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The Hindu–Arabic numeral system or Hindu numeral system is a positional decimal numeral system developed between the 1st and 4th centuries by Indian mathematicians. The system was adopted by Persian Muslim mathematician (Al-Khwarizmi's c. 825 book On the Calculation with Hindu Numerals) and Arab mathematicians (Al-Kindi's c. 830 volumes On the Use of the Indian Numerals) by the 9th century. It later spread to the western world by the High Middle Ages.

The system is based upon ten (originally nine) different glyphs. The symbols (glyphs) used to represent the system are in principle independent of the system itself. The glyphs in actual use are descended from Indian Brahmi numerals, and have split into various typographical variants since the Middle Ages.

These symbol sets can be divided into three main families: the Indian numerals used in India, the Eastern Arabic numerals used in Egypt and the Middle East and the West Arabic numerals used in the Maghreb and in Europe.

Etymology

The Hindu-Arabic numerals were invented in India and thus called "Hindu numerals" by Persian mathematician Khowarizmi. They were later called "Arabic" numerals by Europeans, because they were introduced in the West by Arabized Berbers of North Africa.

Positional Notation

The Hindu 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, and an optional prepended dash to indicate a negative number).

Despite the numeral system being described as the "Hindu–Arabic numeral system", the system had been developed by Indian mathematicians and in use extensively throughout India, before being adopted by Persian mathematicians in India and passed on to the Arabs further west. The numeral system was transmitted to Europe in the Middle Ages. The use of Arabic numerals spread around the world through European trade, books and colonialism. Today they are the most common symbolic representation of numbers in the world.

Although generally found in text written with the Arabic abjad ("alphabet"), numbers written with these numerals also place the most-significant digit to the left, so they read from left to right. The requisite changes in reading direction are found in text that mixes left-to-right writing systems with right-to-left systems.

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