Arabic numerals: Difference between revisions

Content deleted Content added

Inline

Revision as of 17:26, 12 August 2021

Arabic numerals set in Source Sans

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."

They are also called Western Arabic numerals, Ghubār numerals, or digits.

The numerals were developed in the Maghreb in the Western Arabic World. 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. ^[1] 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.

History

Origins

The decimal system usually used with Arabic numerals was developed in India and Arabia, centuries before the numerals were developed. Other symbols were used for the digits, these symbols are not used anywhere today but have evolved into several different sets of digits.^[4]

Origin of the Arabic numeral symbols

A western Arabic variant of the symbols, Ghubari numerals,^[5] came to be used in in North Africa and Andalusia (Maghreb) and Al-Andalus, which are the direct ancestor of the modern Arabic numerals. These symbols started out as Arabic letters (except for zero).^[6]

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.^[7] 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^[8]

Adoption in Europe

The first mentions of the numerals in the West are found in the Codex Vigilanus of 976.^[9]

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,^[10] 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.^[11] By the mid-16th century, they were in common use in most of Europe.^[12] 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.^[13]^[14]^[15]

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.^[16] 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".
^ Smith, David Eugene; Karpinski, Louis Charles (1911). The Hindu-Arabic numerals. Boston, London, Ginn and Company. p. 52.
^ For a modern image
^ "Numbers, its inception, development and operations on it". Retrieved 2 August 2021.
^ 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..."
^ "Origin of the numerals Al-Biruni's testimony" (PDF).
^ "Why are arabic numerals so called when they look nothing like arabic numbers?".
^ 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.
^ https://www.unicode.org/charts/PDF/U0000.pdf

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".

[2] Smith, David Eugene; Karpinski, Louis Charles (1911). The Hindu-Arabic numerals. Boston, London, Ginn and Company. p. 52.

[3] For a modern image

[4] "Numbers, its inception, development and operations on it". Retrieved 2 August 2021.

[5] 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..."

[6] "Origin of the numerals Al-Biruni's testimony" (PDF).

[7] "Why are arabic numerals so called when they look nothing like arabic numbers?".

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

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

[10] "14th century timepiece unearthed in Qld farm shed". ABC News.

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

[12] Mathforum.org

[13] 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.

[14] 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.

[15] 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.

[16] ttps://www.unicode.org/charts/PDF/U0000.pdf

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

@@ Line 19: / Line 19: @@
 ==History==
 ===Origins===
-{{seealso|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>]]
+{{seealso|History of the Hindu–Arabic numeral system}}
-The modern Western Arabic Numerals simply called Arabic Numerals are developed in western Arabic World in North Africa and Andalusia (Maghreb). It is also called Ghubari Numerals.  <ref>{{cite web |title=Why are arabic numerals so called when they look nothing like arabic numbers? |url=https://www.theguardian.com/notesandqueries/query/0,5753,-3840,00.html}}</ref><ref>{{cite web |title=Numbers, its inception, development and operations on it |url=https://www.researchgate.net/publication/332497043_Numbers_its_inception_development_and_operations_on_it |access-date=2 August 2021}}</ref>
+The decimal system usually used with Arabic numerals was developed in India and Arabia, centuries before the numerals were developed. Other symbols were used for the digits, these symbols are not used anywhere today but have evolved into several different sets of digits.<ref>{{cite web |title=Numbers, its inception, development and operations on it |url=https://www.researchgate.net/publication/332497043_Numbers_its_inception_development_and_operations_on_it |access-date=2 August 2021}}</ref>
 ===Origin of the Arabic numeral symbols===
-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>
+[[File:The Brahmi numeral system and its descendants.png|alt=|thumb|Evolution of Indian numerals into Arabic numerals and their adoption in Europe]]
-There are two types of Arabic Numerals: Eastern Arabic Numerals and Western Arabic Numerals. In eastern Arabic world the [[Eastern Arabic numerals]] are used. 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>
+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 in North Africa and Andalusia ([[Maghreb]]) and [[Al-Andalus]], which are the direct ancestor of the modern Arabic numerals. These symbols started out as Arabic letters (except for zero).<ref>{{cite web |title=Origin of the numerals Al-Biruni’s testimony |url=https://arxiv.org/ftp/arxiv/papers/0707/0707.3279.pdf}}</ref>
-Modern Arabic Numerals or Western Arabic Numerals symbols are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, which are used in Sciences and Technologies.
-Eastern Arabic Numerals or "Mashriki" numerals symbols are: ٠ ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩
+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.<ref>{{cite web |title=Why are arabic numerals so called when they look nothing like arabic numbers? |url=https://www.theguardian.com/notesandqueries/query/0,5753,-3840,00.html}}</ref> 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 Numerals which is simply called Arabic Numerals or Ghubari numerals or Arabic Numerals are actually Arabic letters. The shape of the numbers are derived from 9 Arabic letters. The numerals were developed in ""Maghreb"" Western Arabic World.
-<ref>{{cite web |title=Origin of the numerals Al-Biruni’s testimony |url=https://arxiv.org/ftp/arxiv/papers/0707/0707.3279.pdf}}</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 Spain and North Africa, who were then using the digits from Libya to Morocco. In eastern part of Arabic Peninsula, Arabs were also using the [[Eastern Arabic numerals]] (٠١٢٣٤٥٦٧٨٩). The Modern Arabic Numerals (1,2,3,4,5,6,7,8,9) were invented in Western Arabic world. The numbers are actually derived from Arabic letters.
 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 51: / Line 47: @@
 [[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===