Aryabhatiya

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Aryabhatiya

work by Aryabhata

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June 23, 2026

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The Aryabhatiya is a Sanskrit treatise on mathematics and astronomy composed around 499 CE by the Indian mathematician and astronomer Aryabhata. It is divided into four sections: "Gitika" (verses), "Ganita" (mathematics), "Kalakriya" (time calculations), and "Gola" (sphere).1

The "Ganita" section includes algorithms for square and cubic roots, calculations for pi (approximated as 3.1416), and concepts in algebra and arithmetic, such as quadratic equations and linear indeterminate equations. The "Kalakriya" section deals with planetary motion, and the "Gola" section covers spherical astronomy, including the prediction of eclipses and the understanding that the Earth's rotation causes the apparent movement of stars.1

Aryabhata's work was influential, with commentaries written in India and translations into Arabic that impacted Islamic astronomy. India's first satellite, Aryabhata, was launched in his honor in 1975.12

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Bhaskara I
In his commentary on the Aryabhatiya, Bhaskara explains in detail Aryabhata’s method of solving linear equations and provides a number of illustrative astronomical examples. Bhaskara particularly stressed the importance of proving mathematical rules rather than just relying on tradition or expediency. In supporting Aryabhata’s approximation to π, Bhaskara criticized the…
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In his commentary on the Aryabhatiya, Bhaskara explains in detail Aryabhata’s method of solving linear equations and provides a number of illustrative astronomical examples. Bhaskara particularly stressed the importance of proving mathematical rules rather than just relying on tradition or expediency. In supporting Aryabhata’s approximation to π, Bhaskara criticized the…
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Aryabhata
…known as the author of Aryabhatiya, composed about 499 ce. A second work, the Aryabhatasiddhanta (also called the Arya-siddhanta), is mentioned by later writers but did not survive as an independent text.
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…known as the author of Aryabhatiya, composed about 499 ce. A second work, the Aryabhatasiddhanta (also called the Arya-siddhanta), is mentioned by later writers but did not survive as an independent text.
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Indian mathematics
The role of astronomy and astrology
…two major astronomical schools: the Aryabhatiya of Aryabhata (c. 500 ce) and the Brahma-sphuta-siddhanta (628; “Correctly Established Doctrine of Brahma”) of Brahmagupta. Little is known of these authors. Aryabhata lived in Kusumapura (near modern Patna), and Brahmagupta is said to have been from Bhillamala
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…two major astronomical schools: the Aryabhatiya of Aryabhata (c. 500 ce) and the Brahma-sphuta-siddhanta (628; “Correctly Established Doctrine of Brahma”) of Brahmagupta. Little is known of these authors. Aryabhata lived in Kusumapura (near modern Patna), and Brahmagupta is said to have been from Bhillamala
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trigonometry
India and the Islamic world
…sines is found in the Aryabhatiya. Its author, Aryabhata I (c. 475–550), used the word ardha-jya for half-chord, which he sometimes turned around to jya-ardha (“chord-half”); in due time he shortened it to jya or jiva. Later, when Muslim scholars translated this work into Arabic, they retained the word jiva…
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…sines is found in the Aryabhatiya. Its author, Aryabhata I (c. 475–550), used the word ardha-jya for half-chord, which he sometimes turned around to jya-ardha (“chord-half”); in due time he shortened it to jya or jiva. Later, when Muslim scholars translated this work into Arabic, they retained the word jiva…
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