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Algorism
From Wikipedia, the free encyclopedia
Algorism comprises all of the rules of performing arithmetic computations using a decimal system for representing numbers in which numbers written using ten symbols having the values 0 through 9 are combined using a place-value system (positional notation), where each symbol has ten times the weight of the one to its right.
This system superseded earlier, more verbose, decimal systems where the symbols were different for each power of ten (and repeated instances gave the quantity of each power of ten) because at most ten symbols were needed for any range of numbers. The other systems needed a new symbol for every power of ten (and up to nine copies of each symbol for each of these).
Starting with the integer arithmetic developed in India using ten symbols in this way, Arabian mathematicians documented new arithmetic methods and made many other contributions to decimal arithmetic (including the concept of the decimal fractions as an extension of the notation, which in turn led to the notion of the decimal point).
The word algorism comes from the name al-Khwarizmi ("the one from Khwarizm") of an early 9th century Persian mathematician, possibly from what is now Khiva in western Uzbekistan. In English, it was used by Chaucer in about 1230[1]. 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 devolved into the modified form algorithm, with 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.
Algorism is based on the ten-symbol place value system, of which Georges Ifrah wrote[2]
| “ | Thus it would seem highly probable under the circumstances that the discovery of zero and the place-value system were inventions unique to the Indian civilization. As the Brâhmî notation of the first nine whole numbers (incontestably the graphical origin of our present-day numerals and of all the decimal numeral systems in use in India, Southeast and Central Asia and the Near East) was autochthonous and free of any outside influence, there can be no doubt that our decimal place-value system was born in India and was the product of Indian civilization alone. | ” |
- ^ Oxford English Dictionary (first quote c1230CE, Chaucer c1391, and later quotes showing continuing usage since then)
- ^ Ifrah, G. The Universal History of Numbers: From prehistory to the invention of the computer. John Wiley and Sons Inc., 2000. Translated from the French by David Bellos, E.F. Harding, Sophie Wood and Ian Monk