Aryabhatta-II

Aryabhata-II (920-1000) was an mathematician and astronomer of India, and wrote the well-known book the Mahasiddhanta. He is believed to be born in India during c.920 and died at c.1000. These dates are approximately suggested by the modern historians, however there are historians like G.R.Kaye believed that Aryabhata II lived before al-Biruni, whereas Datta in 1926 proved that these dates were too early. Though Pingree considers that Aryabhatta's main publications was published between 950 and 1100, but R.Billiard has proposed a date in the sixteenth century.

Aryabhatta II'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 a even number, when this number of quotients is an odd number, etc.

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. Aryabhatta II played a vital role in it by constructing a sine table, which was accurate up to five decimal places.

Courtesy : Internet