Uncovering the Mystery of Ramanujam's Formula for Pi

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SUMMARY

The discussion centers on Ramanujan's formula for pi, specifically referencing the book "Fractals, Chaos, Power Laws, Minutes from an Infinite Paradise" by Manfred Schroeder, ISBN 0-7167-2136-8, which provides insights into the formula's derivation. Additionally, the paper "Modular Equations and Approximations to Pi" published in the Quarterly Journal of Mathematics (Vol. 45, pp. 350-372) discusses a recursive algorithm related to transformation theory for elliptic integrals that contributes to understanding Ramanujan's work. The formula's elegance suggests that Ramanujan may have intuitively grasped its significance.

PREREQUISITES
  • Understanding of elliptic integrals
  • Familiarity with transformation theory
  • Knowledge of recursive algorithms
  • Basic concepts of fractals and chaos theory
NEXT STEPS
  • Read "Fractals, Chaos, Power Laws, Minutes from an Infinite Paradise" by Manfred Schroeder
  • Study the paper "Modular Equations and Approximations to Pi" in the Quarterly Journal of Mathematics
  • Explore the mathematical foundations of elliptic integrals
  • Investigate the applications of recursive algorithms in mathematical analysis
USEFUL FOR

Mathematicians, researchers in number theory, and anyone interested in the mathematical properties of pi and Ramanujan's contributions to mathematics.

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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