Arab numeration

The Arab numeration comprises several written forms. One can indeed use the letters of the Arabic alphabet, it is about numeration abjad, or of the signs resulting from the Indian writing nagari, these figures indo-Arabic are sometimes called “figures arabo-Indians”. Numeration abjad, especially in its Eastern alternative, is very close to the Hebraic Gematria .

Numeration abjad

Origins

The Alphabet S derived from the phenician, like the Greek , the gotic, the copte, the Cyrillic , the Hebrew , the araméen, etc, were mainly used so much to note sounds (alphabetical value) that numeral values by means of the same signs. Arabic does not make exception and it is moreover oldest of the two numerations used by the people Arabic-speaking people: the use of the Arabic alphabet to note the numbers, or ḥurūf ʾal-ǧumal , goes back to the first inscriptions. The imitation of a Greek or Hebrew model (it is not possible to slice), is not any doubt.

The Arabic alphabet, however, underwent several important modifications during its history (like the addition of points allowing to distinguish several letters, the change of value of certain letters, the reorganization of the alphabetical order, etc), modifications which did not take place same manner everywhere: in fact, when the letters are used for numeration, they are classified in an older order (known as Ordre Levantine, from which the first certificate dates from the ougaritic Alphabet and which one finds in all the alphabets derived from the phenician), but according to whether the alphabet is used by the Westerners or the Eastern ones, the letters are not arranged in the same way. This numeral order is much closer to that of the other alphabets of origin phenician, especially of those used for the Semitic Langues.

There thus exist mainly two numbering systems based on the Arabic alphabet. These two systems coexisted: that of the Arabs of the the Maghreb (i.e. Westerners, because such is the direction of this word) and that of the Eastern Arabs. This last is oldest, the Maghrebian system being a modification of the Eastern one. Obviously, it is not a fixed distinction, and one can find texts Maghrebian using Eastern numeration and vice versa. In fact, only six letters are placed differently between the two alphabets: they are mainly the pointed letters lately created at the 7th century, are rear RTL ثخذضظغ

For more details as for the rehandlings undergone by the Arabic alphabet during its history, to consult the article Arabic alphabet (history) .

This order begins with ʾalif , bāʾ ǧīm and dāl , which forms the word Abjad ; one names abjad thus is an alphabet noting only the consonants, generally Semitic and inherited the Phénicien, that is to say the Arab numeral letters. The traditional term is rear RTL أَبُجَدْ abuǧad , which gives a rear derivative RTL بُجَادِي buǧādī , “ignoramus”, i.e. who “knows only the ABC”.

Procedure

The letters are useful, as in the other alphanuméraux systems, to separately indicate the units, tens, hundreds and thousands: the system is decimal, is not entirely positional and is unaware of the zero. Each letter can note only one value, contrary to the positional system, where the sign “1”, for example, represents according to its place a unit, ten, a hundred, etc

One writes the letters alphanumérales from right to left, in an increasing way except if one dissimulates a number in a written word: it is enough to write a word whose letters will have the desired value. It is the case of the Chronogramme S, for example: Ġālib murd , “Ghâlib died” (it is here about a quotation of the poet of expression urdū Ghâlib, 1797-1869), is written rear RTL غالب مرد, which amounts letter by letter:

that is to say a total of 1277, which, according to the Moslem Calendar, is worth 1860, and indicates the date of the death of Ghâlib (in fact, this one died in 1869; the date of 1860 corresponds to the year of death imagined by the poet himself).

Units

They are noted in the same way in the Western and Eastern alphabets.

Tens

It is from 60 that the Western and Eastern alphabets diverge.

Hundreds

Thousands

Numeration indo-Arabic

Origins

It of India, is traced in their C-W communication nāgarī, that came from new signs allowing, thanks to the Zero positional , a greater flexibility. Moslem astronomers, by learning this science from the Indians at the 8th century, probably imported in the same movement their figures. Al-Khuwarizmi would be the first to be had, at the 9th century, worked on the Indian methods of calculating. It would however not have to be believed that they were essential vis-a-vis the numeral letters: those continued to be used a long time, the more so as they are often used with fine mystics, with the example of what is made with the Kabbale.

Quickly adopted, these signs underwent many modifications before taking following appearance (an alternative is always used in the zones Ourdou phons and persophones: Farsi, Pashto,…) :

To the contact with the Occident, the erudite Moslems transmitted to the European mathematicians these figures which, continuing to change, adopted a definite location at the 15th century.

Procedure

It is the same one as for the European figures, improperly called “Arab numerals” (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). It is to be noticed that in Arabic, as for the European languages, the figures representing the greatest value in a number are on the left, and smallest on the right, this although Arabic is read from right to left. The number is in fact read, in Arabic, while starting with the smallest value, following the example what partially occurs in certain Germanic and Celtic languages (in Dutch for example, 21 says éénentwintig , and one usually says in Breton unan warn-ugent : what amounts saying one and twenty ). cf also problems of endianess in data processing).

See too

Mathematical Arabic
Numeration

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