History of the Hindu–Arabic numeral system

The Hindu–Arabic numeral system is a decimal place-value numeral system that uses a zero glyph as in "205".

Its glyphs are descended from the Indian Brahmi numerals. The full system emerged by the 8th to 9th centuries, and is first described in Al-Khwarizmi's On the Calculation with Hindu Numerals (ca. 825), and Al-Kindi's four volume work On the Use of the Indian Numerals (ca. 830). Today the name Hindu–Arabic numerals is usually used.

Historians trace modern numerals in most languages to the Brahmi numerals, which were in use around the middle of the 3rd century BC. The place value system, however, developed later. The Brahmi numerals have been found in inscriptions in caves and on coins in regions near Pune, Mumbai, and Uttar Pradesh. These numerals (with slight variations) were in use over quite a long time span up to the 4th century.

During the Gupta period (early 4th century to the late 6th century), the Gupta numerals developed from the Brahmi numerals and were spread over large areas by the Gupta empire as they conquered territory. Beginning around 7th century, the Gupta numerals developed into the Nagari numerals.

During the Vedic period (1500–500 BCE), motivated by geometric construction of the fire altars and astronomy, the use of a numerical system and of basic mathematical operations developed in northern India. Hindu cosmology required the mastery of very large numbers such as the kalpa (the lifetime of the universe) said to be 4,320,000,000 years and the "orbit of the heaven" said to be 18,712,069,200,000,000 yojanas. Numbers were expressed using a "named place-value notation", using names for the powers of 10: dasa, shatha, sahasra, ayuta, niyuta, prayuta, arbuda, nyarbuda, samudra, madhya, anta, parardha etc., the last of these being the name for a trillion. For example, the number 26432 was expressed as "2 ayuta 6 sahasra 4 shatha 3 dasa 2." In the Buddhist text Lalitavistara, the Buddha is said to have narrated a scheme of numbers up to 10^53.

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