Hindu-Arabic numeral system
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|Numeral system topics|
|Binaries: 2, 4, 8, 16, 32, 64, 128|
|other: 3, 9, 12, 24, 30, 36, 60, more.|
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.
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.).
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 :
- ... 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 ...
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 .
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 reason explaining the shape Arabic numerals takes today is due to the House of Wisdom in ancient Baghdad (Iraq). There, they used the concept of counting angles to craft symbols for the decimal numbers one through nine with the numeral for zero denoted by a circle which of course contains no angles .
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 of the House of Wisdom.
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.