Jyā table

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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

Template:Side box

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:

Jyā table of Ãryabhaṭa, Radius = 3438[1]
Arc
(minutes)
difference
(AB's table)
jyā length picture of jyā
(pink)
225 225 225 File:Jya tbl small225.png
450 224 449 File:Jya tbl small450.png
675 222 671 File:Jya tbl small675.png
900 219 890 File:Jya tbl small900.png
1125 215 1105 File:Jya tbl small1125.png
1350 210 1315 File:Jya tbl small1350.png
1575 205 1520 File:Jya tbl small1575.png
1800 199 1719 File:Jya tbl small1800.png
2025 191 1910 File:Jya tbl small2025.png
2250 183 2093 File:Jya tbl small2250.png
2475 174 2267 File:Jya tbl small2475.png
2700 164 2431 File:Jya tbl small2700.png
2925 154 2585 File:Jya tbl small2925.png
3150 143 2728 File:Jya tbl small3150.png
3375 131 2859 File:Jya tbl small3375.png
3600 119 2978 File:Jya tbl small3600.png
3825 106 3084 File:Jya tbl small3825.png
4050 93 3177 File:Jya tbl small4050.png
4275 79 3256 File:Jya tbl small4275.png
4500 65 3321 File:Jya tbl small4500.png
4725 51 3372 File:Jya tbl small4725.png
4950 37 3409 File:Jya tbl small4950.png
5175 22 3431 File:Jya tbl small5175.png
5400 7 3438 File:Jya tbl small5400.png

See Also

References

  1. 1.0 1.1 Template:Refia-expand-title
  2. Template:Refia p 71 has a detailed table of jyā tables of early Indian astronomers.
  3. See Template:Refia section 7.18, 7.19, etc.
  4. Template:Refia7.19.1

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