Difference between revisions of "Indian standard circle"
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| − | + | ''Indian standard circle'' is a name given to the standard circle first used in [[Surya Siddhanta (सूर्य सिद्धांता)|Surya Siddhanta]] and later used by several ancient Indian mathematicians and astronomers to improve the [[Indian sine tables]] and for various other calculations. [[Surya Siddhanta (सूर्य सिद्धांता)|Surya Siddhanta]] provides methods for calculating the Jyā (R.sine) values. The circle uses a radius of 3,438 minutes. ''Surya Siddhanta'' calculates the first Jyā (R.sine) as 1/8th of the number of minutes (kalās) in a Rashi (zodiac sign). It says a Rashi (zodiac sign) has 1800 minutes (kalās) and thus calculates the first Jyā to a value of 225 minutes (kalā कला ).<ref>Deva Shastri, Pundit Bapu (1861). "Translation of the Surya Siddhanta". Ch2 Ve15, pp. 15–16.</ref> | |
<br>The Indian standard circles holds significance as it is based on number of minutes in circle thus leads to 360 degrees in a circle which is the basis of modern trigonometry. Although the [[Indian sine tables]] are not based on the angles but rather on the R.sine (Jyā) values. The [[Surya Siddhanta (सूर्य सिद्धांता)|Surya Siddhanta]] data reflect highly sophisticated outcomes of the R.sine values. ''Burgess'' notes that it is remarkable to see that the 2nd order differences increase as the sines and each, in fact, is about 1/225th part of the corresponding sine.<ref>Burgess, Rev. Ebenezer (1860). Translation of the Surya Siddhanta. p. 115.</ref> | <br>The Indian standard circles holds significance as it is based on number of minutes in circle thus leads to 360 degrees in a circle which is the basis of modern trigonometry. Although the [[Indian sine tables]] are not based on the angles but rather on the R.sine (Jyā) values. The [[Surya Siddhanta (सूर्य सिद्धांता)|Surya Siddhanta]] data reflect highly sophisticated outcomes of the R.sine values. ''Burgess'' notes that it is remarkable to see that the 2nd order differences increase as the sines and each, in fact, is about 1/225th part of the corresponding sine.<ref>Burgess, Rev. Ebenezer (1860). Translation of the Surya Siddhanta. p. 115.</ref> | ||
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|+Modern units and Indian units ''(Sanskrit)'' | |+Modern units and Indian units ''(Sanskrit)'' | ||
!Modern units | !Modern units | ||
| − | !Indian units | + | !Indian units ''(Sanskrit)'' |
!value | !value | ||
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Latest revision as of 12:40, 3 July 2021
Indian standard circle is a name given to the standard circle first used in Surya Siddhanta and later used by several ancient Indian mathematicians and astronomers to improve the Indian sine tables and for various other calculations. Surya Siddhanta provides methods for calculating the Jyā (R.sine) values. The circle uses a radius of 3,438 minutes. Surya Siddhanta calculates the first Jyā (R.sine) as 1/8th of the number of minutes (kalās) in a Rashi (zodiac sign). It says a Rashi (zodiac sign) has 1800 minutes (kalās) and thus calculates the first Jyā to a value of 225 minutes (kalā कला ).[1]
The Indian standard circles holds significance as it is based on number of minutes in circle thus leads to 360 degrees in a circle which is the basis of modern trigonometry. Although the Indian sine tables are not based on the angles but rather on the R.sine (Jyā) values. The Surya Siddhanta data reflect highly sophisticated outcomes of the R.sine values. Burgess notes that it is remarkable to see that the 2nd order differences increase as the sines and each, in fact, is about 1/225th part of the corresponding sine.[2]
| Modern units | Indian units (Sanskrit) | value |
|---|---|---|
| Zodiac sign | Rashi (राशी) | 30 degrees |
| Degree | Ansh (अंश ) | 60 minutes |
| Minute | Kalā (कला ) | 60 seconds |
| Second | Vikalā (विकला ) | - |