeral system. It requires a zero to handle the empty powers of ten ....