Arabic numerals
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2020
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| 2020 in print which is now widely used around the world |
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٢٠٢٠
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| 2020 in Arabic-Indian print |
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२०२०
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| 2020 in Devanagari scripture |
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௨௦௨௦
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| 2020 in Tamil script |
The Arabic numerals , also called Indian or Indian-Arabic numerals , are the elementary characters of a numerical script in which numbers are positionally represented on the basis of a decimal system with nine numerals derived from the ancient Indian Brahmi script . The zero as the tenth character is often represented as a numeral written in a circle or period.
Origin and spread
India
The Brahmi number was at the beginning of the development of the Indian numerals . It is together with the Brahmi script from the 3rd century BC. BC in the ancient Indian Maurya empire verifiable.
शून्य (śūnya) - zero
The number zero was born under the word śūnya (n., Sanskrit शून्य , “the void, the nothingness, the non-existence”) . The philosophical basis for this was probably the Buddhist concept śūnyatā (f., Sanskrit शून्यता , "the voidness, the illusory nature of phenomena") as described by Nāgārjuna (2nd century AD) in the doctrine of voidness ( śūnyatāvāda ) Has. Another source of supply is the spelling of the value zero as a space by the Babylonians from the 6th century BC onwards. In consideration. The zero, represented by a point, appears as a gap in the decimal place value system in the Bakhshali manuscript , the oldest part of which was dated to the 3rd to 4th centuries AD in a controversially discussed radiocarbon study .
Brahmasphutasiddhanta
In the year 628 AD, the Indian astronomer and mathematician Brahmagupta wrote the Brahmasphutasiddhanta ("The beginning of the universe"). Apart from the Maya number system , it is the earliest known text in which the zero is treated as a fully-fledged number. In addition, Brahmagupta established rules for arithmetic with negative numbers and with the number 0 in this work , which largely correspond to our modern understanding. The biggest difference was that Brahmagupta also allowed division by 0, while in modern mathematics quotients with the divisor 0 are not defined.
Further development
The worldwide spread of the Indian numerals did not go hand in hand with a worldwide spread of Brahmasphutasiddhanta, but required some intermediate steps.
Arab spread
Between 640 and 644 the Arabs conquered Iraq and Persia. The first traditional references to Indian numerals in the west come from the Syrian Nestorian bishop Severus Sebokht in the 7th century.
Al-Khwarizmi
Around 825, the Persian mathematician, astronomer and geographer al-Chwarizmi wrote his work on calculating with Indian numerals , which is only known in Latin translation ( Algoritmi de numero indorum , 12th century).
The Arabs call the zero ṣifr ( Arabic الصفر, DMG aṣ-ṣifr 'zero, nothing') from the verb ṣafira (“to be empty”) - a loan translation of the word śūnya . This is where the word number came from .
The leap into the west
The Arabic numerals are “the numerals in use today, ie the originally Indian ten numerals adopted by the Arabs. They originated in Catalonia in the 10th century from the western Arabic gobar or dust numerals and were introduced to the West by the monk Gerbert (who later became Pope Silvester II) on the calculating stones (apices) (at that time without the sign for the zero). " "In business life, because of the risk of forgery, they were only slowly gaining ground against Roman numerals , in Germany only in the 15th century."
Liber abaci
The Italian Leonardo Fibonacci followed his father to Algeria around 1192, where he met Abū Kāmil's algebra . In 1202 Fibonacci completed the Liber abaci , in which he introduced, among other things, the Indian numerals and actually referred to them as "Indian numerals" and not as "Arabic numerals". From Italy these digits were then also used in other European countries.
Worldwide distribution
As a result, the Arabic numerals in Europe replaced the bulky Roman numerals. It is true that simple calculations could also be carried out with the Roman. However, only the Arabs made higher mathematics possible. They are now used all over the world.
