|Numeral systems by culture|
|Positional systems by base|
|Non-standard positional numeral systems|
|List of numeral systems|
The first positional numerical system developed in Babylon around the 2nd millennium BC. While it used a zero-like placeholder, the first true zero was developed by ancient mathematicians in the Indian Subcontinent. Arabic numerals are used to represent this Hindu-Arabic numeral system,4 in which a sequence of digits such as "975" is read as a single number. This system is traditionally thought to have been adopted by the Muslim Persian and Arab mathematicians in India, and passed on to the Arabs further west. There is some evidence which suggests that the numerals in their current form developed from Arabic letters in the western regions of the Arab World.5 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 Bejaia that the Italian scholar Fibonacci first encountered the numerals; his work was crucial in making them known throughout Europe, and then further to the Europeans who spread it worldwide. The use of Arabic numerals spread around the world through European trade, books and colonialism.
In English, the term Arabic numerals can be ambiguous. It most commonly refers to the numeral system widely used in Europe and the Americas. Arabic numerals is the conventional name for the entire family of related systems of Arabic and Indian numerals. It may also be intended to mean the numerals used by Arabs, in which case it generally refers to the Eastern Arabic numerals.
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.6 This helps distinguish it from "Arabic numerals" as the East Arabic numerals specific to the Arabs.
By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system. The lack of a positional value (or zero) was indicated by a space between sexagesimal numerals. By 300 BC, a punctuation symbol (two slanted wedges) was co-opted as a placeholder in the same Babylonian system. In a tablet unearthed at Kish (dating from about 700 BC), the scribe Bêl-bân-aplu wrote his zeros with three hooks, rather than two slanted wedges.7
The Babylonian placeholder was not a true zero because it was not used alone. Nor was it used at the end of a number. Thus numbers like 2 and 120 (2×60), 3 and 180 (3×60), 4 and 240 (4×60) looked the same because the larger numbers lacked a final sexagesimal placeholder. Only context could differentiate them.
The decimal Hindu-Arabic numeral system was invented in India around 500 CE.89 The system was revolutionary by including a zero and positional notation. 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 glyphs used to write the numerals, which vary regionally. The glyphs most commonly used in conjunction with the Latin script 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 is first recorded in the 9th century, in an inscription at Gwalior in Central India dated to 870. By this time, the use of the glyph had already reached Persia, and was mentioned in Al-Khwarizmi's descriptions of Indian numerals. Numerous Indian documents on copper plates exist, with the same symbol for zero in them, dated back as far as the 6th century CE.10
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 in Arabic, 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. Their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West.11 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. The decimal point notation was introduced by Sind ibn Ali, he 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 Maghreb and Al-Andalus, called ghubar ("sand-table" or "dust-table") numerals, which are the direct ancestor of the modern Western Arabic numerals used throughout the world. Ghubar numerals themselves are probably of Roman origin.12
Some folk etymologies have argued that the original forms of these symbols indicated their value through the number of angles they contained, but no proof exists of any such origin.13
In 825 Al-Khwārizmī wrote a treatise in Arabic, On the Calculation with Hindu Numerals,14 which survives only as the 12th-century Latin translation, Algoritmi de numero Indorum.1516 Algoritmi, the translator's rendition of the author's name, gave rise to the word algorithm (Latin algorithmus, "calculation method").17
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.
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:
- "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. 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 "Hindu numerals",1920 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 (٠ - ١ - ٢ - ٣ -٤ - ٥ - ٦ - ٧ - ٨ - ٩) used in the Middle East, or any of the numerals currently used inIndian languages (e.g. Devanagari: ०.१.२.३.४.५.६.७.८.९).8
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 1396,21 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 1456.22 By the mid-16th century, they were in common use in most of Europe.23 Roman numerals remained in use mostly for the notation of Anno Domini years, and for numbers on clockfaces. Sometimes, 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.
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.
The numeral system employed, known as algorism, is positional decimal notation. Various symbol sets are used to represent numbers in the Hindu-Arabic numeral system, which may have evolved from the Brahmi numerals, or developed independently from it. 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 script, in the table below labelled European, descended from the West Arabic numerals 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 script, developed primarily in what is now Iraq. A variant of the Eastern Arabic numerals used in the Persian and Urdu languages is shown as East Arabic-Indic. There is substantial variation in usage of glyphs for the Eastern Arabic-Indic digits, especially for the digits four, five, six, and seven.27
- The Devanagari numerals used with Devanagari and related variants are grouped as Indian numerals.
