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Arabic numerals are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The term often implies a decimal number written using these digits (in particular when contrasted with Roman numerals). However, the term can also refer to the digits themselves, such as in the statement "octal numbers are written using Arabic numerals."

The numerals were developed in the Maghreb in North Africa. It was in the Algerian city of Bejaia that the 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 numerals had been in use, such as Chinese and Japanese writing.

They are also called Western Arabic numerals, Ghubār numerals,^[1] or digits.^[2] The Oxford English Dictionary uses lowercase Arabic numerals for them, and capitalized Arabic Numerals to refer to the Eastern digits.^[3]

History

Origin of the Arabic numeral symbols

A western Arabic variant of the symbols, Ghubari numerals,^[4] came to be used in North Africa and Andalusia (Maghreb) and Al-Andalus, which are the direct ancestor of the modern Arabic numerals.

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 Spain and North Africa, who were then using the digits from Libya to Morocco. In eastern part of Arabic Peninsula, Arabs were using the Eastern Arabic numerals or "Mashriki" numerals: ٠ ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩^[5]

Adoption in Europe

The first mentions of the numerals in the West are found in the Codex Vigilanus of 976.^[6]

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.^{[citation needed]}

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

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 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,^[7] 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.^[8] By the mid-16th century, they were in common use in most of Europe.^[9] Roman numerals remained in use mostly for the notation of anno 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 scholar Jean-Étienne Montucla in his Histoire de la Mathematique, which was published in 1757:

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 18th century when Peter the Great replaced it with Arabic numerals.

Adoption in China

Positional notation was introduced to China during the Yuan Dynasty (1271–1368) by the Muslim Hui people. In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese Jesuits.^[10]^[11]^[12]

Encoding

The ten Arabic numerals are encoded in virtually every character set designed for electric, radio, and digital communication, such as Morse code.

They are encoded in ASCII at positions 0x30 to 0x39. Masking to the lower 4 binary bits (or taking the last hexadecimal digit) gives the value of the digit, a great help in converting text to numbers on early computers. These positions were inherited in Unicode.^[13] EBCDIC used different values, but also had the lower 4 bits equal to the digit value.

Binary	Octal	Decimal	Hex	Glyph	Unicode	EBCDIC (Hex)
0011 0000	060	48	30	0	U+0030 DIGIT ZERO	F0
0011 0001	061	49	31	1	U+0031 DIGIT ONE	F1
0011 0010	062	50	32	2	U+0032 DIGIT TWO	F2
0011 0011	063	51	33	3	U+0033 DIGIT THREE	F3
0011 0100	064	52	34	4	U+0034 DIGIT FOUR	F4
0011 0101	065	53	35	5	U+0035 DIGIT FIVE	F5
0011 0110	066	54	36	6	U+0036 DIGIT SIX	F6
0011 0111	067	55	37	7	U+0037 DIGIT SEVEN	F7
0011 1000	070	56	38	8	U+0038 DIGIT EIGHT	F8
0011 1001	071	57	39	9	U+0039 DIGIT NINE	F9

Notes

References

^ "Arabic Numerals (Ghubar Numerals)".
^ Official Unicode Consortium code chart
^ "Arabic", Oxford English Dictionary, 2nd edition
^ 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 (called ḥisāb al-ghubār) was known in the West from the tenth century onward..."
^ Shown right-to-left, zero is on the right, nine on the left.
^ "MATHORIGINS.COM_V". www.mathorigins.com.
^ "14th century timepiece unearthed in Qld farm shed". ABC News.
^ Erdélyi: Magyar művelődéstörténet 1-2. kötet. Kolozsvár, 1913, 1918
^ Mathforum.org
^ Helaine Selin, ed. (1997). Encyclopaedia of the history of science, technology, and medicine in non-western cultures. Springer. p. 198. ISBN 978-0-7923-4066-9.
^ Meuleman, Johan H. (2002). Islam in the era of globalization: Muslim attitudes towards modernity and identity. Psychology Press. p. 272. ISBN 978-0-7007-1691-3.
^ Peng Yoke Ho (2000). Li, Qi and Shu: An Introduction to Science and Civilization in China. Courier Dover Publications. p. 106. ISBN 978-0-486-41445-4.
^ "The Unicode Standard, Version 13.0" (PDF). unicode.org. Retrieved 1 September 2021.{{cite web}}: CS1 maint: url-status (link)

Sources

Kunitzsch, Paul (2003), "The Transmission of Hindu-Arabic Numerals Reconsidered", in J. P. Hogendijk; A. I. Sabra (eds.), The Enterprise of Science in Islam: New Perspectives, MIT Press, pp. 3–22, ISBN 978-0-262-19482-2
Plofker, Kim (2009), Mathematics in India, Princeton University Press, ISBN 978-0-691-12067-6

External links

Development of Hindu Arabic and Traditional Chinese Arithmetic
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.
History of the numerals

[1] "Arabic Numerals (Ghubar Numerals)".

