Ramanujan's Approximations to Pi/4th Root of 9 Squared plus 19 Squared over 22

Approximation to Pi by Srinivasa Ramanujan

$\pi \approx \paren {9^2 + \dfrac {19^2} {22} }^{1/4} = 3 \cdotp 14159 \, 26526 \, 2$

Proof

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Source of Name

This entry was named for Srinivasa Ramanujan.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41972 \ldots$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41971 \ldots$