Sunday, March 15, 2015

π Day and India

Yesterday was π day and my friend Haldar Rana posted this quiz on π. I started to look around the Indian contribution with respect to π. Here are some of the stuff that I found.

Aryabhatta talks about π in following way.

  • Add 4 to 100
  • Multiply by 8
  • Add 62000. 
  • The result is approximately the circumference of the circle whose diameter is 20000. 
With above calculation the value of PI comes to 3.1416.

Madhava has done some more serious work with π. He defines π as the ratio of the circumference (2,827,433,388,233) of a circle of diameter \( 9*10^{11} \). Which yields 3.14159265359.

Madhava also came up with Madhava Series.

\(\fracπ4 = 1 - \frac 13 + \frac 15 - \frac17+...\)

Ramanujam later discovered another series that converged much faster.

I will write another post with details of all that.

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