|Description=Arabic numerals set in [[Source Sans]]}}
|Description=Arabic numerals set in [[Source Sans]]}}
{{numeral systems}}
{{numeral systems}}
'''Arabic numerals''' are the ten [[numerical digit|digits]]: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The term often implies a [[decimal]] [[number]] written using these digits, which is the most common system for the symbolic representation of numbers intheworldtoday,and is also called '''Hindu–Arabic numerals'''.<ref name="HA2">{{Citation|last1=Schipp|first1=Bernhard|title=Statistical Inference, Econometric Analysis and Matrix Algebra: Festschrift in Honour of Götz Trenkler|url=https://books.google.com/?id=t6XfLJzqO_kC&pg=PA387|page=387|year=2008|publisher=[[SpringerScience+Business Media|Springer]]|isbn=9783790821208|last2=Krämer|first2=Walter}}</ref><ref name="Lumpkin2">{{Citation|last1=Lumpkin|first1=Beatrice|title=Multicultural science and math connections: middle school projects and activities|url=https://books.google.com/?id=2LgG8lsJQmAC&pg=PA118|page=118|year=1995|publisher=Walch Publishing|isbn=9780825126598|last2=Strong|first2=Dorothy}}</ref> However the term can mean the digits themselves, such as in the statement "[[octal]] numbers are written using Arabic numerals."
'''Arabic numerals''' are the ten [[numerical digit|digits]]: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The term often implies a [[decimal]] [[number]] written using these digits(inparticularwhencontrastedwith ''[[Romannumerals]]''). However the term can mean the digits themselves, such as in the statement "[[octal]] numbers are written using Arabic numerals."
Although the [[Hindu–Arabic numeral system]] (i.e. decimal) was developed by [[Indian mathematics|Indian mathematicians]] around AD 500,<ref name="Cengage Learning">{{cite book| first1=Richard |last1= Bulliet|first2= Pamela |last2=Crossley|first3= Daniel |last3=Headrick|first4= Steven |last4= Hirsch|first5= Lyman |last5= Johnson| title = The Earth and Its Peoples: A Global History, Volume 1 |page = 192 |quote = Indian mathematicians invented the concept of zero and developed the "Arabic" numerals and system of place-value notation used in most parts of the world today |publisher = Cengage Learning |year = 2010|url = https://books.google.com/books?id=dOxl71w-jHEC&pg=PA192|isbn = 1439084742}}{{better source|date=January 2017}}</ref>they were modified into Arabic numerals later in North Africa. It was in the North African city of [[Bejaia]] that the [[Italian people|Italian]] scholar [[Fibonacci]] first encountered the numerals; his work was crucial in making them known throughout Europe. European trade, books, and [[colonialism]] helped popularize the adoption of Arabic numerals around the world. The numerals have found worldwide use significantly beyond the contemporary [[spread of the Latin alphabet]], intruding into the writing systems in regions where other variants of the Hindu–Arabic numerals had been in use, such as [[Chinese numerals|Chinese]] and [[Japanese numerals|Japanese]] writing.
