Aryabhata

Aryabhata was an Indian mathematician and astronomer whose Sanskrit treatise, the Aryabhatiya, was completed in 499 CE. His work presented influential methods in arithmetic, algebra, trigonometry, and astronomy.

Aryabhatiya: A Sanskrit mathematical and astronomical treatise completed by Aryabhata in 499 CE. This compact work is the principal source for Aryabhata’s mathematical and astronomical ideas.
Kuṭṭaka: An iterative method in Indian mathematics for solving certain linear indeterminate equations. Aryabhata explains this algorithm for problems involving integer remainders.
Kusumapura: An ancient Indian city commonly identified with Pataliputra, present-day Patna. Aryabhata identifies Kusumapura with his scholarly setting, though details of his life remain uncertain.
Indian mathematical astronomy: The mathematical study of celestial motions developed in India through texts, tables, and computational methods. Aryabhata’s treatise became a major reference point within this evolving discipline.
Place-value notation: A numeral system in which a digit’s value depends on its position. Aryabhata used place-based arrangements of syllables to represent large numbers.
Aryabhata's sine table: A table of 24 sine differences used in Aryabhata’s trigonometric calculations. It turns angular divisions into numerical values useful for astronomical computation.
Gupta Empire: An empire that ruled much of northern India from the fourth to sixth centuries CE. Aryabhata’s treatise belongs to the intellectual world of the Gupta period.
Aryabhata school: A lineage of Indian astronomers whose work followed or adapted methods associated with Aryabhata. Later astronomers developed distinct approaches from the tradition linked to his name.
Sanskrit numerals: Systems for expressing numbers through Sanskrit words, syllables, or symbols. The Aryabhatiya uses a distinctive Sanskrit letter-number scheme for expressing values.
Aryabhata's rotation of Earth: Aryabhata’s account that Earth rotates on its axis, making the stars appear to move westward. This model explains apparent daily celestial motion through terrestrial rotation.

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