[2] Official Unicode Consortium code chart

[3] "Arabic", Oxford English Dictionary, 2nd edition

[4] 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 (called ḥisāb al-ghubār) was known in the West from the tenth century onward..."

[5] Shown right-to-left, zero is on the right, nine on the left.

[6] "MATHORIGINS.COM_V". www.mathorigins.com.

[7] "14th century timepiece unearthed in Qld farm shed". ABC News.

[8] Erdélyi: Magyar művelődéstörténet 1-2. kötet. Kolozsvár, 1913, 1918

[9] Mathforum.org

[10] Helaine Selin, ed. (1997). Encyclopaedia of the history of science, technology, and medicine in non-western cultures. Springer. p. 198. ISBN 978-0-7923-4066-9.

[11] Meuleman, Johan H. (2002). Islam in the era of globalization: Muslim attitudes towards modernity and identity. Psychology Press. p. 272. ISBN 978-0-7007-1691-3.

[12] Peng Yoke Ho (2000). Li, Qi and Shu: An Introduction to Science and Civilization in China. Courier Dover Publications. p. 106. ISBN 978-0-486-41445-4.

[13] "The Unicode Standard, Version 13.0" (PDF). unicode.org. Retrieved 1 September 2021.{{cite web}}: CS1 maint: url-status (link)

