| Numeral systems by culture | |
|---|---|
| Hindu-Arabic numerals | |
| Western Arabic (Hindu numerals) Eastern Arabic Indian family Tamil |
Burmese Khmer Lao Mongolian Thai |
| East Asian numerals | |
| Chinese Japanese Suzhou |
Korean Vietnamese Counting rods |
| Alphabetic numerals | |
| Abjad Armenian Āryabhaṭa Cyrillic |
Ge'ez Greek Georgian Hebrew |
| Other systems | |
| Aegean Attic Babylonian Brahmi Egyptian Etruscan Inuit |
Kharosthi Mayan Quipu Roman Sumerian Urnfield |
| List of numeral system topics | |
| Positional systems by base | |
| Decimal (10) | |
| 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 20, 24, 30, 36, 60, 64 | |
| Non-positional system | |
| Unary numeral system (Base 1) | |
| List of numeral systems | |
Arabic numerals or Hindu numerals[1][2] or Hindu-Arabic numerals[2][3] or Indo-Arabic numerals[4] 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, in which a sequence of digits such as "975" is read as a numeral. The Indian numerals were adopted by the Persian mathematicians in India, and passed on to the Arabs further west. 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 known as Hindu numerals or "Hindu-Arabic numerals". The reason they are more commonly known as "Arabic numerals" in Europe and the Americas is that they were introduced to Europe in the 10th century by Arabs of North Africa, who were then using the digits from Libya to Morocco. Europeans did not know about the numerals' origins in ancient India, so they named them "Arabic numerals".[5] Arabs, on the other hand, call the system "Hindu numerals",[6][7] 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 Middle East, or any of the numerals currently used in Indian languages (e.g. Devanagari: ०.१.२.३.४.५.६.७.८.९).[8]
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 CE.[8][9] The system was revolutionary by including 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 script 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.[10] This helps distinguish it from "Arabic numerals" as the East Arabic numerals specific to the Arabs.
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The digits 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, 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 CE.[11]
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.[12] 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. The decimal point notation was introduced by Sind ibn Ali, he also wrote the earliest treatise on Arabic numerals.
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 are the direct ancestor of the modern Western Arabic numerals used throughout the world.[13]
Some folk etymologies argue that the original forms of these symbols indicated their value through the number of angles they contained,[14] however there is no proof of any such origin.
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").
The first mentions of the numerals in the West are found in the Codex Vigilanus of 976.[15] From the 980s, Gerbert of Aurillac (later, Pope Sylvester II) used his position 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.
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:
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 evidence of their use in Britain includes: an equal hour horary quadrant from 1396,[16] in England, 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 Cathedral. (See G.F. Hill, The Development of Arabic Numerals in Europe for more examples.) In central Europe, the King of Hungary Ladislaus the Posthumous, started the use of Arabic numerals, which appear for the first time in a royal document of 1456.[17] By the mid-16th century, they were in common use in most of Europe.[18] 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), for sequential volumes, to differentiate monarchs or family members with the same first names, and (in lower case) to number pages in prefatory material in books.
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 18th century when Peter the Great replaced it with Arabic numerals.
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 the Qing dynasty, both the Chinese numeral characters and the Suzhou numerals were replaced by Arabic numerals in mathematical writings.
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 |
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