Hindu–Arabic numeral system

Eastern Arabic and Western Arabic numerals on a road sign in Abu Dhabi

The Hindu–Arabic numeral system or Indo-Arabic numeral system ^[1] (also called the Arabic numeral system or Hindu numeral system)^{[2][note 1]} is a positional decimal numeral system, and is the most common system for the symbolic representation of numbers in the world.

It was invented between the 1st and 4th centuries by Indian mathematicians. The system was adopted in Arabic mathematics by the 9th century. Influential were the books of Persian Al-Khwārizmī^[3] (On the Calculation with Hindu Numerals, c. 825) and Al-Kindi (On the Use of the Hindu Numerals, c. 830). The system later spread to medieval Europe by the High Middle Ages.

The system is based upon ten (originally nine) 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 Brahmi numerals and have split into various typographical variants since the Middle Ages.

These symbol sets can be divided into three main families: Western Arabic numerals used in the Greater Maghreb and in Europe, Eastern Arabic numerals used in the Middle East, and the Indian numerals in various scripts used in the Indian subcontinent.

Etymology[]

The Hindu-Arabic or Indo-Arabic numerals were invented by mathematicians in India.^[4] Persian and Arabic mathematicians called them "Hindu numerals". Later they came to be called "Arabic numerals" in Europe because they were introduced to the West by Arab merchants.^[5]

Positional notation[]

The Hindu–Arabic 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 a prepended minus sign to indicate a negative number).

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.

Symbols[]

Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, most of which developed from the Brahmi numerals.

The symbols used to represent the system have split into various typographical variants since the Middle Ages, arranged in three main groups:

• The widespread Western "Arabic numerals" used with the Latin, Cyrillic, and Greek alphabets in the table, descended from the "West Arabic numerals" which were developed in al-Andalus and the Maghreb (there are two typographic styles for rendering western Arabic numerals, known as lining figures and text figures).
• The "Arabic–Indic" or "Eastern Arabic numerals" used with Arabic script, developed primarily in what is now Iraq.^{[citation needed]} A variant of the Eastern Arabic numerals is used in Persian and Urdu.
• The Indian numerals in use with scripts of the Brahmic family in India and Southeast Asia. Each of the roughly dozen major scripts of India has its own numeral glyphs (as one will note when perusing Unicode character charts).

Glyph comparison[]