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TheHindu–Arabic numeral system (also known as theIndo-Arabic numeral system,[1]Hindu numeral system, andArabic numeral system)[2][note 1] is apositionalbase-tennumeral system for representingintegers; its extension to non-integers is thedecimal numeral system, which is presently the most common numeral system.
The system was invented between the 1st and 4th centuries byIndian mathematicians. By the 9th century, the system was adopted byArabic mathematicians who extended it to includefractions. It became more widely known through the writings inArabic of the Persian mathematicianAl-Khwārizmī[3] (On the Calculation with Hindu Numerals,c. 825) and Arab mathematicianAl-Kindi (On the Use of the Hindu Numerals,c. 830). The system had spread to medieval Europe by theHigh Middle Ages, notably followingFibonacci's 13th centuryLiber Abaci; until the evolution of theprinting press in the 15th century, use of the system in Europe was mainly confined toNorthern Italy.[4]
It is based upon tenglyphs representing the numbers from zero to nine, and allows representing anynatural number by a unique sequence of these glyphs. The symbols (glyphs) used to represent the system are in principle independent of the system itself. The glyphs in actual use are descended fromBrahmi numerals and have split into various typographical variants since theMiddle Ages.
These symbol sets can be divided into three main families:Western Arabic numerals used in theGreater Maghreb and inEurope;Eastern Arabic numerals used in theMiddle East; and the Indian numerals in various scripts used in theIndian subcontinent.
Sometime around 600 CE, a change began in the writing of dates in theBrāhmī-derived scripts of India and Southeast Asia, transforming from an additive system with separate numerals for numbers of different magnitudes to a positional place-value system with a single set of glyphs for 1–9 and a dot for zero, gradually displacing additive expressions of numerals over the following several centuries.[5]
When this system was adopted and extended by medieval Arabs and Persians, they called ital-ḥisāb al-hindī ("Indian arithmetic"). These numerals were gradually adopted in Europe starting around the 10th century, probably transmitted by Arab merchants;[6] medieval and Renaissance European mathematicians generally recognized them as Indian in origin,[7] however a few influential sources credited them to the Arabs, and they eventually came to be generally known as "Arabic numerals" in Europe.[8] According to some sources, this number system may have originated in ChineseShang numerals (1200 BCE), which was also adecimalpositional numeral system.[9]
The Hindu–Arabic system is designed forpositional notation in adecimal system. In a more developed form, positional notation also uses adecimal marker (at first a mark over the ones digit but now more commonly a decimal point or a decimal comma which separates the ones place from the tenths place), and also a symbol for "these digits recurad infinitum". In modern usage, this latter symbol is usually avinculum (a horizontal line placed over the repeating digits). In this more developed form, the numeral system can symbolize anyrational number using only 13 symbols (the ten digits, decimal marker, vinculum, and a prependedminus sign to indicate anegative number).
Although generally found in text written with the Arabicabjad ("alphabet"), which is written right-to-left, numbers written with these numerals place the most-significant digit to the left, so they read from left to right (though digits are not always said in order from most to least significant[10]). The requisite changes in reading direction are found in text that mixes left-to-right writing systems with right-to-left systems.
Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, most of which developed from theBrahmi numerals.
The symbols used to represent the system have split into various typographical variants since theMiddle Ages, arranged in three main groups:
TheBrahmi numerals at the basis of the system predate theCommon Era. They replaced the earlierKharosthi numerals used since the 4th century BCE. Brahmi and Kharosthi numerals were used alongside one another in theMaurya Empire period, both appearing on the 3rd century BCEedicts of Ashoka.[11]
Buddhist inscriptions from around 300 BCE use the symbols that became 1, 4, and 6. One century later, their use of the symbols that became 2, 4, 6, 7, and 9 was recorded. TheseBrahmi numerals are the ancestors of the Hindu–Arabic glyphs 1 to 9, but they were not used as apositional system with azero, and there were rather[clarification needed] separate numerals for each of the tens (10, 20, 30, etc.).
The modern numeral system, including positional notation and use of zero, is in principle independent of the glyphs used, and significantly younger than the Brahmi numerals.
