- Hindu-Arabic numeral system
The Hindu-Arabic numeral system is a
positional decimal numeral systemfirst documented in the ninth century. The system is based on ten, originally nine, different glyphs. The symbols (glyphs) used to represent the system are in principle independent of the system itself. The glyphs in actual use are descended from Indian Brahmi numerals, and have split into various typographical variants since the Middle Ages. These symbol sets can be divided into three main families: the West Arabic numerals used in the Maghreb and in Europe, the Eastern Arabic numeralsused in Egypt and the Middle East, and the Indian numeralsused in India.
The Hindu-Arabic numeral system is designed for
positional notationin a decimalsystem. In a more developed form, positional notation also uses a decimal marker (at first a mark over the ones digit but now more usually a decimal point or a decimal comma which separates the ones place from the tenths place), and also a symbol for "these digits recur " ad infinitum". In modern usage, this latter symbol is usually a vinculum (a horizontal line placed over the repeating digits). In this more developed form, the numeral system can symbolize any rational numberusing only 13 symbols (the ten digits, decimal marker, vinculum or division sign, and an optional prepended dashto indicate a negative number).
Various symbol sets are used to represent numbers in the Hindu-Arabic numeral, all of which evolved from the
The symbols used to represent the system have split into various typographical variants since the
*the widespread Western "
Arabic numerals" used with the Latin alphabet, in the table below labelled "European", descended from the "West Arabic numerals" which were developed in al-Andalusand the Maghreb(There are two typographic styles for rendering European numerals, known as lining figures and text figures).
*the "Arabic-Indic" or "
Eastern Arabic numerals" used with the Arabic alphabet, developed primarily in what is now Iraq. A variant of the Eastern Arabic numerals used in Persian and Urdu.
*the "Devanagari numerals" used with Devanagari and related variants grouped as Indian numerals.
As in many numbering systems, the numbers 1, 2, and 3 represent simple tally marks. 1 being a single line, 2 being two lines (now connected by a diagonal) and 3 being three lines (now connected by two vertical lines). After three, numbers tend to become more complex symbols (examples are the Chinese/Japanese numbers and
Roman numerals). Theorists believe that this is because it becomes difficult to instantaneously count objects past three. [ [http://www.newscientist.com/article.ns?id=dn6303 Language may shape human thought] , NewScientist.com news service, Celeste Biever, 19:00 19 August 2004.]
List of symbols in contemporary use
"Note: Some symbols may not display correctly if your browser does not support
Unicodefonts."Note: Tamil zero is a modern innovation. Unicode 4.1 and later defines an encoding for it [ [http://unicode.org/faq/tamil.html#11 FAQ - Tamil Language and Script - Q: What can you tell me about Tamil Digit Zero?] ] [ [http://www.unicode.org/notes/tn21/ Unicode Technical Note #21: Tamil Numbers] ] .
At present the following sets are being used:
;Hindu-Arabic numeralsThese are the most widely-used symbols, used in western parts of the Arab world, west of
Egypt, in European and Western countries and worldwide. They are known as Arabic numerals, Western numerals, European numerals or digits [http://msdn.microsoft.com/library/default.asp?url=/library/en-us/intl/nls_0to3.asp] , Western Arabic numerals, Arabic Western numeralsFact|date=February 2007. In Arabic they are called "Western Numerals". (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
;Devanagari numeralsThese symbols are used in languages that use the
Devanagari script. (०, १, २, ३, ४, ५, ६, ७, ८, ९) They are sometimes called late Devanagari numerals to distinguish them from the early Devanagari numerals.
