# Aryabhata II

**Āryabhaṭa** (c. 920 – c. 1000) was an Indian mathematician and astronomer, and the author of the *Maha-Siddhanta*. The numeral II is given to him to distinguish him from the earlier and more influential Āryabhaṭa I.

## Mahasiddhanta

Aryabhata's most eminent work was Mahasiddhanta. The treatise consists of eighteen chapters and was written in the form of verse in Sanskrit. The initial twelve chapters deals with topics related to mathematical astronomy and covers the topics that Indian mathematicians of that period had already worked on. The various topics that have been included in these twelve chapters are: the longitudes of the planets, lunar and solar eclipses, the estimation of eclipses, the lunar crescent, the rising and setting of the planets, association of the planets with each other and with the stars.

The next six chapters of the book includes topics such as geometry, geography and algebra, which were applied to calculate the longitudes of the planets. In about twenty verses in the treatise, he gives elaborate rules to solve the indeterminate equation: by = ax + c. These rules have been applied to a number of different cases such as when c has a positive value, when c has a negative value, when the number of the quotients is an even number, when this number of quotients is an odd number, etc.

## Other contributions to maths

Aryabhata II also deduced a method to calculate the cube root of a number, but his method was already given by Aryabhata I, many years earlier. Indian mathematicians were very keen to give the correct sine tables since they played a vital role to calculate the planetary positions as accurately as possible. Aryabhata II played a vital role in it by constructing a sine table, which was accurate up to five decimal places.

## References

- O'Connor, John J.; Robertson, Edmund F., "Aryabhata II",
*MacTutor History of Mathematics archive*, University of St Andrews.

## Further reading

- Vagiswari, A. (2007). "Āryabhaṭa II". In Thomas Hockey; et al.
*The Biographical Encyclopedia of Astronomers*. New York: Springer. p. 64. ISBN 978-0-387-31022-0. (PDF version)