Although the [[Hindu–Arabic numeral system]]<ref name="HA2">{{Citation|last1=Schipp|first1=Bernhard|title=Statistical Inference, Econometric Analysis and Matrix Algebra: Festschrift in Honour of Götz Trenkler|url=https://books.google.com/?id=t6XfLJzqO_kC&pg=PA387|page=387|year=2008|publisher=[[Springer Science+Business Media|Springer]]|isbn=9783790821208|last2=Krämer|first2=Walter}}</ref><ref name="Lumpkin2">{{Citation|last1=Lumpkin|first1=Beatrice|title=Multicultural science and math connections: middle school projects and activities|url=https://books.google.com/?id=2LgG8lsJQmAC&pg=PA118|page=118|year=1995|publisher=Walch Publishing|isbn=9780825126598|last2=Strong|first2=Dorothy}}</ref> (i.e. decimal) was developed by [[Indian mathematics|Indian mathematicians]] around AD 500,<ref name="Cengage Learning">{{cite book| first1=Richard |last1= Bulliet|first2= Pamela |last2=Crossley|first3= Daniel |last3=Headrick|first4= Steven |last4= Hirsch|first5= Lyman |last5= Johnson| title = The Earth and Its Peoples: A Global History, Volume 1 |page = 192 |quote = Indian mathematicians invented the concept of zero and developed the "Arabic" numerals and system of place-value notation used in most parts of the world today |publisher = Cengage Learning |year = 2010|url = https://books.google.com/books?id=dOxl71w-jHEC&pg=PA192|isbn = 1439084742}}{{better source|date=January 2017}}</ref>quite different forms for the digits were used initially. They were modified into Arabic numerals later in North Africa. It was in the North African city of [[Bejaia]] that the [[Italian people|Italian]] scholar [[Fibonacci]] first encountered the numerals; his work was crucial in making them known throughout Europe. European trade, books, and [[colonialism]] helped popularize the adoption of Arabic numerals around the world. The numerals have found worldwide use significantly beyond the contemporary [[spread of the Latin alphabet]], intruding into the writing systems in regions where other variants of the Hindu–Arabic numerals had been in use, such as [[Chinese numerals|Chinese]] and [[Japanese numerals|Japanese]] writing.
The term ''Arabic numerals'' may be intended to mean the numerals used in [[Arabic]] writing, such as the [[Eastern Arabic numerals]]. The ''[[Oxford English Dictionary]]'' uses lowercase ''Arabic numerals'' to refer tothese digits, and capitalized ''Arabic Numerals'' to refer to the Eastern digits.<ref>"Arabic", ''Oxford English Dictionary'', 2nd edition</ref>
The term ''Arabic numerals'' may be intended to mean the numerals used in [[Arabic]] writing, such as the [[Eastern Arabic numerals]]. The ''[[Oxford English Dictionary]]'' uses lowercase ''Arabic numerals'' to refer toWestern digits, and capitalized ''Arabic Numerals'' to refer to the Eastern digits.<ref>"Arabic", ''Oxford English Dictionary'', 2nd edition</ref>
Other alternative names are ''Western Arabic numerals'', ''Western numerals'', ''Hindu numerals'', and [[Unicode]] ''digits''.<ref>[https://www.unicode.org/charts/PDF/U0000.pdf Official Unicode Consortium code chart]</ref>
Other alternative names are ''Western Arabic numerals'', ''Western numerals'', ''Hindu-Arabic numerals'', and [[Unicode]] just uses the unadorned term ''digits''.<ref>[https://www.unicode.org/charts/PDF/U0000.pdf Official Unicode Consortium code chart]</ref>
Arabic numerals are the tendigits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The term often implies adecimalnumber written using these digits (in particular when contrasted withRoman numerals). However the term can mean the digits themselves, such as in the statement "octal numbers are written using Arabic numerals."
Although theHindu–Arabic numeral system[1][2] (i.e. decimal) was developed byIndian mathematicians around AD 500,[3] quite different forms for the digits were used initially. They were modified into Arabic numerals later in North Africa. It was in the North African city ofBejaia that theItalian scholarFibonacci first encountered the numerals; his work was crucial in making them known throughout Europe. European trade, books, andcolonialism helped popularize the adoption of Arabic numerals around the world. The numerals have found worldwide use significantly beyond the contemporaryspread of the Latin alphabet, intruding into the writing systems in regions where other variants of the Hindu–Arabic numerals had been in use, such asChinese andJapanese writing.
