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In mathematics, Bhaskara I's sine approximation formula is a rational expression in one variable for the computation of the approximate values of the trigonometric sines discovered by Bhaskara I (c. 600 – c. 680), a seventh-century Indian mathematician. This formula is given in his treatise titled ''Mahabhaskariya''. It is not known how Bhaskara I arrived at his approximation formula. However, several historians of mathematics have put forward different theories as to the method Bhaskara might have used to arrive at his formula. The formula is elegant, simple and enables one to compute reasonably accurate values of trigonometric sines without using any geometry whatsoever.〔 ==The approximation formula== The formula is given in verses 17 – 19, Chapter VII, Mahabhaskariya of Bhaskara I. A translation of the verses is given below: *(Now) I briefly state the rule (for finding the ''bhujaphala'' and the ''kotiphala'', etc.) without making use of the Rsine-differences 225, etc. Subtract the degrees of a ''bhuja'' (or ''koti'') from the degrees of a half circle (that is, 180 degrees). Then multiply the remainder by the degrees of the ''bhuja'' or ''koti'' and put down the result at two places. At one place subtract the result from 40500. By one-fourth of the remainder (thus obtained), divide the result at the other place as multiplied by the anthyaphala'' (that is, the epicyclic radius). Thus is obtained the entire ''bahuphala'' (or, ''kotiphala'') for the sun, moon or the star-planets. So also are obtained the direct and inverse Rsines. (The reference "Rsine-differences 225" is an allusion to Aryabhata's sine table.) In modern mathematical notations, for an angle ''x'' in degrees, this formula gives〔 : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bhaskara I's sine approximation formula」の詳細全文を読む スポンサード リンク
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