- Arabic numerals
The arabic numerals (often capitalized) are the ten
digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), which—along with the system by which a sequence "(e.g." "406") was read as a number—were originally defined by Indian mathematicians, later modified and transferred to North African Arab mathematicians and transmitted to Europein the Middle Ages, whence they spread through European colonialism. Today they are the most common symbolic representation of number in the world.
The term Arabic numerals may refer to the closely related
Eastern Arabic numerals(٠.١.٢.٣.٤.٥.٦.٧.٨.٩) which are, to Westerners today, more closely associated with Arabic speakers than the Western Arabic numerals.
Finally, arabic numerals is the conventional name for the family of
numerals, invented by Indian mathematicians in around AD 500, which are related to or ancestral to the Western numerals.Ifrah, Georges. 1999. "The Universal History of Numbers : From Prehistory to the Invention of the Computer", Wiley. ISBN 0-471-37568-3.] O'Connor, J.J. and E.F. Robertson. 2000. [http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Indian_numerals.html 'Indian Numerals'] , "MacTutor History of Mathematics Archive", School of Mathematics and Statistics, University of St. Andrews, Scotland.] This invention, which involved zeroand a decimal positional notation, is considered an important milestone in the development of mathematics.
One may distinguish between the positional decimal system involved in interpreting the numerals, known as the
Hindu-Arabic numeral system, which is identical throughout the family, and the precise characters used to write these numerals, which vary regionally. The characters most commonly used in conjunction with the Latin alphabetsince Early Modern times are 0 1 2 3 4 5 6 7 8 9.
The reason that (0,1,2,3,4,5,6,7,8,9) are known as arabic numerals is that they are the characters used by western Arabs from Morocco to Libya, from where they were introduced to Europe in the tenth century. The Arabs themselves call them "Hindu numerals", but this term is not restricted to the characters (0,1,2,3,4,5,6,7,8,9), but also includes (٠.١.٢.٣.٤.٥.٦.٧.٨.٩) as well.
Although the phrase "arabic numeral" is frequently capitalized, it is sometimes written in lower case, for instance in its entry in the
Oxford English dictionary. ["Arabic", "Oxford English dictionary," 2nd edition] This helps distinguish it from the East Arabic numeralsspecific to the Arabs.
The symbols for 1 to 9 in the Hindu-Arabic numeral system evolved from the
Brahmi numerals. Buddhistinscriptions from around 300 BC use the symbols which became 1, 4 and 6. One century later, their use of the symbols which became 2, 7 and 9 was recorded.
The first universally accepted inscription containing the use of the 0 glyph is first recorded in the 9th century, in an inscription at
Gwaliorin Central Indiadated to 870. However, by this time, the use of the glyph had already reached Persia, and is mentioned in Al-Khwarizmi's descriptions of Indian numerals. Indian documents on copper plates, with the same symbol for zero in them, dated back as far as the 6th century AD, abound. [Kaplan, Robert. (2000). "The Nothing That Is: A Natural History of Zero". Oxford: Oxford University Press.]
Brahmi numerals in Indiain the 1st century AD]
numeral systemcame to be known to both the Persian mathematician Al-Khwarizmi, whose book "On the Calculation with Hindu Numerals" written about 825, and the Arabmathematician Al-Kindi, who wrote four volumes, "On the Use of the Indian Numerals" ("Ketab fi Isti'mal al-'Adad al-Hindi") about 830, are principally responsible for the diffusion of the Indian system of numeration in the Middle Eastand the West. [ [http://www-gap.dcs.st-and.ac.uk/%7Ehistory/HistTopics/Indian_numerals.html The MacTutor History of Mathematics archive] ] In the 10th century, Middle-Eastern mathematicians extended the decimal numeral system to include fractions, as recorded in a treatise by Syrianmathematician Abu'l-Hasan al-Uqlidisiin 952–53.
In the Arab world—until modern times—the arabic numeral system was used only by mathematicians. Muslim scientists used the Babylonian numeral system, and merchants used the
Abjad numerals. It was not until Fibonaccithat the arabic numeral system was used by a large population.
A distinctive West Arabic variant of the symbols begins to emerge around the 10th century in the
Maghreband Al-Andalus, called "ghubar" ("sand-table" or "dust-table") numerals, which is the direct ancestor to the modern Western Arabic numerals used throughout the world. [citation|title=The Origin of the Ghubār Numerals, or the Arabian Abacus and the Articuli|first=Solomon|last=Gandz|journal=Isis|volume=16|issue=2|date=November 1931|pages=393-424]
The first mentions of the numerals in the West are found in the "
Codex Vigilanus" of 976. [ [http://www.mathorigins.com/V.htm Mathorigins.com] ] From the 980s, Gerbert of Aurillac (later, Pope Silvester II) began to spread knowledge of the numerals in Europe. Gerbert studied in Barcelonain his youth, and he is known to have requested mathematical treatises concerning the astrolabefrom Lupitus of Barcelonaafter he had returned to France.