The termArabic numerals may be intended to mean the numerals used inArabic writing, such as theEastern Arabic numerals. TheOxford English Dictionary uses lowercaseArabic numerals to refer to Western digits, and capitalizedArabic Numerals to refer to the Eastern digits.[4]
Other alternative names areWestern Arabic numerals,Western numerals,Hindu-Arabic numerals, andUnicode just uses the unadorned termdigits.[5]
The numeral "zero" as it appears in two numbers (50 and 270) in an inscription inGwalior, India. Dated to the 9th century.[6][7]
The decimal Hindu–Arabic numeral system with zero was developed in India by around 700.[8] The development was gradual, spanning several centuries, but the decisive step was probably provided byBrahmagupta's formulation ofzero as a number in 628. Prior to Brahmagupta, zero was in use in various forms but was regarded as a 'blank spot' (sunya sthana) in a positional number. It was only used by mathematicians (ganakas—people doing calculations) while the general populace used the traditionalBrahmi numerals. After 700, the decimal numbers with zero replaced the Brahmi numerals. The system was revolutionary by limiting the number of individual digits to ten. It is considered an important milestone in the development of mathematics.[citation needed]
The numerals used in theBakhshali manuscript, dated to sometime between the 3rd and 7th century AD.
Thenumeral system came to be known to thecourt of Baghdad, where mathematicians such as thePersianAl-Khwarizmi, whose bookOn the Calculation with Hindu Numerals (Template:Lang-ar) was written about 825 inArabic, and then the Arab mathematicianAl-Kindi, 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.[9]
According toAl-Beruni, there were multiple forms of numerals in use in India, and "Arabs chose among them what appeared to them most useful"[citation needed]. Al-Nasawi wrote in the early eleventh century that the mathematicians had not agreed on the form of numerals, but most of them had agreed to train themselves with the forms now known asEastern Arabic numerals.[10] The oldest specimens of the written numerals available from Egypt in 873–874 show three forms of the numeral "2" and two forms of the numeral "3", and these variations indicate the divergence between what later became known as the Eastern Arabic numerals and the (Western) Arabic numerals.[11]
Calculations were originally performed using a dust board (takht, Latin:tabula) which involved writing symbols with a stylus and erasing them as part of calculations.Al-Uqlidisi then invented a system of calculations with ink and paper "without board and erasing" (bi-ghayr takht wa-lā maḥw bal bi-dawāt wa-qirṭās).[12] The use of the dust board appears to have introduced a divergence in terminology as well: whereas the Hindu reckoning was calledḥisāb al-hindī in the east, it was calledḥisāb al-ghubār in the west (literally, "calculation with dust").[13] The numerals themselves were referred to in the west asashkāl al‐ghubār (dust figures, in Ibn al-Yāsamin) orqalam al-ghubår (dust letters).[14]
The western Arabic variants of the symbols came to be used inMaghreb andAl-Andalus, which are the direct ancestor of the modern "Arabic numerals" used throughout the world.[15]The divergence in the terminology has led some scholars to propose that the Western Arabic numerals had a separate origin in the so-called "ghubār numerals" but the available evidence indicates no separate origin.[16]Woepecke has also 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.[17][18][19]
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.[20]
Adoption in Europe
Evolution of Indian numerals into Arabic numerals and their adoption in EuropeWoodcut showing the 16th centuryastronomical clock ofUppsala Cathedral, with two clockfaces, one with Arabic and one with Roman numerals.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 presents them with theHebrew alphabet andastrology.Late 18th-century French revolutionary "decimal" clockface.
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 were also using theEastern Arabic numerals (٠١٢٣٤٥٦٧٨٩) in other areas.
