Arabic numerals
Arabic numerals, known formally as
Hindu-Arabic numerals, and also known as
Indian numerals,
Hindu numerals,
European numerals, and
Western numerals, are the most common
symbolic representation of
numbers around the world. They are considered an important milestone in the development of
mathematics.
One may distinguish between the
decimal system involved, also known as the
Hindu-Arabic numeral system, and the precise
glyphs used. The glyphs most commonly used in conjunction with the
Latin alphabet since
Early Modern times are
0 1 2 3 4 5 6 7 8 9.
The numbers were developed in
India by the
Hindus around
400 BCE. However, because it was
Arabs who relayed this system to the
West after the Hindu numerical system found its way to
Baghdad, the numeral system became mis-identified as "Arabic" in the eyes of the
Europeans. Arabs themselves call the
Eastern Arabic numerals "Indian numerals," أرقام هندية, (
arqam hindiyyah) and use a different set of Arabic symbols as numerals.
Origins
The symbols for 1 to 9 in the
Hindu-Arabic numeral system evolved from the
Brahmi numerals.
Buddhist inscriptions from around 300 BCE 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.
Use of the 0 glyph is first recorded in the
9th century, in an inscription at
Gwalior dated to
870, and in the work of
Al-Khwarizmi.
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Modern day Arab telephone keypad with Hindu-Arabic numerals and corresponding Arabic-language numerals |
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
Arab mathematician
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-East and the West [
1]. In the
10th century,
Middle-Eastern mathematicians extended the decimal numeral system to include fractions, as recorded in a treatise by
Syrian mathematician
Abu'l-Hasan al-Uqlidisi in
952-
953.
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. Therefore, it was not until
Fibonacci that the Arabic numeral system was used by a large population.
A distinctive "West Arabic" variant of the symbols begins to emerge in ca. the
10th century in the
Maghreb and
Al-Andalus, called the
ghubar ("sand-table" or "dust-table") numerals.
The first mentions of the numerals in the West are found in the Codex Vigilanus of
976 [
2]. From the
980s,
Gerbert of Aurillac began to spread knowledge of the numerals in Europe. Gerbert studied in
Barcelona in his youth, and he is known to have requested mathematical treatises concerning the
astrolabe from
Lupitus of Barcelona after he had returned to France.
Adoption in Europe
|
German manuscript page teaching use of Arabic numerals (Talhoffer Thott, 1459). At this time, knowledge of the numerals was still widely seen as esoteric, and Talhoffer teaches them together with the Hebrew alphabet and astrology. |
 |
Woodcut showing the 16th century astronomical clock of Uppsala cathedral, with two clockfaces, one with Arabic and one with Roman numerals. |
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Late 18th century French revolutionary "decimal" clockface. |
Al-Khwarizmi's
825 treatise
On the Calculation with Hindu Numerals was translated into Latin in the
12th century, as
Algoritmi de numero Indorum (
Algoritmi being the translator's rendition of the author's name,
, ultimately leading to the term
algorithm).
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, 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 Bugia acting 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 running from left to right, unlike the Arabic alphabet, this resulted in an inverse arrangement of the place-values relative to the direction of reading.
The European acceptance of the numerals was accelerated by the invention of the
printing press, and they became commonly known during the
15th century. The first known use in
England was on a 1487 inscription (the date being written in Arabic numerals) at
Piddletrenthide church,
Dorset. By the mid
16th century, they were in common use in most of Europe.[
3] Roman numerals remained in use mostly for the notation of years of the
Common Era, 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.
The numeral system employed, known as
Algorism, is
positional decimal notation.Various symbol sets are used to represent numbers in the
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" which were developed in
al-Andalus and 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 languages as shown as "East Arabic-Indic".
*the "Devanagari numerals" used with
Devanagari and related variants grouped as
Indian numerals.
The Arabic numerals are encoded in
ASCII (and
Unicode) at positions 48 to 57:
| Binary | Dec | Hex | Glyph |
|---|
| 0011 0000 | 48 | 30 | 0 |
| 0011 0001 | 49 | 31 | 1 |
| 0011 0010 | 50 | 32 | 2 |
| 0011 0011 | 51 | 33 | 3 |
| 0011 0100 | 52 | 34 | 4 |
| 0011 0101 | 53 | 35 | 5 |
| 0011 0110 | 54 | 36 | 6 |
| 0011 0111 | 55 | 37 | 7 |
| 0011 1000 | 56 | 38 | 8 |
| 0011 1001 | 57 | 39 | 9 |
*
Hindu-Arabic numeral system*
History of Counting Systems and Numerals. Retrieved
11 December 2005.
*
The Evolution of Numbers.
16 April 2005.
*O'Connor, J. J. and Robertson, E. F.
Indian numerals. November 2000.
*History of the Numerals
**
Arabic numerals:
**
Hindu-Arabic numerals:
