Number Theory

    

Two New Derivations of Ramanujan's Formula Pi^4 Approx 97.5-1/11

Authors: Janko Kokosar

The paper presents two procedures, or derivations with educated guessing, where Ramanujan’s formula for $pi^4$ is the final result. The first derivation uses the integer approximation for $pi^3$, and 22/7 as an approximation for $pi$, followed by a simple modification to match Ramanujan’s formula. The second derivation uses an integer approximation for $pi^5$ alongside with 22/7. Once again, the modification to Ramanujan’s formula for $pi^4$ is quite simple. The aim is also to explore whether further approximations of this formula exist. Some hints are provided on this subject.

Comments: 5 Pages.

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Submission history

[v1] 2024-12-24 01:30:36

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