The place-value system is used in theBakhshali manuscript, the earliest leaves being radiocarbon dated to the period 224–383 CE.[12] The development of the positional decimal systemtakes its origins in[clarification needed]Indian mathematics during theGupta period. Around 500, the astronomerAryabhata uses the wordkha ("emptiness") to mark "zero" in tabular arrangements of digits. The 7th centuryBrahmasphuta Siddhanta contains a comparatively advanced understanding of the mathematical role ofzero. The Sanskrit translation of the lost 5th century PrakritJaina cosmological textLokavibhaga may preserve an early instance of the positional use of zero.[13]
The first dated and undisputed inscription showing the use of a symbol for zero appears on a stone inscription found at theChaturbhuja Temple atGwalior in India, dated 876 CE.[14]
These Indian developments were taken up inIslamic mathematics in the 8th century, as recorded inal-Qifti'sChronology of the scholars (early 13th century).[15]
In 10th centuryIslamic mathematics, the system was extended to include fractions, as recorded in a treatise byAbbasid Caliphate mathematicianAbu'l-Hasan al-Uqlidisi, who was the first to describe positional decimal fractions.[16] According to J. L. Berggren, the Muslims were the first to represent numbers as we do since they were the ones who initially extended this system of numeration to represent parts of the unit by decimal fractions, something that the Hindus did not accomplish. Thus, we refer to the system as "Hindu–Arabic" rather appropriately.[17][18]
The numeral system came to be known to both thePersian mathematicianKhwarizmi, who wrote a book,On the Calculation with Hindu Numerals in about 825 CE, and theArab mathematicianAl-Kindi, who wrote a book,On the Use of the Hindu Numerals (كتاب في استعمال العداد الهندي [kitāb fī isti'māl al-'adād al-hindī]) around 830 CE.Persian scientistKushyar Gilani who wroteKitab fi usul hisab al-hind (Principles of Hindu Reckoning) is one of the oldest surviving manuscripts using the Hindu numerals.[19] These books are principally responsible for the diffusion of the Hindu system of numeration throughout theIslamic world and ultimately also to Europe.
In Christian Europe, the first mention and representation of Hindu–Arabic numerals (from one to nine, without zero), is in theCodex Vigilanus (akaAlbeldensis), anilluminated compilation of various historical documents from theVisigothic period inSpain, written in the year 976 CE by three monks of theRiojan monastery ofSan Martín de Albelda. Between 967 and 969 CE,Gerbert of Aurillac discovered and studied Arab science in the Catalan abbeys. Later he obtained from these places the bookDe multiplicatione et divisione (On multiplication and division). After becomingPope Sylvester II in the year 999 CE, he introduced a new model ofabacus, the so-calledAbacus of Gerbert, by adopting tokens representing Hindu–Arabic numerals, from one to nine.
Leonardo Fibonacci brought this system to Europe. His bookLiber Abaci introducedModus Indorum (the method of the Indians), today known as Hindu–Arabic numeral system or base-10 positional notation, the use of zero, and the decimal place system to the Latin world. The numeral system came to be called "Arabic" by the Europeans. It was used in European mathematics from the 12th century, and entered common use from the 15th century to replaceRoman numerals.[20][21]
The familiar shape of the Western Arabic glyphs as now used with the Latin alphabet (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are the product of the late 15th to early 16th century, when they entered earlytypesetting. Muslim scientists used theBabylonian numeral system, and merchants used theAbjad numerals, a system similar to theGreek numeral system and theHebrew numeral system. Similarly, Fibonacci's introduction of the system to Europe was restricted to learned circles. The credit for first establishing widespread understanding and usage of the decimal positional notation among the general population goes toAdam Ries, an author of theGerman Renaissance, whose 1522Rechenung auff der linihen und federn (Calculating on the Lines and with a Quill) was targeted at the apprentices of businessmen and craftsmen.
![A calculation table [de], used for arithmetic using Roman numerals](/mt/?noimg=&dark=on&url=https%3a%2f%2fen.wikipedia.org%2fwiki%2fFile%3aRechentisch.png)
The '〇' is used to write zero inSuzhou numerals, which is the only surviving variation of therod numeral system. TheMathematical Treatise in Nine Sections, written byQin Jiushao in 1247, is the oldest surviving Chinese mathematical text to use the character ‘〇’ for zero.[22]
The origin of using the character '〇' to represent zero is unknown.Gautama Siddha introduced Hindu numerals with zero in 718 CE, butChinese mathematicians did not find them useful, as they already had the decimal positionalcounting rods.[23][24] Some historians suggest that the use of '〇' for zero was influenced by Indian numerals imported by Gautama,[24] but Gautama’s numeral system represented zero with a dot rather than a hollow circle, similar to theBakhshali manuscript.[25]
An alternative hypothesis proposes that the use of '〇' to represent zero arose from a modification of the Chinese text space filler "□", making its resemblance to Indian numeral systems purely coincidental. Others think that the Indians acquired the symbol '〇' from China, because it resembles aConfucian philosophical symbol for "nothing".[23]
Chinese andJapanese finally adopted the Hindu–Arabic numerals in the 19th century, abandoning counting rods.
The "Western Arabic" numerals as they were in common use in Europe since theBaroque period have secondarily found worldwide use together with theLatin alphabet, and even 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, but also in conjunction withChinese andJapanese writing (seeChinese numerals,Japanese numerals).
When the Arabian empire was expanding and contact was made with India, the Hindu numeral system and the early algorithms were adopted by the Arabs
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