In 825Al-Khwārizmī wrote a treatise in Arabic,On the Calculation with Hindu Numerals,[21] which survives only as the 12th-century Latin translation,Algoritmi de numero Indorum.[22][23]Algoritmi, the translator's rendition of the author's name, gave rise to the wordalgorithm.[24]
The first mentions of the numerals in the West are found in theCodex Vigilanus of 976.[25]
From the 980s, Gerbert ofAurillac (later,Pope Sylvester II) used his position to spread knowledge of the numerals in Europe. Gerbert studied inBarcelona in his youth. He was known to have requested mathematical treatises concerning theastrolabe fromLupitus of Barcelona after he had returned to France.[citation needed]
When my father, who had been appointed by his country as public notary in the customs atBugia acting for thePisan 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 European acceptance of the numerals was accelerated by the invention of theprinting press, and they became widely known during the 15th century. Early evidence of their use inBritain includes: an equal hour horaryquadrant from 1396,[26] in England, a 1445 inscription on the tower ofHeathfield Church,Sussex; a 1448 inscription on a wooden lych-gate ofBray Church,Berkshire; and a 1487 inscription on the belfry door atPiddletrenthide church,Dorset; and inScotland a 1470 inscription on the tomb of the first Earl of Huntly inElgin Cathedral. (See G.F. Hill,The Development of Arabic Numerals in Europe for more examples.) In central Europe, theKing of HungaryLadislaus the Posthumous, started the use of Arabic numerals, which appear for the first time in a royal document of 1456.[27] By the mid-16th century, they were in common use in most of Europe.[28]Roman numerals remained in use mostly for the notation ofanno Domini years, and for numbers on clockfaces.
The evolution of the numerals in early Europe is shown here in a table created by the French scholarJean-Étienne Montucla in hisHistoire de la Mathematique, which was published in 1757:
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.
Iron plate with an order 6magic square in Persian/ Arabic numbers from China, dating to theYuan Dynasty (1271–1368).
Positional notation was introduced to China during theYuan Dynasty (1271–1368) by the MuslimHui people. In the early 17th century, European-style Arabic numerals were introduced by Spanish and PortugueseJesuits.[29][30][31]
Encoding
The ten Arabic numerals are encoded in virtually every character set designed for electric, radio, and digital communication, such asMorse code.
They are encoded inASCII at positions 0x30 to 0x39.Masking to the lower 4 binary bits (or taking the lasthexadecimal digit) gives the value of the digit, a great help in converting text to numbers on early computers. These positions were inherited inUnicode.[32]EBCDIC used different values, but also had the lower 4 bits equal to the digit value.
^Bulliet, Richard; Crossley, Pamela; Headrick, Daniel; Hirsch, Steven; Johnson, Lyman (2010).The Earth and Its Peoples: A Global History, Volume 1. Cengage Learning. p. 192.ISBN1439084742.Indian mathematicians invented the concept of zero and developed the "Arabic" numerals and system of place-value notation used in most parts of the world today[better source needed]
^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.
^Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered 2003, pp. 12–13: "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 (calledḥisāb al-ghubār) was known in the West from the tenth century onward..."
^Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered 2003, p. 10: 'I should think that, therefore, it is no longer justified for us to call the Western Arabic forms of the Hindu-Arabic numerals "ghubār numerals." Rather we should speak of the Eastern and the Western Arabic forms of the nine numerals.'
^Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered 2003, pp. 12–13: "Since edition of and research on the Pseudo-Boethius[41] 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."
^Gandz, Solomon (November 1931), "The Origin of the Ghubār Numerals, or the Arabian Abacus and the Articuli",Isis,16 (2):393–424,doi:10.1086/346615,JSTOR224714
^Ifrah, Georges (1998).The universal history of numbers: from prehistory to the invention of the computer; translated from the French by David Bellos. London: Harvill Press. pp. 356–357.ISBN9781860463242.
Burnett, Charles (2006), "The Semantics of Indian Numerals in Arabic, Greek and Latin",Journal of Indian Philosophy,34 (1–2), Springer-Netherlands:15–30,doi:10.1007/s10781-005-8153-z.
Hayashi, Takao (1995),The Bakhshali Manuscript, An ancient Indian mathematical treatise, Groningen: Egbert Forsten,ISBN906980087X.
Ifrah, Georges (2000),A Universal History of Numbers: From Prehistory to Computers, New York: Wiley,ISBN0471393401.
Katz, Victor J. (ed.) (20 July 2007),The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton, New Jersey: Princeton University Press,ISBN0691114854{{citation}}:|first1= has generic name (help);Cite has empty unknown parameter:|publication-year= (help).
