Continuous invasions by the Mughals had made mathematics to dry in northen and central India. But South India was not much affected by Mughals and hence mathematics kept on growing in south. Most notable contributer from that period in the field of mathematics and astronomy was Madhava. Madhava (1340 – 1425 AD) was born in Sangamagrama, Kerala. He was the founder of Kerala school of Astronomy and Mathematics. Madhava is considered as the greatest mathematician and astronomer from Medieval Period. He had major contributions in fields of mathematics like Trigonometry, Geometry, Algebra and Calclulus. He was first all over the world to use infinite series of approximation for a range of trigonometric functions which led to passage of infinity and which finally led to modern Mathematical Analysis topics like Differentiation, Integration, Limits and Infinite series. Madhava wrote following books: Golavada Madhyamanayanaprakara Mahajyanayanaprakara Lagnaprakara Venavaroha Sphutacandrapati Aganita-grahacara Candravakyani Most of his work (except some of his astronomical books) is lost but his pupils from his school had written books on mathematics and almost all his discoveries are mentioned in those commentaries. Value of pi: In his book Mahajyanayanaprakara he derived a formula for pi by infinite series expansion which is now called as Madhava- Leibnitz series, i.e. by successively adding and subtracting odd number fractions till infinity, he could arrive to exact formula for π. π/4 = 1 - 1/3 + 1/5 -1/7 + ... (-1)n/(2n+1) + ….. and was extended by Nilkanta Somayaji in his book ‘Tantrasangraha’ as tan-1x = x - x3/3 + x5/5 - ... Another his formula for pi, on taking 21 terms, can lead to exact value of pi upto 11 decimals.. π = √12(1 - 1/(3×3) + 1/(5×32) - 1/(7×33) + .. π = 3.14159265359 (Correc upto 11 decimal places). Trignometry and Infinite Series of Trigonometric Functions Following were the 1st algebraic formulae to … [Read more...]