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Encyclopedia > Arabic numeral

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Numeral systems


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Arabic numerals (also called Hindu numerals or Hindu-Arabic numerals) are by far the most common form of symbolism used to represent numbers. The Arabic numeral system is a positional base 10 numeral system with 10 distinct glyphs representing the 10 numerical digits. The leftmost digit of a number has the greatest value. In a more developed form, the Arabic numeral system 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 repeat ad infinitum” (recur). In modern usage, this latter symbol is usually a vinculum (a horizontal line placed over the repeating digits); the need for it can be removed by representing fractions as simple ratios with a division sign, but this obviates many of Arabic numbers’ more obvious advantages, such as the ability to immediately determine which of two numbers is greater. Historically, however, there has been much variation. In this more developed form, the Arabic numeral system can symbolize any rational number using only 13 glyphs (the ten digits, decimal marker, vinculum or division sign, and an optional prepended dash to indicate a negative number).

It is interesting to note that, like 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.

The Arabic numeral system has used many different sets of glyphs. These glyph sets can be divided into two main families—namely the West Arabic numerals, and the East Arabic numerals. East Arabic numerals—which were developed primarily in what is now Iraq—are shown in the table below as Arabic-Indic. East Arabic-Indic is a variety of East Arabic numerals. West Arabic numerals—which were developed in al-Andalus and the Maghreb—are shown in the table, labelled European. (There are two typographic styles for rendering European numerals, known as lining figures and text figures).

European 0 1 2 3 4 5 6 7 8 9
Arabic-Indic ٠ ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩
Eastern Arabic-Indic
(Persian and Urdu)
۰ ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹
Tamil (Blank) 

If your browser does not have all required fonts, this table might be rendered incorrectly. In that case, look at this graphic.

In Japan, Arabic numerals and the Roman alphabet are both used under the name of rōmaji. So, if a number is written in Arabic numerals, they would say “it is written in rōmaji” (as opposed to Japanese numerals). This translates as ‘Roman characters’, and may sound confusing for those who know about Roman numerals.

The Arabic numeral system is considered one of the most significant developments in mathematics. Most historians agree that it was first conceived of in India (particularly as Arabs themselves call the numerals they use “Indian numerals”, أرقام هندية, arqam hindiyyah), and was then transmitted to the Islamic world and thence, via Spain, to Europe.

The first inscriptions using 0 in India have been traced to approximately 400 AD. Aryabhata's numerical code also represents a full knowledge of the zero symbol. By the time of Bhaskara I (i.e., the seventh century AD) a base 10 numeral system with 9 glyphs was widely used in India, and the concept of zero (represented by a dot) was known (see the Vāsavadattā of Subandhu, or the definition by Brahmagupta). It is possible, however, that the invention of the zero sign took place sometime in the first century when the Buddhist philosophy of shunyata (zero-ness) gained ascendancy.

This numeral system had reached the Middle East by 670. Muslim mathematicians working in what is now Iraq, such as Al-Khwarizmi, were already familiar with the Babylonian numeral system, which used the zero digit between nonzero digits (although not after nonzero digits), so the more general system would not have been a difficult step. In the tenth century AD, Arab mathematicians extended the decimal numeral system to include fractions, as recorded in a treatise by Abu'l-Hasan al-Uqlidisi in 952-3.

Fibonacci, an Italian mathematician who had studied in Bejaia (Bougie), Algeria, promoted the Arabic numeral system in Europe with his book Liber Abaci, which was published in 1202. The system did not come into wide use in Europe, however, until the invention of printing (See, for example, the 1482 Ptolemaeus map of the world (http://bell.lib.umn.edu/map/PTO/TOUR/1482u.html) printed by Lienhart Holle in Ulm, and other examples in the Gutenberg Museum in Germany.)

It should be noted that in the Muslim World—until modern times—the Arabic numeral system was used only by mathematicians. Muslim scientists used the Babylonian numeral system, and merchants used a numeral system similar to the Greek numeral system and the Hebrew numeral system. Therefore, it was not until Fibonacci that the Arabic numeral system was used by a large population.

External links

  • Unicode reference charts (http://www.unicode.org/charts/):
    • Arabic (http://www.unicode.org/charts/PDF/U0600.pdf) (See codes U+0660_U+0669, U+06F0_U+06F9)
    • Devanagari (http://www.unicode.org/charts/PDF/U0900.pdf) (See codes U+0966_U+096F)
    • Tamil (http://www.unicode.org/charts/PDF/U0B80.pdf) (See codes U+0BE6_U+0BEF)
  • History of the Numerals
    • The Evolution of Numbers (http://www.laputanlogic.com/articles/2003/06/01_95210802.html)
    • Indian numerals (http://www_gap.dcs.st_and.ac.uk/%7Ehistory/HistTopics/Indian-numerals.html):
    • Arabic numerals (http://www_gap.dcs.st_and.ac.uk/%7Ehistory/HistTopics/Arabic-numerals.html):
    • Hindu_Arabic numerals (http://www.scit.wlv.ac.uk/university/scit/modules/mm2217/han.htm):

  Results from FactBites:
Numerals in many different writing systems (133 words)
The Urdu numerals are also known as 'East Arab' numerals and differ slightly from those used in Arabic.
The numerals 1, 2, 3, etc. are also known as Arabic numerals, or Hindu-Arabic numerals, Indian numerals, Hindu numerals, European numerals, and Western numerals.
These numerals where first used in India in about 400 BC, were later used in Persia, then were brought to Europe by the Arabs.
Arabic numerals (2212 words)
The Indian numerals discussed in our article Indian numerals form the basis of the European number systems which are now widely used.
The numerals had changed their form somewhat 100 years later when this copy of one of al-Biruni's astronomical texts was made.
The form of the numerals in the west of the Arabic empire look more familiar to those using European numerals today which is not surprising since it is from these numerals that the Indian number system reach Europe.
  More results at FactBites »



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