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Arabic numerals are the most widely used numerals. The Numerals are based on ancient Indian numerals that had already drifted to the Middle East before the rise of the Arab nation and were popularised in the Arab and Islamic Worlds in the 9th century AD. Two sets of symbols developed there over time, the Arabic Eastern numeral script, and the Arabic Western numeral script. The Eastern Arabic variety forms the basis of the symbols now used in the Eastern parts of the Arab world, and in Eastern languages that use the Arabic script. The other, western variety, was used used in Western parts of the Arab world and were intorduced to Europe in the 13th century and then further spread to be now used in most of the world.

Description

Arabic numerals use a positional base 10 numeral system with ten distinct symbols representing the 10 numerical digits. Each digit has a value which is multiplied by a power of ten according to its position in the number; the left-most 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 symbols (the ten digits, decimal marker, vinculum or division sign, and an optional prepended dash to indicate a negative number).

History

The Arabic (Western) Numerals, used in the West and throughout the world are based on ancient Hindu numerals, but are referred to in the West as Arabic numerals, since it reached Europe, after considerable modification, through the Arabs.

The Hindu-Arabic Numerals also include the Arabic (Eastern) Numerals, which the Arabs still call the "Indian numerals", أرقام هندية, arqam hindiyyah), and are used in Egypt and East to it. The Arabic (Western) Numerals are now called Western Numerals by the Arabs, in reference to their adoption by the West, as well their historical use in Western parts of the Arab World. So for a young Arab, this ironic situation can be a source of confusion, in that the West would call them Arabic Numerals but the Arabs would call them Western Numerals.

The nine numerals now in use trace their origin to Indian numerals, before the rise of the Arab nation, and were already moving West and mentioned in Syria in 662 AD by the Nestorian scholar Severus Sebokht who wrote:

I will omit all discussion of the science of the Indians, ... , of their subtle discoveries in astronomy, discoveries that are more ingenious than those of the Greeks and the Babylonians, and of their valuable methods of calculation which surpass description. I wish only to say that this computation is done by means of nine signs. If those who believe, because they speak Greek, that they have arrived at the limits of science, would read the Indian texts, they would be convinced, even if a little late in the day, that there are others who know something of value.

In his authoritative work The Arithmetic of Al-Uqlîdisî (Dordrecht: D. Reidel, 1978), A.S. Saidan's studies were unable to answer in full how the numerals reached the Arab world:

It seems plausible that it drifted gradually, probably before the seventh century, through two channels, one starting from Sind, undergoing Persian filtration and spreading in what is now known as the Middle East, and the other starting from the coasts of the Indian Ocean and extending to the southern coasts of the Mediterranean.

He notes, however, that Al-Uqlidisi's work, Kitâb al-FusÞl fî al-Hisâb al-Hindî, "the earliest extant Arabic work of Hindu-Arabic arithmetic", written in Damascus in AD 952–953, showed “this system at its earliest stages and the first steps in its development.” (ibid, p. xi.), especially so that "The manuscript claimed to have a collection of all past knowledge on arithmetic" and "a clear exposition of what was currently known about the subject". Saidan also writes:

Whatever the case may be, it should be pointed out that Arabic works give no reference whatsoever to any Sanskrit text or Hindu arithmetician, nor do they quote any Sanskrit term or statement.

This is in line with what Professor Lam Lay Yon, member of the International Academy of the History of Science, points out in her 1996 paper titled "The Development of Hindu-Arabic and Traditional Chinese Arithmetic":

There are no descriptions of the Hindu-Arabic numeral system and the fundamental operations of arithmetic among the early Hindu treatises. With the exception of the Bakhshali Manuscript, whose date is controversial (could be as late as the 12th century), the treatises do not use the Hindu-Arabic numerals to represent numbers. Rather, numbers are generally written in Sanskrit in a terse stanza form. The Aryabhatiya, written by Aryabhata (b. 476 AD), contains a description of an alphabetic notation for numerals.(Kripa S. Shukla (ed.), Aryabhatiya of Aryabhata (New Delhi: Indian National Science Academy, 1976), pp. 3–5; S. N. Sen, “Aryabhata’s Mathematics,” Bulletin of the National Institute of Sciences of India no. 21 (1962), pp. 298–305.)

