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History Of Indian Mathematics

1.4 Trigonometry

The study of astronomy is not possible without the knowledge of trigonometry. All the Siddhanta scripts revealed the advanced knowledge of plane and spherical trigonometry. All the basic identities and formulae were applied in astronomical calculations while also formulating sine tables. Infinite series for sine, cosine and tangent functions were developed.

Value of Pi ratio

Shulva sutras mentioned the value of ratio of circumference of circle to its diameter now popularly known as π ratio as in between 3.1 to 3.125. Later Aryabhata recorded the value (62832/20000) which is equal to 3.1416. Later other mathematicians found values of π correct up to 7 to 17 decimal places. Mathematicians also developed infinite series for π, π/4, π/12 etc.

1.5 Other Disciplines

Indian scholars developed first and second ordered forward and backward interpolation techniques to evaluate intermediate values of sine of angle not given in the tables. The concept of tatkalika gati clearly indicates the beginning of advancement of knowledge of calculus. Rules for constructing Magic squares, Magic rectangles Magic stars are also found developed to perfection.