Indian decimal place-value system and Aryabhata sine
Sistema decimal posicional indio y seno de Aryabhata
- Date
- 499 · confidence medium
- Place
- Kusumapura (Pataliputra, present-day Patna), India
- Credited to
- Aryabhata (Aryabhatiya); earlier Indian tradition
- People
- 👤 Aryabhata476–550
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
A base-10 place-value numeral system that makes arithmetic uniform for numbers of any size; Aryabhata also introduces the sine function (jya) and sine tables, and approximates pi as 3.1416.
The Bakhshali manuscript was radiocarbon-dated in 2017 with folios of widely differing ages (3rd-4th, 7th-8th and 9th-10th centuries), which sparked a sharp methodological controversy (Plofker et al., 2017) over whether the relevant date is that of the oldest or the most recent folio; in 2024 Oxford revised the dating of the whole manuscript to 799-1102 CE, much later than first reported. The origin date of the Indian decimal place-value system remains debated, but it can no longer be claimed with the same confidence that Bakhshali attests the zero dot in the 3rd-7th centuries. The word sine comes from a mistranslation of the Arabic jiba.
What it led to
- zero as a number (Brahmagupta)
- Hindu-Arabic numerals
- al-Khwarizmi's algorithms
- sine-based trigonometry
Built on
- Brahmi numerals
- Greek and Babylonian astronomy
Made possible
- Zero as a number (India)628
- Bhaskara I's sine approximationc. 629
- Brahmagupta's second-order interpolation665
- Al-Uqlidisi's decimal fractions952-953
- Trigonometry as a disciplinec. 980
- universal written arithmetic
- accounting and trade