Hindu–Arabic numeral system
The Indian numerals ( in Europe as the Indo- Arabic numerals or colloquial Arabic numerals known ) are a number of writing, in which numbers positionally based on a decimal system with nine of the ancient Indian Brahmi script to be derived number sign and a private, often a circle or a point characters written for the zero are shown.
- 2.2.1 Arab dissemination 2.2.1.1 al - Khwarizmi
- Liber abaci 2.2.2.1
- 3.1 Indian variants
- 3.2 Arab variants
- 3.3 European variants 3.3.1 Lining and old style figures
- 3.3.2 Global dissemination of European variant
Term use in the German
As Indic digits in the strict sense are in today's jargon German first only in India itself created and used expressions that number font, as far as they go back in a broader sense, their adaptations in other literate cultures to direct Indian model. This includes the incurred after the Indian model in the early Middle Ages Arabic or Hindu-Arabic (also Indo- Arabic or Hindu- Arabic mentioned ) digits, which in turn since the 12th century ( with precursors since the 10th century ) of the Latin and Greek literary culture of Europe were adapted and established themselves from Western Europe in the late Middle Ages since its unified form of writing the printed book as the world today next dominant or locally dominant number other writings at least widely voraussetzbarer standard.
A generic generic term that refers to both the in the strict sense of Indian as well as all the rest of it directly or indirectly derived and type after much similar numbers systems is not generally established in the German technical language, most likely comes this but the term " Indo- Arab " digits in question, if he is in an additive meaning ( Indian and Arabic) and not in contrastive meaning (Arabic adapted and taught ) as an antonym to " Indian" meant. In the German general language, the terms " Indian " and " Indian- Arabic numerals " largely unknown, there is only " Arabic numerals " for the common use today numeric system was established, and this term is then also in technical language contexts, often in extended meaning neglect of the genuinely Indian and not Arab influence variants used as a generic generic term.
Emergence and spread
India - from start to completion
At the beginning of the development of Indian numerals was the Brahmi font number. It is along with the Brahmi script from the 3rd century BC in the ancient Indian Maurya Empire assignable. The origin of the Brahmi script is unknown.
शून्य ( Sunya ) - null
Under the word Sunya (Sanskrit, n, शून्य, emptiness, nothingness, the absence) of the number zero was born. The philosophical basis for this was probably the Buddhist concept śūnyatā (Sanskrit, f, शून्यता, the emptiness, the illusory nature of phenomena ) as Nāgārjuna (2nd century AD) described in the doctrine of emptiness ( śūnyatāvāda ) has. As a further source of the spelling of the value zero is used as blanks by the Babylonians from the 6th century BC into consideration.
Brahmasphutasiddhanta
628 AD wrote the Indian astronomer and mathematician Brahmagupta the Brahmasphutasiddhanta ( The beginning of the universe). It is, apart from the number system of the Maya, the earliest known text in which the zero is treated as a full number. In addition, Brahmagupta presented in this work on rules for arithmetic with negative numbers and with the number 0, which largely correspond to already our modern understanding. The biggest difference was that Brahmagupta also the division by 0 is allowed, while in modern mathematics quotients are not defined by the divisor 0.
Worldwide distribution
The worldwide spread of Indian numerals was not associated directly with a global spread of Brahmasphutasiddhanta, but needed some intermediate steps.
Arab dissemination
Between 640 and 644 the Arabs occupy Iraq and Persia. The first recorded evidence of Indian numerals in the West originating from the Syrian Nestorian bishop Severus Sebokht in the 7th century.
Al - Khwarizmi
To 825 the Persian mathematician, astronomer and geographer al - Ḫwārizmī writes his work on calculating with Indian numerals, which is known only in Latin translation ( Algoritmi de numero indorum, 12th century ).
The zero will be " empty" when the Arabs as sifr (Arabic الصفر, DMG aṣ - sifr, zero, nothing ') from the verb denotes Safira - a loan translation of the word Sunya. From this point the word originated.
The leap to the West
Liber abaci
The Italian Leonardo Fibonacci was followed in 1192 by his father to Algeria and met Abu Kamil's algebra know. 1202 completed the Liber abaci Fibonacci, in which he imagines the Hindu numerals among other things, and this referred to as " Indian numbers " and not as " Arabic numerals " in fact.
Typographic variants
This section is devoted to the historical emergence of various typographical variants and the common use today forms of Indian numerals.
Indian variants
Since astronomical observations have been systematically and operated at a high level in India already several thousand years ago, large numbers were needed - Lakh [ lak ʰ ] and crores [ Kror ] (Hindi: करोड़, Karor ). A Lakh corresponds to 100,000, a crore are 100 lakh, thus corresponds to 10,000,000. These figures have, although they were officially replaced by the thousands system kept and are still to be found today in common parlance.
Arab variants
In Arabic script the spelling from right to left developed from an originally vertical labeling of the papyri from top to bottom (they were of longitudinal strips glued together ), but which was then rotated for reading 90 degrees. Similarly, the Indian numerals were recorded in the Scriptures against the Indian stock partially received therefore a rotated shape and then the graphic style of the Arabic script were adjusted. The structure of the Arabic words of the Indian numerals is similar to that in Western languages from the highest priority (ie, the left-most digit ) from. For example, the word for 10.000 put ( asharat alaf ) from the word ashara for 10 and alf for 1000 together. Similarly as in Western languages , there are also special rules apply as with the tens - for example, is the name for 19 tisata -shahr from tisa for 9 and Aschara for 10 as well as in the Nineteen in German. Be written numbers but also in the form of digits from right to left according to the general direction of writing in Arabic. The position of the digits is as usual in the decimal system (ie the number with the highest value left).
Before the Arabs took over the Indian place value system, they used for the representation of numbers, the letters of their alphabet, which was assigned as with many other writing systems such as ancient Greek, Roman or Hebrew in addition to the phonetic value of each a numerical value (see Arabic alphabet ). This possibility is even today sometimes still used in certain situations, comparable to the use of Roman numbers in the western -speaking world.
European variants
Lining and old style figures
In Europe can be mainly two forms of representation of numbers differ: Lining and old style figures.
The most common variant Lining: all numbers have the same height, namely the uppercase ( capital) letters. To enable a clean table set, lining figures are mostly all the same width, ie the width of an en space. This variant is also known as table numbers. Less common are proportional -caps numerals, where in particular the 1 is narrower than the other digits. The disadvantage of lining figures is that they form an optical foreign body in the running text, and that in some half- square - wide digits and the letter spacing looks too wide ( as in 1).
For this reason, have well-developed writings on a second set of digits that old style figures. These have as lowercase upper and lower lengths and usually an individual, the character shape adapted walking distance. Thus, they fit seamlessly and typographically correct viewpoints in the text. Some fonts also offer old style figures of the same width for the table record.
Worldwide distribution of European variant
From Morocco to Libya is used today instead of the Arab European variant.