Arabic numerals
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).
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 picture 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 picture, labelled European.
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.
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The Arabic numeral system is considered one of the most significant developments in mathematics, ergo, theories have been advanced about its origin. These theories include
History
In fact, the idea may have passed successively through each of these places. Very few historians debate that the Arabic numeral system was influenced by Indian mathematics—particularly as Arabs call the numerals they use “Indian numerals” (أرقام هندية, arqam hindiyyah).
Somewhat speculatively, the origin of a base-10 positional number system used in India can possibly be traced to China. Because the Chinese Hua Ma system (see Chinese numerals) is also a positional base-10 system, Hua Ma numerals—or some numeral system similar to it—may have been the inspiration for the base-10 positional numeral system that evolved in India. This hypothesis is made stronger by the fact that years from 400 to 700, during which a positional base-10 system emerged in India, were also the period during which the number of Buddhist pilgrims traveling between China and India peaked. What is certain is that by the time of Bhaskara I (i.e., the seventh century AD) a base 10 numeral system with 9 glyphs was being used in India, and the concept of zero (represented by a dot) was known (see the Vāsavadattā of Subandhu, or the definition by Brahmagupta).
This numeral system had reached the Middle East by 670. Muslim mathematicians working in what is now Iraq 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 printed by Lienhart Holle in Ulm, and other examples in the Gutenberg Museum in Mainz.)
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.
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