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Arabic-Hindu Numeral System
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Positional decimal numeral systemdeveloped by the 9th century by
Indian mathematicians
Adopted by Persian (Al-Khwarizmi's
circa 825 book On the Calculationwith Hindu Numerals)
Adopted by Arabic mathematicians(Al-Kindi's circa 830 volumes On
the Use ofthe Indian Numerals)
Spread to the western world by theHigh Middle Ages.
The HinduArabic numeral system is a
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BriefHistory
The numeral system
was developed in
ancient India, and
was well established
by the time ofthe
Bakhshali manuscript
(ca. 3d c. CE).
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BriefHistory
Despite its Indian origins itwas initially known in theWest as "Arabic numerals"because ofits introductionto Europe through Arabictexts such as Al-Khwarizmi's "On theCalculation with Hindu
Numerals" (ca. 825), andAl-Kindi's four volumework "On the Use oftheIndian Numerals" (ca. 830)
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Predecessors
The Brahmi numerals are the basis ofthe system. It replaces the earlier Kharosthi numerals indigenous toIndia following the conquests ofAlexander the Great inthe 4th century BC
Brahmi and Kharosthi numerals were used alongsideone another in the Maurya Empire period, bothappearing on the 3rd century BC edicts ofAshoka.
Brahmi numerals are the ancestors ofthe HinduArabicglyphs 1 to 9, but they were not used as a positionalsystem with a zero, and there were rather separatenumerals for each ofthe tens (10, 20, 30, etc.).
The actual numeral system, including positionalnotation and use ofzero, is in principle independent ofthe glyphs used, and significantly younger than theBrahmi numerals.
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Development
The development ofthe positional decimalsystem takes its origins in Indian mathematicsduring the Gupta period.
Around 500 CE the astronomer Aryabhatauses the word kha ("emptiness") to mark"zero" in tabular arrangements ofdigits.
The 7th century Brahmasphuta Siddhantacontains a comparatively advancedunderstanding ofthe mathematical role ofzero
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The Sanskrit translation ofthe lost 5th centuryPrakrit Jaina cosmological text Lokavibhaga
preserve an early instance ofpositional use ofzero.
These Indian developments were taken up inIslamic mathematicsin the 8th century, asrecorded in al-Qifti's Chronologyofthe scholars(early 13th century).
The numeral system came to be known to boththe Persian mathematician Al-Khwarizmi whowrote a book, On the Calculation with Hindu
Numerals in about 825, and the Arabmathematician Al-Kindi, who wrote four volumes,On the Use ofthe Indian Numerals ( ] kitab fi isti'malal-'adad al-hindi])
around 830
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These books are principally responsible for thediffusion ofthe Indian system ofnumeration
throughout the Islamic world and ultimately
also to Europe.
The first dated and undisputed inscriptionshowing the use ofzero at is at Gwalior, dating
to 876 AD.
In 10th century Islamic mathematics, the
system was extended to include fractions, asrecorded in a treatise by Syrian mathematician
Abu'l-Hasan al-Uqlidisi in 952953
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976
In Christian Europe, the first mention and
representation ofHindu-Arabic numerals(from one to nine, without zero), is in the
Codex Vigilanus, an illuminated compilation
ofvarious historical documents from theVisigothic period in Spain, written in the
year 976 by three monks ofthe RiojanmonasteryofSan Martn de Albelda.
In the last few centuries, the European
variety ofArabic numbers was spreadaround the world and gradually became the
most commonly used numeral system in
the world.
1202
Fibonacci, an Italian mathematician whohad studied in Bjaa (Bougie), Algeria,
promoted the Arabic numeral system inEurope with his book "Liber Abaci", which
was published in 1202.
Even in many countries in languages which
have their own numeral systems, theEuropean Arabic numerals are widely used
in commerce and mathematics.
Adoption in
Europe
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Adoption
in East
Asia
Chinese and Japanesefinally adopted the
HinduArabic numerals
in the 19th century,
abandoning counting
rods.
In China, Gautama Siddhaintroduced Indian numerals
with zero in 718, but Chinesemathematicians did not find
them useful, as they hadalready had the decimal
positional counting rods