Eastern Arabic numeralsIn English they are also called Eastern Arabic numerals, Arabic-Indic numerals, Arabic Eastern Numerals. In Arabic though, they are called "Indian numerals", أرقام هندية, "arqam hindiyyah". They are sometimes called Indic Numerals in English [http://www-306.ibm.com/software/globalization/topics/locales/numeric_intro.jsp] , however, this nomenclature is sometimes discouraged as it "leads to confusion with the digits currently used with the scripts of India" [http://www.unicode.org/glossary/] . They are used in Egyptand Arabic countries east of it, and were also in the no longer used Ottoman Turkish script(٠.١.٢.٣.٤.٥.٦.٧.٨٩)
A variant of the Eastern Arabic numerals is used in Persian and
Urdu* languages. (۰، ۱، ۲، ۳، ۴، ۵، ۶، ۷، ۸، ۹)
* For Urdu and other languages used by Muslims in India and Pakistan there is used the following Hindu-Arabic numeral system:
;Gurmukhi numeralsUsed in the
Punjabi language. (੦, ੧, ੨, ੩, ੪, ੫, ੬, ੭, ੮, ੯)
;Bengali numeralsUsed in the Bengali and
Assamese languages (০, ১, ২, ৩, ৪, ৫, ৬, ৭, ৮, ৯)
;Oriya numeralsUsed in the
Oriya language(୦, ୧, ୨, ୩, ୪, ୫, ୬, ୭, ୮, ୯)
;Tamil numeralsUsed in the
Tamil language(௦, ௧, ௨, ௩, ௪, ௫, ௬, ௭, ௮, ௯)
;Kannada numeralsUsed in the
Kannada language(೦, ೧, ೨, ೩, ೪, ೫, ೬, ೭, ೮, ೯)
;Malayalam numeralsUsed in the
Malayalam language(൦, ൧, ൨, ൩, ൪, ൫, ൬, ൭, ൮, ൯)
Thai numeralsUsed in the Thai language(๐, ๑, ๒, ๓, ๔, ๕, ๖, ๗, ๘, ๙)
;Tibetan numeralsUsed in the
Tibetan language(༠, ༡, ༢, ༣, ༤, ༥, ༦, ༧, ༨, ༩)
;Burmese numeralsUsed in the
Burmese language(၀, ၁, ၂, ၃, ၄, ၅, ၆, ၇, ၈, ၉)
;Eastern Cham numeralsUsed in
;Western Cham numeralsUsed in
;Khmer numeralsUsed in
Cambodia(០, ១, ២, ៣, ៤, ៥, ៦, ៧, ៨, ៩)
;Javanese numeralsUsed in Java since the time of
;Lepcha numeralsUsed in
;Lao numeralsUsed in
Lao language(໐, ໑, ໒, ໓, ໔, ໕, ໖, ໗, ໘, ໙)
The Hindu-Arabic numeral system originated in
India. Flegg, pages 67-70.] Graham Flegg (2002) dates the history of the Hindu-Arabic system to the Indus valley civilization. The inscriptions on the edicts of Ashoka( 1st millennium BCE) display this number system being used by the Imperial Mauryas. This system was later transmitted to Europeby the Arabs. 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, 4, 6, 7 and 9 was recorded. These Brahmi numerals are the ancestors of the Hindu-Arabic glyphs 1 to 9, but they were not used as a positional system with a zero, and there were rather separate numerals for each of the tens (10, 20, 30, etc.).
Positional notation without the use of zero (using an empty space in tabular arrangements, or the word "kha" "emptiness") is known to have been in use in
Indiafrom the 6th century. The oldest known authentic document that may be argued to contain the use of zero and decimal notation is the Jaina cosmological text "Lokavibhaga", which was completed on August 25, 458. [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 ]
The first inscription showing the use of zero which is dated and is not disputed by any historian is the inscription at
Gwaliordated 933 in the Vikramacalendar (876 CE.) [http://www-gap.dcs.st-and.ac.uk/%7Ehistory/HistTopics/Indian_numerals.html] [http://www.uni-tuebingen.de/sinologie/eastm/back/cs13/cs13-3-lam.pdf] .
This 9th century date is currently thought to be the first physical evidence for the use of positional zero in India. According to
Lam Lay Yong, :"the earliest appearance in India of a symbol for zero in the Hindu-Arabic numeral system is found in an inscription at Gwalior which is dated 876 AD". [http://www.uni-tuebingen.de/sinologie/eastm/back/cs13/cs13-3-lam.pdf] . Professor EF Robertson and DR JJ O'Connor report: :"The first record of the Indian use of zero which is dated and agreed by all to be genuine was written in 876" on the Gwalior tablet stone [http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Zero.html] . However, Arabic court records (see next section titled "Adoption by the Arabs") and the Persian mathematician Al-Khwarizmi's book "On the Calculation with Hindu Numerals", clearly indicate that this system and the use of zero by the Indians predates 876 AD; with the aforementioned documents dated as 776 AD and 825 AD respectively.