Michael Schmidt-Salomon justifies this success in an evolutionary-humanistic way . The preference for these digits is not due to cultural imperialism , but to the “particular fertility of Arabic numbers”.
Typographic variants
This section is devoted to the historical development of the various typographical variants and the forms of Indian numerals in use today.
Indian variants
Since astronomical observations were carried out systematically and at a high level in India a few thousand years ago, large numbers were required - lakh [ lakʰ ] and crore [ kror ] ( Hindi : लाख , lākh ; करोड़ , karoṛ ). One lakh equals 100,000, a crore equals 100 lakh, i.e. 10,000,000. Although they were officially exchanged for the thousands system, these numbers have held up and are still in common usage today.
Arabic variants
In Arabic script , the spelling developed from right to left from an originally vertical lettering on the papyri from top to bottom (they were glued together from vertical strips), which was then rotated by 90 degrees for reading. The Indian numerals were also noted, which are therefore partly rotated in the script compared to the Indian original and then further adapted to the graphic style of the Arabic script. The structure of the Arabic words of the Indian numerals is based on the highest priority (i.e. the left digit), similar to that in western languages. For example, the word for 10,000 ( ʕashrat ʔalāf ) was made up of the word ʔashara for 10 and ʔalf for 1000. Similar to western languages, however, there are also special rules such as for the tens - for example, the name for 19 is tisʕata-ʕschar from tisʕa for 9 and ʕaschara for 10, as is the case with nineteen in German. Numbers are written in the form of digits from left to right (as opposed to letters that are written from right to left in Arabic). The position of the digits is as usual in the decimal system (i.e. the digits with the highest priority on the left).
Before the Arabs adopted the Indian place value system, they used the letters of their alphabet to represent numbers, which, as in many other writing systems such as ancient Greek, Roman or Hebrew, were assigned a numerical value in addition to the sound value (see Arabic alphabet ). This possibility is still used in certain situations today, comparable to the use of Roman numerals in western-speaking countries.
In the Maghreb , that is, in the Arabic-speaking countries west of the Nile Valley , numerals are traditionally used that are identical to the European ones and not the characters presented here as Arabic.
European variants
In Europe, there are two main forms of representation of digits: uppercase digits and old-style digits .
The most widespread variant are uppercase numbers: all numbers have the same height, namely that of the capital letters (uppercase). In order to enable a clean table set, all capitals are usually all the same width, namely as wide as a half-square . This variant is also referred to as table numbers. Uppercase proportional digits are less common , with the 1 in particular being narrower than the other digits. The disadvantage of the uppercase numbers is that they form an optical foreign body in the scrolling text and that with some half-quarter-width digits (such as the 1) the spacing between the letters seems too wide.
For this reason, well-developed fonts have a second set of digits, the old style digits. Like lower case letters, these have ascenders and descenders and, as a rule, an individual spacing that is adapted to the character shape . This means that they fit seamlessly and correctly into the text from a typographical point of view. Some fonts also offer old style figures of the same width for table typesetting.
literature
- Paul Kunitzsch : On the history of the 'Arabic' numerals. Bavarian Academy of Sciences, Phil.-hist. Class, meeting reports, 2005: 3. Beck, Munich 2005. Digitized
swell
- ↑ The logic of the doctrine of the void: The Shunyata of Nagarjuna ( Memento of July 30, 2003 in the web archive archive.today )
- ↑ Robert Kaplan : The History of Zero. Campus-Verlag, Frankfurt am Main et al. 2000, ISBN 3-593-36427-1 .
- ↑ National Geographic - Origin of the Number 0
- ↑ Arabic Numerals, McTutor archive
- ↑ http://universal_lexikon.deacademic.com/12606/arabische_Zypen
- ↑ Michael Schmidt-Salomon : Hope human. A better world is possible. , Piper Verlag, Munich 2014, p. 200
- ↑ Ifrah Universal History of Numbers , English edition, Wiley 2000, p. 533