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 {{short description|The ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9}}
 {{About|the digits (symbols) only|writing numbers in base 10|Hindu–Arabic numeral system|other uses}}{{Use dmy dates|date=May 2020}}
-{{Use dmy dates|date=May 2020}}
 {{CSS image crop
 |Image=Hindu-Arabic numerals.svg
@@ Line 13: / Line 12: @@
 '''Arabic numerals''' are the ten [[numerical digit|digits]]: 0,&nbsp;1,&nbsp;2,&nbsp;3,&nbsp;4,&nbsp;5,&nbsp;6,&nbsp;7,&nbsp;8 and&nbsp;9. The term often implies a [[decimal]] [[number]] written using these digits (in particular when contrasted with ''[[Roman numerals]]''). However, the term can also refer to the digits themselves, such as in the statement "[[octal]] numbers are written using Arabic numerals."
-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/books?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/books?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 = 978-1439084748}}{{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 [[Algeria|Algerian]] 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 numerals were developed in [[the Maghreb]] in [[North Africa]]. It was in the [[Algeria|Algerian]] 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 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 to Western digits, and capitalized ''Arabic Numerals'' to refer to the Eastern digits.<ref>"Arabic", ''Oxford English Dictionary'', 2nd edition</ref>
+They are also called '''Western Arabic numerals''', '''Ghubār numerals''',<ref>{{cite web |title=Arabic Numerals (Ghubar Numerals)|url=http://materiaislamica.com/index.php/Arabic_Numerals}}</ref> or '''digits'''.<ref>[https://www.unicode.org/charts/PDF/U0000.pdf Official Unicode Consortium code chart]</ref> The ''[[Oxford English Dictionary]]'' uses lowercase ''Arabic numerals'' for them, and capitalized ''Arabic Numerals'' to refer to the [[Eastern Arabic numerals|Eastern digits]].<ref>"Arabic", ''Oxford English Dictionary'', 2nd edition</ref>
-Other alternative names are ''Western Arabic numerals'', ''Western numerals'' and ''Hindu–Arabic numerals''. [[Unicode]] just uses the unadorned term ''digits''.<ref>[https://www.unicode.org/charts/PDF/U0000.pdf Official Unicode Consortium code chart]</ref>
 ==History==
-===Origins===
-{{Main|History of the Hindu–Arabic numeral system}}
-[[File:Gwalior zeros.jpg|thumb|The numeral "zero" as it appears in two numbers (50 and 270) in 9th century inscription in [[Gwalior|Gwalior, India]].<ref>{{cite book |last1=Smith |first1=David Eugene |last2=Karpinski |first2=Louis Charles |title=The Hindu-Arabic numerals |date=1911 |publisher=Boston, London, Ginn and Company |page=52 |url=https://archive.org/stream/hinduarabicnumer00smitrich#page/52/mode/2up}}</ref><ref>[https://www.flickr.com/photos/cristic/8727810760/ For a modern image]</ref>]]
-The decimal Hindu–Arabic numeral system was developed in India by around 700.<ref name=oconnor>O'Connor, J. J. and E. F. Robertson. 2000.  [http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Indian_numerals.html Indian Numerals], ''MacTutor History of Mathematics Archive'', School of Mathematics and Statistics, University of St. Andrews, Scotland.</ref> The development was gradual, spanning several centuries, but the decisive step was probably provided by [[Brahmagupta]]'s formulation of [[zero]] as a numeral in 628.
-[[File:Bakhshali numerals 2.jpg|thumb|right|upright=1.6|The numerals used in the [[Bakhshali manuscript]], dated to sometime between the 3rd and 7th century AD.]]
-The [[numeral system]] came to be known to the [[Abbasid Caliphate|court of Baghdad]], where mathematicians such as the [[Persian people|Persian]] [[Muhammad ibn Musa al-Khwarizmi|Al-Khwarizmi]], whose book ''On the Calculation with Hindu Numerals'' ({{Lang-ar|الجمع والتفريق بالحساب الهندي}} ''Al-Jam` wal-Tafrīq bil-Ḥisāb al-Hindī'') was written about 825 in [[Arabic]], and then the Arab mathematician [[Al-Kindi]], who wrote four volumes, ''On the Use of the Indian Numerals'' ({{lang-ar|كتاب في استعمال الأعداد الهندية}} ''Kitāb fī Isti`māl al-'A`dād al-Hindīyyah'') in about 830. Their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West.<ref>[https://mathshistory.st-andrews.ac.uk/HistTopics/Indian_numerals/ The MacTutor History of Mathematics archive]</ref>
-[[Middle-East]]ern mathematicians extended the decimal numeral system to include [[fractions]], as recorded in a treatise by the Arab mathematician [[Abu'l-Hasan al-Uqlidisi]] in 952–953. The [[decimal point]] notation was introduced{{when|date=September 2020}} by [[Sind ibn Ali]], who also wrote the earliest treatise on Arabic numerals.
 ===Origin of the Arabic numeral symbols===
+[[File:The Brahmi numeral system and its descendants.png|alt=|thumb|Evolution of Indian numerals into Arabic numerals and their adoption in Europe]]