According to Menninger (p. 400): :"This long journey begins with the Indian inscription which contains the earliest true zero known thus far (Fig. 226). This famous text, inscribed on the wall of a small temple in the vicinity of Gvalior (near Lashkar in Central India) first gives the date 933 (A.D. 870 in our reckoning) in words and in Brahmi numerals. Then it goes on to list four gifts to a temple, including a tract of land "270 royal hastas long and 187 wide, for a flower-garden." Here, in the number 270 the zero first appears as a small circle [...] ; in the twentieth line of the inscription it appears once more in the expression "50 wreaths of flowers" which the gardeners promise to give in perpetuity to honor the divinity." "The Encyclopaedia Britannica says," "Hindu literature gives evidence that the zero may have been known before the birth of Christ, but no inscription has been found with such a symbol before the 9th century." [http://members.aol.com/jeff570/constants.html] .
Adoption by the Arabs
These nine numerals were adopted by the
Arabsin the 8th century. How the numbers came to the Arabs is recorded in al-Qifti's "Chronology of the scholars", which was written around the end the 12th century, quoting earlier sources [http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Arabic_numerals.html] : :"... a person from India presented himself before the Caliph al-Mansurin the year 776 who was well versed in the siddhanta method of calculation related to the movement of the heavenly bodies, and having ways of calculating equations based on the half-chord [essentially the sine] calculated in half-degrees ... Al-Mansur ordered this book to be translated into Arabic, and a work to be written, based on the translation, to give the Arabs a solid base for calculating the movements of the planets ..."
This book presented by the Indian scholar was probably "Brahmasphuta Siddhanta" ("The Opening of the Universe") which was written in 628 (Ifrah) [http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Arabic_numerals.html] by the Indian mathematician
The numeral system came 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" ( _ar. كتاب في استعمال العداد الهندي [kitab 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 use of zero in positional systems dates to about this time, representing the final step to the system of numerals we are familiar with today. The first dated and undisputed inscription showing the use of zero at is at
Gwalior, dating to 876 AD. There were, however, Indian precursors from about 500 AD, positional notations without a zero, or with the word "kha" indicating the absence of a digit. It is, therefore, uncertain whether the crucial inclusion of zero as the tenth symbol of the system should be attributed to the Indians, or if it is due to Al-Khwarizmi or Al-Kindi of the House of Wisdom.
In the 10th century,
Arabmathematicians extendedFact|date=October 2008 the decimal numeral system to include fractions, as recorded in a treatise by Syrian mathematician Abu'l-Hasan al-Uqlidisiin 952-953.
In the Arab World—until modern times—the Hindu-Arabic numeral system was used only by mathematicians. Muslim scientists used the Babylonian numeral system, and merchants used the
Abjad numerals, a system similar to the Greek numeral system and the Hebrew numeral system. Therefore, it was not until Fibonaccithat the Hindu-Arabic numeral system was used by a large population.
Adoption in Europe
Leonardo Fibonacci brought this system to Europe, translating the Arabic text into Latin, calling it
Liber Abaci. The numeral system came to be called "Arabic" by the Europeans. It was used in European mathematics from the 12th century, and entered common use from the 15th century. Robert Chester translated the Latin into English.
Adoption in East Asia
China, Gautama Siddhaintroduced Indian numerals with zero in 718, but Chinese mathematicians didn't find them useful, as they had already had the decimal positional counting rods[ Citation
title=Zhongguo Shuxue Shi (The history of Chinese mathematics)
place=Beijing] [ Citation
title=Sangi o koeta otoko (The man who exceeded counting rods)
Even though, in Chinese numerals a circle (〇) is used to write zero in
Suzhou numerals. Many historians think it was imported from Indian numeralsby Gautama Siddhain 718, but some think it was created from the Chinese text space filler "□" Citation
title=Zhongguo Shuxue Shi (The history of Chinese mathematics)
Japanese finally adopted the Western Arabic numerals in the 19th century, abandoning counting rods.
* Flegg, Graham (2002). "Numbers: Their History and Meaning". Courier Dover Publications. ISBN 0486421651.
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