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Arabic numerals, also called Hindu–Arabic numerals,

are the ten : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, based on the Hindu–Arabic numeral system,

(2018). 9781439084748, Cengage Learning. .
the most common system for the symbolic representation of in the world today. In this , a sequence of digits such as "975" is read as a single number, using the position of the digit in the sequence to interpret its value. They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians around AD 500.

The system was adopted by Arabic mathematicians in and passed on to the Arabs farther west. There is some evidence to suggest that the numerals in their current form developed from in the , the western region of the . On the Origin of Arabic Numerals - A. Boucenna - Université Ferhat Abbas The current form of the numerals developed in North Africa, distinct in form from the Indian and Eastern Arabic numerals. It was in the North African city of that the scholar first encountered the numerals; his work was crucial in making them known throughout Europe. The use of Arabic numerals spread around the world through European trade, books and .

The term Arabic numerals is ambiguous. It most commonly refers to the numerals widely used in Europe and the Americas; to avoid confusion, calls these European digits. Arabic numerals is also the European name for the entire family of related numerals of Arabic and . It may also be intended to mean the numerals used by Arabs, in which case it generally refers to the Eastern Arabic numerals. It would be more appropriate to refer to the Arabic numeral system, where the value of a digit in a number depends on its position.

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,"Arabic", Oxford English Dictionary, 2nd edition which helps to distinguish it from "Arabic numerals" as the East Arabic numerals specific to the Arabs.


History

Origins
The decimal Hindu–Arabic numeral system with zero was developed in India by around AD 700.O'Connor, J. J. and E. F. Robertson. 2000. Indian Numerals, MacTutor History of Mathematics Archive, School of Mathematics and Statistics, University of St. Andrews, Scotland. The development was gradual, spanning several centuries, but the decisive step was probably provided by 's formulation of as a number in AD 628. The system was revolutionary by including zero in positional notation, thereby limiting the number of individual digits to ten. 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 used to write the numerals, which varied regionally.

The glyphs most commonly used in conjunction with the since early modern times are 0 1 2 3 4 5 6 7 8 9. The first universally accepted inscription containing the use of the 0 glyph in India is first recorded in the 9th century, in an inscription at in dated to 870. Numerous Indian documents on copper plates exist, with the same symbol for zero in them, dated back as far as the 6th century AD, but their dates are uncertain. Inscriptions in and dating to AD 683 have also been found.

The came to be known to the court of Baghdad, where mathematicians such as the Al-Khwarizmi, whose book On the Calculation with Hindu Numerals was written about 825 in , and the mathematician , who wrote four volumes, On the Use of the Indian Numerals ( Ketab fi Isti'mal al-'Adad al-Hindi) about 830, propagated it in the Arab world. Their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West. The MacTutor History of Mathematics archive

In the 10th century, mathematicians extended the decimal numeral system to include , as recorded in a treatise by mathematician Abu'l-Hasan al-Uqlidisi in 952–953. The notation was introduced by Sind ibn Ali, who 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 and (sometimes called ghubar numerals, though the term is not always accepted), which are the direct ancestor of the modern "Arabic numerals" used throughout the world.

"While specimens of Western Arabic numerals from the early period—the tenth to thirteenth centuries—are still not available, we know at least that Hindu reckoning (called ḥisāb al-ghubār) was known in the West from the tenth century onward..."
Woepecke has proposed that the Western Arabic numerals were already in use in Spain before the arrival of the Moors, purportedly received via Alexandria, but this theory is not accepted by scholars.
"Since edition of and research on the Pseudo-Boethius41 we now know that the texts running under his name and carrying Arabic numerals date from the eleventh century. Thus the assumed way of transmission from Alexandria to Spain is impossible and this theory can no longer be taken as serious."


Popular myths
Some popular myths have argued that the original forms of these symbols indicated their numeric value through the number of angles they contained, but no evidence exists of any such origin.
(1998). 9781860463242, Harvill Press.


