Scientists Have Accidentally Discovered a New Formula for Pi

Описание: This new formula is something else 😳
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Note, at 9:27, the n values should be minus 1 and the expression on the righthandside should be multiplied by 4. What I meant to write was:
n = 1: 4(1 - 1/3) ~= 2.66
n = 2: 4(1 - 1/3 + 1/5) ~= 3.42
n = 3: 4(1 - 1/3 + 1/5 - 1/7) ~= 2.89

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Sources:
[1] Saha, A. P., & Sinha, A. Field Theory Expansions of String Theory Amplitudes. *Physical Review Letters*, 132(22), 221601, 2024. https://doi.org/10.1103/PhysRevLett.1...
[2] Berggren, L., Borwein, J., & Borwein, P. Pi: A Source Book (3rd ed.). New York: Springer, 2004.
[3] Gupta, R. C. On the Remainder Term in the Madhava-Leibniz's Series. *Ganita Bharati*, 14(1–4), 68–71, 1992.
[4] Ramanujan, S. Modular Equations and Approximations to π. *Quarterly Journal of Mathematics*, 45, 350–372, 1914.
[5] The Man Who Knew Infinity. Directed by Matt Brown. [Film]. Sony Pictures Classics, 2015.

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