How did Ramanujan derive his formula for pi?

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Sam_
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Hi, can you please explain to me how Ramanujam got this formula for pi.

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Thank you.
 

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I can't tell you how this formula was derived, but it is mentioned in the book: "Fractals, Chaos, Power Laws, Minutes from an infinite paradise" by Manfred Schroeder, ISBN 0-7167-2136-8. Also mentioned here is a different formula from Ramanujan which is based on a recursive algorithm from transformation theory for elliptic integrals. This work is written in the paper: "Modular equations and approximations to pi" Quar. J. Math. 45, 350-372. This is not much information, but it might be a start.
 
He probably just saw it in his head and thought it was immediately obvious.
 

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