**Govindasvami**(or Govindasvamin) was an Indian mathematical astronomer whose most famous treatise was a commentary on the

*Mahabhaskariya*Ⓣ of Bhaskara I.

Bhaskara I wrote the *Mahabhaskariya* Ⓣ in about 600 A. D. It is an eight chapter work on Indian mathematical astronomy and includes topics which were fairly standard for such works at this time. It discussed topics such as the longitudes of the planets, conjunctions of the planets with each other and with bright stars, eclipses of the sun and the moon, risings and settings, and the lunar crescent.

Govindasvami wrote the *Bhasya* in about 830 which was a commentary on the *Mahabhaskariya* Ⓣ. In Govindasvami's commentary there appear many examples of using a place-value Sanskrit system of numerals. One of the most interesting aspects of the commentary, however, is Govindasvami's construction of a sine table.

Indian mathematicians and astronomers constructed sine table with great precision. They were used to calculate the positions of the planets as accurately as possible so had to be computed with high degrees of accuracy. Govindasvami considered the sexagesimal fractional parts of the twenty-four tabular sine differences from the *Aryabhatiya* Ⓣ. These lead to more correct sine values at intervals of 90 °/24 = 3 °45 '. In the commentary Govindasvami found certain other empirical rules relating to computations of sine differences in the argumental range of 60 to 90 degrees. Both of the references [1] and [2] are concerned with the sine tables in Govindasvami's work.

**Article by:** *J J O'Connor* and *E F Robertson*