The
Arabic numerals are the ten
digits
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
They are descended from the
Hindu-Arabic numeral system
developed by
Indian
mathematicians, by which a sequence of digits such as "975" is
read as a whole
number. The Indian numerals
were adopted by the
Persian
mathematicians in India, and passed on to the Arabs further
west. The numerals were modified in shape as they were passed
along; developing their modern European shapes by the time they
reached
North Africa. From there they
were transmitted to
Europe in the
Middle Ages. The use of Arabic numerals spread
around the world through European trade, books and
colonialism. Today they are the most common
symbolic representation of numbers in the world.
As befitting their history, the digits (0,1,2,3,4,5,6,7,8,and 9)
are also known as
Hindu or
Hindu-Arabic
numerals. The reason that they are more commonly known as
"Arabic numerals" in Europe and the Americas is that they were
introduced to Europe in the tenth century from Arabs of North
Africa. There they were (and still are) the digits used by western
Arabs from Libya to Morocco. Arabs, on the other hand, call the
system "
Hindu numerals", referring to their
origin in India. This is not to be confused with what the Arabs
call the "Hindi numerals", namely the
Eastern Arabic numerals
(٠.١.٢.٣.٤.٥.٦.٧.٨.٩) used in the
Mideast,
or any of the
numerals currently
used in India (e.g.
Devanagari:
०.१.२.३.४.५.६.७.८.९).
In English, the term
Arabic numerals can be ambiguous. It
most commonly refers to the numeral system widely used in Europe
and the Americas.
Arabic numerals is the conventional name
for the entire family of related systems of Arabic and
Indian numerals. It may also be intended to
mean the numerals used by Arabs, in which case it generally refers
to the Eastern Arabic numerals.
The decimal Hindu-Arabic numeral system was invented in India
around 500 AD. The system was revolutionary in that it included a
zero and
positional notation. It is considered an
important milestone in the development of mathematics. One may
distinguish between this positional
system, which is
identical throughout the family, and the precise
glyphs used to write the numerals, which vary
regionally. 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.
Although the phrase "Arabic numeral" is frequently capitalized, it
is sometimes written in lower case: for instance, in its entry in
the
Oxford English
dictionary. This helps distinguish it from "Arabic numerals" as
the East Arabic numerals specific to the Arabs.
History
Origins
The
digits 1 to 9 in the
Hindu-Arabic numeral system
evolved from the
Brahmi numerals.
Buddhist inscriptions from around 300 BC
use the symbols which became 1, 4 and 6. One century later, their
use of the symbols which became 2, 7 and 9 was recorded.
The first
universally accepted inscription containing the use of the 0 glyph
is first recorded in the 9th century, in an inscription at Gwalior in Central India dated to 870. By this
time, the use of the glyph had already reached Persia, and was
mentioned in
Al-Khwarizmi's descriptions
of
Indian numerals. Numerous Indian
documents on
copper
plates exist, with the same symbol for zero in them, dated back
as far as the 6th century AD.
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 in
Arabic, 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. Their
work was principally responsible for the diffusion of the Indian
system of numeration in the
Middle East
and the West.
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 952–53.
A
distinctive West Arabic variant of the symbols begins to emerge
around the 10th century in the Maghreb and
Al-Andalus, called ghubar ("sand-table" or
"dust-table") numerals, which is the direct ancestor to the modern
Western Arabic numerals used throughout the world.
The first mentions of the numerals in the West are found in the
Codex Vigilanus of 976.
From the 980s, Gerbert of Aurillac (later,
Pope Sylvester II) used his office to
spread knowledge of the numerals in Europe.
Gerbert studied in
Barcelona in his youth. He was known to have requested
mathematical treatises concerning the
astrolabe from
Lupitus of Barcelona after he had
returned to France.
Common misconceptions
Despite evidence to the contrary, some
folkloric explanations for the origin of modern
Arabic numerals persist. While these hypotheses continue to
propagate due to their seemingly well-constructed arguments, they
were based entirely on speculation by individuals who, while
genuinely intrigued by the subject, were either ignorant of the
relevant archeological facts, or simply lived in an era preceding
much of their modern rediscovery. One popular example of such myths
claims that the original forms of these symbols indicated their
value through the quantity of angles they contained.
Adoption in Europe
Late 18th century French revolutionary
"decimal" clockface.
In 825
Al-Khwārizmī wrote a treatise in
Arabic,
On the Calculation with Hindu Numerals, which was
translated into Latin from Arabic in the 12th century as
Algoritmi de numero Indorum, where
Algoritmi, the
translator's rendition of the author's name, gave rise to the word
algorithm (Latin
algorithmus, "calculation method").
Fibonacci, a mathematician born in the
Republic of Pisa who had studied in
Bejaia (Bougie), Algeria, promoted
the Indian numeral system in Europe with his
book Liber Abaci, which was
written in 1202:
- "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. Languages written in the Latin alphabet run from left to
right, unlike languages written in the Arabic alphabet. Hence, from
the point of view of the reader, numerals in Western texts are
written with the highest power of the base first whereas numerals
in Arabic texts are written with the lowest power of the base
first.
The European acceptance of the numerals was accelerated by the
invention of the
printing press, and
they became widely known during the 15th century.
Early uses in Britain include a 1445
inscription on the tower of Heathfield Church, Sussex; a 1448 inscription on a wooden lych-gate of
Bray Church, Berkshire; and a 1487
inscription on the belfry door at Piddletrenthide church, Dorset; and in
Scotland a 1470 inscription on the tomb of the first Earl of
Huntly in Elgin, (Elgin,
Moray) Cathedral. (See G.F. Hill,
The
Development of Arabic Numerals in Europe for more examples.)
By the mid-16th century, they were in common use in most of Europe.
Roman numerals remained in use mostly for the notation of
Anno Domini years, 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.
Adoption in Russia
Cyrillic numerals were a numbering
system derived from the
Cyrillic
alphabet, used by
South and
East Slavic
peoples. The system was used in Russia as late as the early
1700s when
Peter the Great
replaced it with Arabic numerals.
Adoption in China
During
Ming and Qing dynasties (when Arabic numerals were first
introduced into China), some Chinese mathematicians used Chinese numeral characters as positional
system digits. After Qing dynasty, both the Chinese numeral
characters and the Suzhou numerals were replaced by Arabic numerals
in mathematical writings.
Evolution of symbols
The numeral system employed, known as
algorism, is
positional decimal notation. Various symbol sets are used to
represent numbers in the Hindu-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 evolution of the numerals in early Europe is shown on a table
created by the French scholar J.E. Montucla in his
Histoire de
la Mathematique, which was published in 1757:
The Arabic numerals are encoded in
ASCII (and
Unicode) at positions 48 to 57:
Binary |
Octal |
Decimal |
Hexadecimal |
Glyph |
0011 0000 |
060 |
48 |
30 |
0 |
0011 0001 |
061 |
49 |
31 |
1 |
0011 0010 |
062 |
50 |
32 |
2 |
0011 0011 |
063 |
51 |
33 |
3 |
0011 0100 |
064 |
52 |
34 |
4 |
0011 0101 |
065 |
53 |
35 |
5 |
0011 0110 |
066 |
54 |
36 |
6 |
0011 0111 |
067 |
55 |
37 |
7 |
0011 1000 |
070 |
56 |
38 |
8 |
0011 1001 |
071 |
57 |
39 |
9 |
See also
Notes
References
External links