Jyā table

Early Indian astronomers used Jyā (R Sine) extensively in their astronomical computations. For this purpose, they used jyā lookup tables precomputed by scholars.

The contains jyā tables, as do the works of, , Brahmagupta, Deva, Lalla, Vaṭeśvara, Mañjula, and others. Many of these astronomers also developed various methods for pre-calculating jyā, koṭijyā, etc, more accurately.

Bhaskara I described a direct formula to approximate jyā, to find bāhuphala and koṭiphala of the planets.

Āryabhaṭa


Āryabhaṭa, in his, gives his jyā table by 'differences'. He also uses a radius of 3438 units in length. Starting at a 0° arc, he moves up in intervals of 3°45' (or 225 minutes), giving the the additional length required to make jyā for each arc, until he has gone through 24 different intervals, ending at 5400 minutes of arc, or 90°.

IE, for the arc of a circle of radius 3438 units:
 * The jyā for  225 minutes arc = 225
 * The jyā for 2*225 minutes arc = 225+224 => 449
 * The jyā for 3*225 minutes arc = 225+224+222 => 671
 * etc etc etc.

The result: