Aryabhata

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ĀRYABHATA

ĀRYABHATA (476–c. 550), the first of the great astronomers of the classical age of India Āryabhata was born in a.d. 476 in Ashmaka but later lived in Kusumapura, which his commentator Bhāskara I (a.d. 629) identifies with Pātaliputra (modern Patna). It appears that he was the kulapati (head) of the University at Nalanda in Magadha.

There is no agreement about the location of Ashmaka, but since the Āryabhatian school has remained most strong in Kerala in South India, many believe that he may have belonged to that region. In addition, Āryabhata employed the Kali era (3102 b.c.), which was most popular in South India.

He wrote at least two books: the Āryabhatiya and the Āryabhata-siddhānta, of which the latter is known only through references in other works. Bhāskara I (seventh century), who wrote a commentary on Āryabhata's work, tells us that Āryabhata's disciples included the astronomers Pānduranga-svāmi, Lātadeva, and Nishanku.

Āryabhata's main contributions to mathematics included the good approximation of 3.1416 for π, a table of sine-differences, and a method to solve indeterminate equations of a certain type that are important in astronomy. He used a novel representation of numbers as words. His figure for the sidereal rotation of the earth was extremely accurate. Āryabhata made important innovations in planetary computations by using simplifying hypotheses, and he presented a method of finding the celestial latitudes of the planets. The Āryabhatīya presented Āryabhata's astronomical and mathematical theories, in which the earth was taken to be spinning on its axis and the periods of the planets were given with respect to the sun. In this book, the day was reckoned from one sunrise to the next, whereas in his Āryabhata-siddhānta, he took the day from one midnight to another. There was also difference in some astronomical parameters.

It appears that the Āryabhatīya used the earlier Paitāmaha Siddhānta as a model, whereas the Āryabhatasiddhānta used the conventions of the Sūrya-siddhānta. The Āryabhata-siddhānta was incorporated with some emendations into the Khanda-khādyaka by the celebrated seventh-century astronomer Brahmagupta (born 598).

The later Kerala school of astronomy and mathematics followed Āryabhata. Nīlakantha Somayāji (1444–1545) made significant contributions to the Āryabhata system of astronomy.

The Āryabhatīya was translated into Arabic as Arajbahara, and in turn it influenced Western astronomers. The Khanda-khādyaka was translated into Arabic under the title Zij-al-Arkand and Az-Zij Kandakatik al-Arabi. From the Arab world, this book reached Europe.

Subhash Kak

See alsoĀryabhatīya ; Astronomy