Question

Write about the contribution of any great Indian mathematician.​

Answer 1

Indian mathematics. ... In the classical period of Indian mathematics (400 AD to 1200 AD), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, and Varāhamihira. The decimal number system in use today was first recorded in Indian mathematics....

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Answer 2

Here is your answer..

In mathematics there is a distinction between insight and formulating or working through a proof. Ramanujan proposed an abundance of formulae that could be investigated later in depth. G. H. Hardy said that Ramanujan's discoveries are unusually rich and that there is often more to them than initially meets the eye. As a byproduct of his work, new directions of research were opened up. Examples of the most intriguing of these formulae include infinite series for π, one of which is given below:

{\displaystyle {\frac {1}{\pi }}={\frac {2{\sqrt {2}}}{9801}}\sum _{k=0}^{\infty }{\frac {(4k)!(1103+26390k)}{(k!)^{4}396^{4k}}}.}{\displaystyle {\frac {1}{\pi }}={\frac {2{\sqrt {2}}}{9801}}\sum _{k=0}^{\infty }{\frac {(4k)!(1103+26390k)}{(k!)^{4}396^{4k}}}.}

This result is based on the negative fundamental discriminant d = −4 × 58 = −232 with class number h(d) = 2. Further, 26390 = 5 × 7 × 13 × 58 and 16 × 9801 = 3962, which is related to the fact that

{\textstyle e^{\pi {\sqrt {58}}}=396^{4}-104.000000177\dots .}{\textstyle e^{\pi {\sqrt {58}}}=396^{4}-104.000000177\dots .}

This might be compared to Heegner numbers, which have class number 1 and yield similar formulae.

Ramanujan's series for π converges extraordinarily rapidly (exponentially) and forms the basis of some of the fastest algorithms currently used to calculate π. Truncating the sum to the first term also gives the approximation

9801√2

/

4412

for π, which is correct to six decimal places; truncating it to the first two terms gives a value correct to 14 decimal places. See also the more general Ramanujan–Sato series.

One of Ramanujan's remarkable capabilities was the rapid solution of problems, illustrated by the following anecdote about an incident in which P. C. Mahalanobis posed a problem: