# 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. ^{[1]}

The Template:Ref-SuSi contains jyā tables, as do the works of Template:Ref-AB, Template:Ref-VM, Brahmagupta, Deva, Lalla, Vaṭeśvara, Mañjula, and others. ^{[2]} Many of these astronomers also developed various methods for pre-calculating jyā, koṭijyā, etc, more accurately. ^{[3]}

Bhaskara I described a direct formula to approximate jyā, to find bāhuphala and koṭiphala of the planets. ^{[4]}

## Āryabhaṭa

Āryabhaṭa, in his Template:Ref-ABh, 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:

## See Also

- Jyā
- Aryabhata's sine table (wikipedia)

## References

- ↑
^{1.0}^{1.1}Template:Refia-expand-title - ↑ Template:Refia p 71 has a detailed table of jyā tables of early Indian astronomers.
- ↑ See Template:Refia section 7.18, 7.19, etc.
- ↑ Template:Refia7.19.1

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