-According to [[Al-Biruni]], there were multiple forms of numerals in use in India, and "Arabs chose among them what appeared to them most useful"{{Citation needed|date=February 2020}}. 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 as [[Eastern Arabic numerals]].<ref>{{harvnb|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003|p=7}}: "Les personnes qui se sont occupées de la science du calcul n'ont pas été d'accord sur une partie des formes de ces neuf signes; mais la plupart d'entre elles sont convenues de les former comme il suit."</ref> 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.{{sfn|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003|p=5}}
+A western Arabic variant of the symbols, Ghubari numerals,<ref>{{harvnb|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 (called ''ḥisāb al-ghubār'') was known in the West from the tenth century onward..."</ref> came to be used in North Africa and Andalusia ([[Maghreb]]) and [[Al-Andalus]], which are the direct ancestor of the modern Arabic numerals.
+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 Spain and North Africa, who were then using the digits from Libya to Morocco. In eastern part of Arabic Peninsula, Arabs were using the [[Eastern Arabic numerals]] or "Mashriki" numerals: ٠ ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩<ref>Shown right-to-left, zero is on the right, nine on the left.</ref>
-The western Arabic variants of the symbols came to be used in [[Maghreb]] and [[Al-Andalus]], which are the direct ancestor of the modern Arabic numerals.<ref>{{harvnb|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 (called ''ḥisāb al-ghubār'') was known in the West from the tenth century onward..."</ref>
-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'').{{sfn|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003|pp=7–8}} The use of the dust board appears to have introduced a divergence in terminology as well: whereas the Hindu reckoning was called ''ḥisāb al-hindī'' in the east, it was called ''ḥisāb al-ghubār'' in the west (literally, "calculation with dust").{{sfn|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003|p=8}} The numerals themselves were referred to in the west as ''ashkāl al‐ghubār'' (dust figures, in Ibn al-Yāsamin) or ''qalam al-ghubår'' (dust letters).{{sfn|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003|p=10}} 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.<ref>
-{{harvnb|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.'</ref>
-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.<ref>{{harvnb|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."</ref><ref>{{citation |last1=Smith |first1=D. E. |author-link1=D. E. Smith |author-link2=Louis Charles Karpinski |first2=L. C. |last2=Karpinski |title=The Hindu-Arabic Numerals |publisher=Dover |year= 2013 |orig-year=first published in Boston, 1911 |isbn=978-0486155111 |url=https://www.gutenberg.org/ebooks/22599#download |at=Chapter V}}</ref><ref>{{citation|title=The Origin of the Ghubār Numerals, or the Arabian Abacus and the Articuli|first=Solomon|last=Gandz|journal=[[Isis (journal)|Isis]]|volume=16|issue=2|date=November 1931|pages=393–424|doi=10.1086/346615|jstor=224714|s2cid=144993740}}</ref>
-Some popular myths argue 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.<ref name=ifrah>{{cite book|last1=Ifrah|first1=Georges|title=The universal history of numbers: from prehistory to the invention of the computer; translated from the French by David Bellos|date=1998|publisher=Harvill Press|location=London|isbn=9781860463242|pages=356–357}}</ref>
 ===Adoption in Europe===
 [[File:Codex Vigilanus Primeros Numeros Arabigos.jpg|thumb|right|The first Arabic numerals in the West appeared in the ''[[Codex Albeldensis]]'' in Spain.]]
-[[File:The Brahmi numeral system and its descendants.png|alt=|thumb|Evolution of Indian numerals into Arabic numerals and their adoption in Europe]]
 [[File:Ms.Thott.290.2º 150v.jpg|thumb|A German manuscript page teaching use of Arabic numerals ([[Hans Talhoffer|Talhoffer]] Thott, 1459). At this time, knowledge of the numerals was still widely seen as esoteric, and Talhoffer presents them with the [[Hebrew alphabet]] and [[astrology]].]]
-[[File:Clock-french-republic.jpg|thumb|right|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 the [[Eastern Arabic numerals]] (٠١٢٣٤٥٦٧٨٩) in other areas.
-In 825 [[Muḥammad ibn Mūsā al-Khwārizmī|Al-Khwārizmī]] wrote a treatise in Arabic, ''On the Calculation with Hindu Numerals'',<ref>[https://books.google.com/books?id=DuyMjOwWWnUC&pg=PA38 Philosophy Of Mathematics] Francis, John – 2008 – Page 38</ref> which survives only as the 12th-century Latin translation, ''Algoritmi de numero Indorum''.<ref>[https://books.google.com/books?id=twWkDe1Y9YQC&pg=PT99 The Ellipse: A Historical and Mathematical Journey] Arthur Mazer – 2011</ref><ref>{{cite web|url=http://www.britannica.com/EBchecked/topic/317171/al-Khwarizmi|title=al-Khwarizmi - Muslim mathematician}}</ref> ''Algoritmi'', the translator's rendition of the author's name, gave rise to the word ''[[algorithm]]''.<ref>[https://books.google.com/books?id=FPFsnzzebhQC&pg=PA1 Models of Computation: An Introduction to Computability Theory – Page 1] Maribel Fernández – 2009</ref>
 The first mentions of the numerals in the West are found in the ''[[Codex Vigilanus]]'' of 976.<ref>{{cite web|url=http://www.mathorigins.com/V.htm|title=MATHORIGINS.COM_V|website=www.mathorigins.com}}</ref>
@@ Line 60: / Line 31: @@
 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.{{Citation needed|date=December 2019}}
-[[Leonardo Fibonacci]] ([[Leonardo of Pisa]]), a mathematician born in the [[Republic of Pisa]] who had studied in [[Béjaïa]] (Bougie), [[Algeria]], promoted the Indian numeral system in Europe with his 1202 book ''[[Liber Abaci]]'':
+[[Leonardo Fibonacci]] (also known as Leonardo of Pisa), a mathematician born in the [[Republic of Pisa]] who had studied in [[Béjaïa]] (Bougie), [[Algeria]], promoted the Indian numeral system in Europe with his 1202 book ''[[Liber Abaci]]'':
 <blockquote>When my father, who had been appointed by his country as public notary in the customs at [[Béjaïa|Bugia]] acting for the [[Pisa]]n 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.</blockquote>
@@ Line 69: / Line 40: @@
 [[File:EuropeanFormOfArabianDigits.png|frameless|upright=2.25|Table of numerals]]
-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, as well as on clockfaces.
 ===Adoption in Russia===
@@ Line 76: / Line 45: @@
 ===Adoption in China===
-[[File:Yuan dynasty iron magic square.jpg|thumb|right|Iron plate with an order 6 [[magic square]] in Persian/Arabic numbers from China, dating to the [[Yuan Dynasty]] (1271–1368).]]
+[[File:Yuan dynasty iron magic square.jpg|thumb|Iron plate with an order 6 [[magic square]] in Persian/Arabic numbers from China, dating to the [[Yuan Dynasty]] (1271–1368).]]
-Positional notation was introduced to China during the [[Yuan dynasty|Yuan Dynasty]] (1271–1368) by the Muslim [[Hui people]]. In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese [[Society of Jesus|Jesuits]].<ref>{{cite book|editor=Helaine Selin|editor-link=Helaine Selin|title=Encyclopaedia of the history of science, technology, and medicine in non-western cultures|url=https://books.google.com/books?id=raKRY3KQspsC&pg=PA198|year=1997|publisher=Springer|isbn=978-0-7923-4066-9|page=198}}</ref><ref>{{cite book|last=Meuleman|first=Johan H.|title=Islam in the era of globalization: Muslim attitudes towards modernity and identity|url=https://books.google.com/books?id=YNArhqy4emwC&pg=PA272|year=2002|publisher=Psychology Press|isbn=978-0-7007-1691-3|page=272}}</ref><ref>{{cite book|author=Peng Yoke Ho|title=Li, Qi and Shu: An Introduction to Science and Civilization in China|url=https://books.google.com/books?id=_P6C4JO4JCUC&pg=PA106|year=2000|publisher=Courier Dover Publications|isbn=978-0-486-41445-4|page=106}}</ref>
+[[Positional notation]] was introduced to China during the [[Yuan Dynasty]] (1271–1368) by the Muslim [[Hui people]]. In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese [[Jesuits]].<ref>{{cite book|editor=Helaine Selin|editor-link=Helaine Selin|title=Encyclopaedia of the history of science, technology, and medicine in non-western cultures|url=https://books.google.com/books?id=raKRY3KQspsC&pg=PA198|year=1997|publisher=Springer|isbn=978-0-7923-4066-9|page=198}}</ref><ref>{{cite book|last=Meuleman|first=Johan H.|title=Islam in the era of globalization: Muslim attitudes towards modernity and identity|url=https://books.google.com/books?id=YNArhqy4emwC&pg=PA272|year=2002|publisher=Psychology Press|isbn=978-0-7007-1691-3|page=272}}</ref><ref>{{cite book|author=Peng Yoke Ho|title=Li, Qi and Shu: An Introduction to Science and Civilization in China|url=https://books.google.com/books?id=_P6C4JO4JCUC&pg=PA106|year=2000|publisher=Courier Dover Publications|isbn=978-0-486-41445-4|page=106}}</ref>
 ==Encoding==
@@ Line 84: / Line 53: @@
 The ten Arabic numerals are encoded in virtually every character set designed for electric, radio, and digital communication, such as [[Morse code]].
-They are encoded in [[ASCII]] at positions 0x30 to 0x39. [[Mask (computing)|Masking]] to the lower 4 binary bits (or taking the last [[hexadecimal]] digit) gives the value of the digit, a great help in converting text to numbers on early computers. These positions were inherited in [[Unicode]].<ref>https://www.unicode.org/charts/PDF/U0000.pdf</ref> [[EBCDIC]] used different values, but also had the lower 4 bits equal to the digit value.
+They are encoded in [[ASCII]] at positions 0x30 to 0x39. [[Mask (computing)|Masking]] to the lower 4 binary bits (or taking the last [[hexadecimal]] digit) gives the value of the digit, a great help in converting text to numbers on early computers. These positions were inherited in [[Unicode]].<ref>{{cite web |url=https://www.unicode.org/charts/PDF/U0000.pdf |title=The Unicode Standard, Version 13.0 |website=unicode.org |access-date=1 September 2021 |url-status=live}}</ref> [[EBCDIC]] used different values, but also had the lower 4 bits equal to the digit value.
 {| class="wikitable"
@@ Line 168: / Line 137: @@
 ==See also==
+{{Div col|small=yes}}
-{{Columns-list|colwidth=30em|
-* [[Text figures]]
 * [[Abjad numerals]]
 * [[Chinese numerals]]
 * [[Counting rods]] – decimal positional numeral system with zero
 * [[Decimal]]
-* [[Seven-segment display]]
 * [[Greek numerals]]
 * [[Japanese numerals]]
 * [[Maya numerals]]
 * [[Regional handwriting variation#Arabic numerals|Regional variations in modern handwritten Arabic numerals]]
+* [[Seven-segment display]]
-}}
+* [[Text figures]]
+{{Div col end}}
 ==Notes==