Until Al-Uglidisi's work, the Indian numerals and arithmetics required the use of a sand board, which was an obstacle to their use in official manuscripts. As-Suli in the first half of the tenth Century:

Official scribes nevertheless avoid using because it requires equipment and they consider that a system that requires nothing but the members of the body is more secure and more fitting to the dignity of a leader.

In his work cited above, Al-Uglidisi showed required modification to the numerals and arithmetics to make them suitable for use by pen and paper, which was a major improvement.

Al-Uqlidisi book was also the earliest known text to offer treatment of decimal fraction.

The numerals though were already in wide use throughout the Arab empire, as Avicenna who was born in 980 tells in his autobiography that he learnt them, as a child, from a humble vegetable seller. He also tells that when his father, in Bukhara, was visited by scholars from Egypt in 997, including Abu Abdullah al-Natili, they taught him more about them. J J O'Connor and E F Robertson point out:

He also tells of being taught Indian calculation and algebra by a seller of vegetables. All this shows that by the beginning of the eleventh century calculation with the Indian symbols was fairly widespread and, quite significantly, was known to a vegetable trader.

Of prime importance in the Hindu-Arabic Numeral system is the use of 0 (zero). There are two different concepts here, the first is the use of zero as a place holder (a mathematical punctuation mark), and then as a number.

It should not be assumed that 0 was the invention of the Hindu-Arabic numeral system however, since the Babylonians were in fact the first known to use it. The 0 is thought by some to have come from O, which is omicron, the first letter in the Greek word for nothing, namely "ouden". An alternative theory is that it stood for "obol", a coin of almost no value, and that it arose when counters were used on sand board, so that a removed coin would leave a depression in the sand that looked like an O. Ptolemy, writing in 130 AD in his work the Almagest, used the Babylonian system with the empty place holder O, and "many historians of mathematics believe that the Indian use of zero evolved from its use by Greek astronomers".

According to Professor EF Robertson and DR JJ O'Connor, "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. This is also verified by Professor Lam Lay Yong, an an Effective Member of the International Academy of the History of Science "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 870 AD".

The numerals came to fame due to their use in the pivotal work of the Arab mathematician Al-Khwarizmi, whose book On the Calculation with Hindu Numerals was written about 825, and the Arab mathematician Al-Kindi, who wrote four volumes (see ) "On the Use of the Indian Numerals" (Ketab fi Isti'mal al-'Adad al-Hindi) about 830. They, amongst other works, contributed to the diffusion of the Indian system of numeration in the Middle-East and the West.

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, Germany.)

In the last few centuries, the European variety of Arabic numbers was spread around the world and gradually became the most commonly used numeral system in the world. Even in many countries in languages which have their own numeral systems, the European Arabic numerals are widely used in commerce and mathematics.

Symbols

The Arabic numeral system has used many different sets of symbols. These symbol 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).

Table of numerals

It is interesting to note that, like 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 numbers and Roman numerals). Theorists believe that this is because it becomes difficult to instantaneously count objects past three.

External links

• Unicode reference charts:
  • Arabic (See codes U+0660-U+0669, U+06F0-U+06F9)
  • Devanagari (See codes U+0966-U+096F)
• Charles Seife (2000). Zero: The Biography of a Dangerous Idea (paperback ed.). Crown Publishing. ISBN 0140296476.

• History of the Numerals
  • "The Development of Hindu-Arabic and Traditional Chinese Arithmetic" by Professor Lam Lay Yon, member of the International Academy of the History of Science
  • Indian numerals:
  • Arabic numerals:
  • Hindu-Arabic numerals:

• Numerals page at http://St-Takla.org
• http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Arabic_numerals.html - The Arabic numeral system by: J J O'Connor and E F Robertson

• Numeration
• Elementary mathematics
• Arabic language