Arabic numerals

Arabic numerals, known formally as Hindu-Arabic numerals, and also known as Indian numerals, Hindu numerals, Western Arabic numerals, European numerals, or 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 numerals arose in India between 400 BCE and 400 CE.^[1]^[2]They were transmitted first to West Asia, where they find mention in the 9th century CE, and eventually to Europe in the 10th century CE.^[1] Since knowledge of the numerals reached Europe through the work of Arab mathematicians and astronomers, the numerals came to be called "Arabic numerals."^[2]In Arabic language itself, the Eastern Arabic numerals are called "Indian numerals," أرقام هندية, (arqam hindiyyah) and a different set of symbols are used as numerals.

History

Origins

The symbols for 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.

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.

Brahmi numerals in India in the first century CE

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 (later, Pope Silvester II) 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

(See this link for a 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.)

Late 18th century French revolutionary "decimal" clockface.

Al-Khwārizmī, the Persian scientist, wrote in 825 a treatise On the Calculation with Hindu Numerals, which was translated into Latin in the 12th century, as Algoritmi de numero Indorum, which title was likely intended to mean "Algoritmi about the numbers of the Indians", where "Algoritmi" was the translator's rendition of the author's name; but people misunderstanding the title treated Algoritmi as a Latin plural and this led to the word algorithm (Latin algorithmus) coming to mean "calculation method".

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 written 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. Early uses in England include a 1445 inscription on the tower of Heathfield Church, Sussex, a 1448 inscription on a wooden lych-gate of Bray Church, Berkshire, a 1470 inscription on the tomb of the first Earl of Huntly in Elgin Cathedral, and a 1487 inscription on the belfry door at Piddletrenthide church, Dorset. [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.[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.

Evolution of symbols

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 evolution of the numerals in early Europe ist shown on a table created by the French scholar J.E.Montucla in his Histoire de la Mathematique, which was published in 1758:

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

Latest explanation about the origin of the “Arab numerals”

According to a popular tradition, still tough in Egypt and North Africa, the “Arab” figures would be the invention of a glazier geometrician originating in the Maghreb, which would have imagined to give to the nine significant figures an evocative form depending on the number of the angles contained in the drawing of each one of them: an angle for the graphics of figure 1, two angles for figure 2, three angles for the 3, and so on:

File:Nouvelle image (2).png

And we will have the following format :

File:Nouvelle image (1).png

This remained after nine and zero as they are. make turn around eight, six, five, four, three and one.Reverse number two and the figure of seven. The delivery of some of these forms to each other, without change in the arrangement, we get this form:

File:Nouvelle image.png

This is an Arab sentence meaning: my goal it is calculation (وهدَفي حسابْ) in kufi writing(This name and called on all lines, which tend to location, and engineering).

References

^ ^a ^b Ifrah, Georges. 1999. The Universal History of Numbers : From Prehistory to the Invention of the Computer, Wiley. ISBN 0-471-37568-3.
^ ^a ^b 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.

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.

External links

History of the Numerals
- Arabic numerals:
- Hindu-Arabic numerals:

[ifrah-1] Ifrah, Georges. 1999. The Universal History of Numbers : From Prehistory to the Invention of the Computer, Wiley. ISBN 0-471-37568-3.

[oconnor-2] 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.

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