Hindu-Arabic numeral system
The
Hindu-Arabic numeral system (also called
Algorism) is a
positional decimal numeral system documented from the
9th century.
The symbols (glyphs) used to represent the system are in principle independent of the system itself. The glyphs in actual use are descended from the
Brahmi numerals, and have split into various typographical variants since the
Middle Ages. These symbol sets can be divided into three main families: the
West Arabic numerals used in the Maghreb and in Europe, the
Eastern Arabic numerals used in Egypt and the Middle East, and the
Indian numerals used in India.
The Hindu-Arabic numeral system is designed for
positional notation in a
decimal system. In a more developed form, positional notation also uses a
decimal marker (at first a mark over the ones digit but now more usually a decimal point or a decimal comma which separates the ones place from the tenths place), and also a symbol for "these digits recur
ad infinitum". In modern usage, this latter symbol is usually a
vinculum (a horizontal line placed over the repeating digits). In this more developed form, the numeral system can symbolize any
rational number using only 13 symbols (the ten digits, decimal marker, vinculum or division sign, and an optional prepended
dash to indicate a
negative number).
Various symbol sets are used to represent numbers in the Hindu-Arabic numeral, all of which evolved from the
Brahmi numerals.
The symbols used to represent the system have split into various typographical variants since the
Middle Ages:
*the widespread Western "
Arabic numerals" used with the
Latin alphabet, in the table below labelled "European", descended from the "West Arabic numerals" which were developed in
al-Andalus and the
Maghreb (There are two
typographic styles for rendering European numerals, known as lining figures and
text figures).
*the "Arabic-Indic" or "
Eastern Arabic numerals" used with the
Arabic alphabet, developed primarily in what is now
Iraq. A variant of the Eastern Arabic numerals used in Persian and Urdu.
*the "Devanagari numerals" used with
Devanagari and related variants grouped as Indian numerals.
As in many numbering systems, the numbers 1, 2, and 3 represent simple tally marks. 1 being a single line, 2 being two lines (now connected by a diagonal) and 3 being three lines (now connected by two vertical lines). After three, numbers tend to become more complex symbols (examples are the Chinese/Japanese numbers and
Roman numerals). Theorists believe that this is because it becomes difficult to instantaneously count objects past three[
1].
Origins
Buddhist inscriptions from around 300 BCE use the symbols which became 1, 4 and 6. One century later, their use of the symbols which became 2, 4, 6, 7 and 9 was recorded. These
Brahmi numerals are the ancestors of the Hindu-Arabic glyphs 1 to 9, but they were not used as a positional system with a zero, and there were rather separate numerals for each of the tens (10, 20, 30, etc.).
Positional notation without the use of zero (using an empty space in tabular arrangements, or the word
kha "emptiness") is known to have been in use in
India from the
6th century.
Adoption by the Arabs
These nine numerals were adopted by the
Arabs in the
8th century. How the numbers came to the Arabs is recorded in
al-Qifti's "Chronology of the scholars", which was written around the end the
12th century, quoting earlier sources [
2]:
... a person from India presented himself before the Caliph al-Mansur in the year 776 who was well versed in the siddhanta method of calculation related to the movement of the heavenly bodies, and having ways of calculating equations based on the half-chord [essentially the sine] calculated in half-degrees ... Al-Mansur ordered this book to be translated into Arabic, and a work to be written, based on the translation, to give the Arabs a solid base for calculating the movements of the planets ... |
An Arab telephone keypad with both the Western "Arabic numerals" and the Arabic "Arabic-Indic numerals" variants. |
This book presented by the Indian scholar was probably
Brahmasphutasiddhanta (The Opening of the Universe) which was written in
628(Ifrah) [
3] by the Indian mathematician
Brahmagupta.
The numeral system came to be known to both the
Persian mathematician
Al-Khwarizmi, whose book
On the Calculation with Hindu Numerals written about
825, and the
Arab mathematician
Al-Kindi, who wrote four volumes,
On the Use of the Indian Numerals (Ketab fi Isti'mal al-'Adad al-Hindi) about
830, are principally responsible for the diffusion of the Indian system of numeration in the
Middle-East and the West [
4].
The use of
zero in positional systems dates to about this time, representing the final step to the system of numerals we are familiar with today. The first dated and undisputed inscription showing the use of zero at is at
Gwalior, dating to
876 CE. There were, however, Indian precursors from about
500 CE, positional notations without a zero, or with the word
kha indicating the absence of a digit. It is, therefore, uncertain whether the crucial inclusion of zero as the tenth symbol of the system should be attributed to the Indians, or if it is due to Al-Khwarizmi or Al-Kindi.
In the
10th century,
Middle-Eastern mathematicians extended the decimal numeral system to include fractions, as recorded in a treatise by
Syrian mathematician
Abu'l-Hasan al-Uqlidisi in
952-
953.
In the Arab World—until modern times—the Hindu-Arabic numeral system was used only by mathematicians. Muslim scientists used the
Babylonian numeral system, and merchants used the
Abjad numerals, a system similar to the
Greek numeral system and the
Hebrew numeral system. Therefore, it was not until
Fibonacci that the Hindu-Arabic numeral system was used by a large population.
Adoption in Europe
Leonardo Fibonacci brought this system to Europe, translating the Arabic text into Latin, called
Liber Abaci 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. Robert Chester translated the Latin into English.
*
List of glyphs used with the Hindu-Arabic numeral system