Adoption in Europe

In 825 Al-Khwārizmī wrote a treatise in Arabic, On the Calculation with Hindu Numerals, Philosophy Of Mathematics Francis, John – 2008 – Page 38 which survives only as the 12th-century Latin translation, Algoritmi de numero Indorum. The Ellipse: A Historical and Mathematical Journey Arthur Mazer – 2011 Algoritmi, the translator's rendition of the author's name, gave rise to the word . Models of Computation: An Introduction to Computability Theory – Page 1 Maribel Fernández – 2009

The first mentions of the numerals in the West are found in the of 976.

From the 980s, Gerbert of (later, Pope Sylvester II) used his position to spread knowledge of the numerals in Europe. Gerbert studied in in his youth. He was known to have requested mathematical treatises concerning the from Lupitus of Barcelona after he had returned to France.

Leonardo Fibonacci (Leonardo of Pisa), a mathematician born in the Republic of Pisa who had studied in Béjaïa (Bougie), , promoted the Indian numeral system in Europe with his 1202 book :

When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the 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 reason the digits are more commonly known as "Arabic numerals" in Europe and the Americas is that they were introduced to Europe in the 10th century by Arabic-speakers of North Africa, who were then using the digits from Libya to Morocco. Arabs, on the other hand, call the system " 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 ( - - - - - - - - - ) used in the Middle East, or any of the numerals currently used in Indian languages (e.g. : ०.१.२.३.४.५.६.७.८.९).

The European acceptance of the numerals was accelerated by the invention of the , and they became widely known during the 15th century. Early evidence of their use in Britain includes: an equal hour horary quadrant from 1396, in England, a 1445 inscription on the tower of Heathfield Church, ; a 1448 inscription on a wooden lych-gate of Bray Church, ; and a 1487 inscription on the belfry door at church, ; and in 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.Erdélyi: Magyar művelődéstörténet 1-2. kötet. Kolozsvár, 1913, 1918 By the mid-16th century, they were in common use in most of Europe. Mathforum.org remained in use mostly for the notation of years, and for numbers on clockfaces.

Today, 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.


Adoption in Russia
Cyrillic numerals were a numbering system derived from the Cyrillic alphabet, used by and . The system was used in Russia as late as the early 18th century when Peter the Great replaced it with Arabic numerals.


Adoption in China

Arabic numerals were introduced to China during the Yuan Dynasty (1271–1368) by the Muslim . In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese Jesuits.

(1997). 9780792340669, Springer. .
(2002). 9780700716913, Psychology Press. .
(2000). 9780486414454, Courier Dover Publications. .


Evolution of symbols
The numeral system employed, known as , is positional notation. Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, potentially including both symbols that evolved from the , and symbols that developed independently. The symbols used to represent the system have split into various typographical variants since the :

  • The widespread Western Arabic numerals used with the , in the table below labelled European, descended from the West Arabic numerals developed in (Andalucía, ) and the . Spanish scholars, because of the geographic proximity, trade, and constant warfare with the Muslim kingdoms of Southern Spain, saw a potential in the simplicity of Arabic numbers, and decided to adopt those symbols, and later other Europeans followed suit. There are two styles for rendering European numerals, known as .
  • The Arabic–Indic or Eastern Arabic numerals, used with the , developed primarily in what is now . A variant of the Eastern Arabic numerals used in the Persian and Urdu languages is shown below as East Arabic-Indic.
  • The Devanagari numerals used with and related variants are grouped as .

The evolution of the numerals in early Europe is shown here in a table created by the French scholar Jean-Étienne Montucla in his Histoire de la Mathematique, which was published in 1757:

The Arabic numeral glyphs 0–9 are encoded in and at positions 0x30 to 0x39, matching up with the second digit for convenience:

0011 000006048300
0011 000106149311
0011 001006250322
0011 001106351333
0011 010006452344
0011 010106553355
0011 011006654366
0011 011106755377
0011 100007056388
0011 100107157399


See also

Sources

Further reading
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