Hindu–Arabic numeral system
| Part of a series on |
| Numeral systems |
|---|
| List of numeral systems |
The Hindu-Arabic numeral system (also called Algorism) is a positional decimal numeral system documented from the 9th century. An important characteristic of the system is the use of a numeral digit zero. Further enhancements of the system include use of a decimal marker and a symbol for "these digits recur ad infinitum".
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.
ARABIC NUMERAL SYSTEM
Christina Campo-Abdoun & Seifed-Din Abdoun
Center For Arabic Culture (CAC) http://www.cacac.org/index.htm http://www.cacac.org/Arabic_Numeral_System.htm
The Indian numerals discussed in our article Indian numerals form the basis of the European number systems which are now widely used. However they were not transmitted directly from India to Europe but rather came first to the Arabic/Islamic peoples and from them to Europe. The story of this transmission is not, however, a simple one. The eastern and western parts of the Arabic world both saw separate developments of Indian numerals with relatively little interaction between the two. By the western part of the Arabic world we mean the regions comprising mainly North Africa and Spain. Transmission to Europe came through this western Arabic route, coming into Europe first through Spain.
There are other complications in the story, however, for it was not simply that the Arabs took over the Indian number system. Rather different number systems were used simultaneously in the Arabic world over a long period of time. For example there were at least three different types of arithmetic used in Arab countries in the eleventh century: a system derived from counting on the fingers with the numerals written entirely in words, this finger-reckoning arithmetic was the system used for by the business community; the sexagesimal system with numerals denoted by letters of the Arabic alphabet; and the arithmetic of the Indian numerals and fractions with the decimal place-value system.
The first sign that the Indian numerals were moving west comes from a source which predates the rise of the Arab nations. In 662 AD Severus Sebokht, a Nestorian bishop who lived in Keneshra on the Euphrates river, wrote:-
I will omit all discussion.....Log On: http://www.cacac.org/Arabic_Numeral_System.htm
Positional notation
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; historically, however, there has been much variation). 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).
Symbols
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 languages as shown as "East Arabic-Indic".
- 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 two[1].
History
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.).
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 ...
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 Arabic numeral system was used only by mathematicians. Muslim scientists used the Babylonian numeral system, and merchants used a numeral system similar to the Greek numeral system and the Hebrew numeral system. Therefore, it was not until Fibonacci that the Arabic numeral system was used by a large population.
Adoption in Europe
The Arabs brought this system to Europe, and 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.