Adoption in Europe
In 825 Al-Khwārizmī, the Persian scientist, wrote a treatise, "On the Calculation with Hindu Numerals", which was translated into Latin in the 12th century as "Algoritmi de numero Indorum", where "Algoritmi", the translator's rendition of the author's name, gave rise to the word "
algorithm" (Latin "algorithmus", "calculation method").
Fibonacci, a mathematician born in the
Republic of Pisawho had studied in Bejaia( Bougie), Algeria, promoted the Arabic numeral system in Europewith his book " Liber Abaci", which was written in 1202, still describing the numerals as Indian rather than Arabic.
:"When my father, who had been appointed by his country as public notary in the customs at
Bugiaacting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else and I came to understand it.."
The numerals are arranged with their lowest value digit to the right, with higher value positions added to the left. This arrangement was adopted identically into the numerals as used in Europe. The Latin alphabet runs from left to right, unlike the Arabic alphabet. Hence, numerals in western texts have an inverse arrangement of their glyphs relative to the direction of writing.
The European acceptance of the numerals was accelerated by the invention of the
printing press, and they became commonly known during the 15th century. Early uses in Britain include a 1445 inscription on the tower of Heathfield Church, Sussex, a 1448 inscription on a wooden lych-gate of Bray Church, Berkshire, and a 1487 inscription on the belfry door at Piddletrenthidechurch, Dorsetand in Scotlanda 1470 inscription on the tomb of the first Earl of Huntly in Elgin, ( Elgin, Moray) Cathedral. (See G.F. Hill, "The Development of Arabic Numerals in Europe" for more examples.) By the mid-16th century, they were in common use in most of Europe. [ [http://mathforum.org/library/drmath/view/52545.html Mathforum.org] ] Roman numerals remained in use mostly for the notation of Anno Dominiyears, and for numbers on clockfaces. Sometimes, Roman numerals are still used for enumeration of lists (as an alternative to alphabetical enumeration), and numbering pages in prefatory material in books.
Evolution of symbols
The numeral system employed, known as
algorism, is positional decimalnotation. Various symbol sets are used to represent numbers in the Hindu-Arabic numeral system, all of which evolved from the Brahmi numerals. The symbols used to represent the system have split into various typographical variants since the Middle Ages:
*The widespread Western Arabic numerals used with the
Latin alphabet, in the table below labelled "European", descended from the West Arabic numerals developed in al-Andalusand the Maghreb. (There are two typographicstyles for rendering European numerals, known as lining figures and text figures).
*The Arabic-Indic or
Eastern Arabic numeralsused with the Arabic alphabetdeveloped primarily in what is now Iraq. A variant of the Eastern Arabic numerals used in the Persian and Urdu languages is shown as East Arabic-Indic.
Devanagari numeralsused with Devanagariand related variants are grouped as Indian numerals.
The evolution of the numerals in early Europe is shown on a table created by the French scholar J.E. Montucla in his "Histoire de la Mathematique", which was published in 1757:
The arabic numerals are encoded in
ASCII(and Unicode) at positions 48 to 57:
Hindu-Arabic numeral system
Counting rods- decimal positional numeral system with zero
title=The Semantics of Indian Numerals in Arabic, Greek and Latin
journal=Journal of Indian Philosophy,
last=Encyclopaedia Britannica (Kim Plofker)
title=mathematics, South Asian
journal=Encyclopædia Britannica Online
May 18, 2007.
title=The Bakhshali Manuscript, An ancient Indian mathematical treatise
title=A Universal History of Numbers: From Prehistory to Computers
first1=Victor J. (ed.)
July 20 2007
title=The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook
publisher=Princeton University Press,
* [http://www.historyworld.net/wrldhis/PlainTextHistories.asp?historyid=ab34 History of Counting Systems and Numerals] . Retrieved
11 December 2005.
* [http://www.laputanlogic.com/articles/2003/06/01-95210802.html The Evolution of Numbers] .
16 April 2005.
*O'Connor, J. J. and Robertson, E. F. [http://www-gap.dcs.st-and.ac.uk/%7Ehistory/HistTopics/Indian_numerals.html Indian numerals] . November 2000.
*History of the Numerals
** [http://www-gap.dcs.st-and.ac.uk/%7Ehistory/HistTopics/Arabic_numerals.html Arabic numerals] :
** [http://www.scit.wlv.ac.uk/university/scit/modules/mm2217/han.htm Hindu-Arabic numerals] :
** [http://www.archimedes-lab.org/numeral.html Numeral & Numbers' history and curiosities] :
** [http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=1187&bodyId=1327 Gerbert d'Aurillac's early use of Hindu-Arabic numerals] at [http://mathdl.maa.org/convergence/1/ Convergence]
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