The evolution of the numerals in early Europe is shown on a table created by the French scholar J.E. Montucla in his Histoire de la Mathematique, which was published in 1757:
- Abjad numerals
- Chinese numerals
- Counting rods – decimal positional numeral system with zero
- Hindu-Arabic numeral system
- Japanese numerals
- Maya numerals
- Numeral system
- Numerical digit
- Positional numeral system
- Regional variations in modern handwritten Arabic numerals
- Roman numerals
- Schipp, Bernhard; Krämer, Walter (2008), Statistical Inference, Econometric Analysis and Matrix Algebra: Festschrift in Honour of Götz Trenkler, Springer, p. 387, ISBN 9783790821208
- Lumpkin, Beatrice; Strong, Dorothy (1995), Multicultural science and math connections: middle school projects and activities, Walch Publishing, p. 118, ISBN 9780825126598
- Fenna, Donald (2002). A Dictionary of Weights, Measures, and Units. New York: Oxford University Press. pp. 90 & 202. ISBN 978-0198605225.; "Fibonacci, in a book of 1202, brought the Indo-Arabic numerals, with their zero cypher and decimal point, into European culture."; "... these characters are more appropriately called at least Indo-Arabic numerals."
- 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. ISBN 1439084742. "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"
- On the Origin of Arabic Numerals - A. Boucenna - Université Ferhat Abbas Setif (French)
- "Arabic", Oxford English Dictionary, 2nd edition
- Kaplan, Robert. (2000). The Nothing That Is: A Natural History of Zero. Oxford: Oxford University Press.
- Ifrah, Georges. 1999.The Universal History of Numbers : From Prehistory to the Invention of the Computer, Wiley. ISBN 0-471-37568-3.
- O'Connor, J.J. and E.F. Robertson. 2000. Numerals', MacTutor History of Mathematics Archive, School of Mathematics and Statistics, University of St. Andrews, Scotland.
- Kaplan, Robert. (2000). The Nothing That Is: A Natural History of Zero, Oxford: Oxford University Press
- The MacTutor History of Mathematics archive
- 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
- bigstrand4476 (13 March 2009). "Number Story". Scribd.com. Retrieved 2011-08-05.
- Philosophy Of Mathematics Francis, John – 2008 – Page 38
- The Ellipse: A Historical and Mathematical Journey Arthur Mazer – 2011
- Encyclopædia Britannica: al-Khwārizmī
- Models of Computation: An Introduction to Computability Theory – Page 1 Maribel Fernández – 2009
- Rowlett, Russ (4 July 2004), Roman and "Arabic" Numerals, University of North Carolina at Chapel Hill, retrieved 22 June 2009
- Achenbach, Joel (16 September 1994), Article: Take a Number, Please., The Washington Post, retrieved 22 June 2009
- "14th century timepiece unearthed in Qld farm shed". ABC News.
- Erdélyi: Magyar művelődéstörténet 1-2. kötet. Kolozsvár, 1913, 1918
- Helaine Selin, ed. (31 July 1997). Encyclopaedia of the history of science, technology, and medicine in non-western cultures. Springer. pp. 198–. ISBN 978-0-7923-4066-9. Retrieved 3 March 2012.
- Meuleman, Johan H. (23 August 2002). Islam in the era of globalization: Muslim attitudes towards modernity and identity. Psychology Press. p. 272. ISBN 978-0-7007-1691-3. Retrieved 3 March 2012.
- Peng Yoke Ho (16 October 2000). Li, Qi and Shu: An Introduction to Science and Civilization in China. Courier Dover Publications. p. 106. ISBN 978-0-486-41445-4. Retrieved 3 March 2012.
- The Unicode Standard 5.0 – Electronic edition, Chapter 8 Middle Eastern Scripts
- Ore, Oystein (1988), "Hindu-Arabic numerals", Number Theory and Its History, Dover, pp. 19–24, ISBN 0486656209.
- Burnett, Charles (2006), "The Semantics of Indian Numerals in Arabic, Greek and Latin", Journal of Indian Philosophy, (Springer-Netherlands) 34 (1–2): 15–30, doi:10.1007/s10781-005-8153-z.
- Encyclopædia Britannica (Kim Plofker) (2007), "mathematics, South Asian", Encyclopædia Britannica Online: 1–12, retrieved 18 May 2007.
- Hayashi, Takao (1995), The Bakhshali Manuscript, An ancient Indian mathematical treatise, Groningen: Egbert Forsten, ISBN 906980087X.
- Ifrah, Georges (2000), A Universal History of Numbers: From Prehistory to Computers, New York: Wiley, ISBN 0471393401.
- Katz, Victor J. (ed.) (20 July 2007), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton, New Jersey: Princeton University Press, ISBN 0691114854.
|Wikimedia Commons has media related to Arabic numerals.|
- Development of Hindu Arabic and Traditional Chinese Arithematicsdead link
- 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