Ramanujan's Approximations to Pi

Ramanujan's Approximations to Pi

$\left({9^2 + \dfrac {19^2} {22} }\right)^{1/4}$

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

$\dfrac {63} {25} \left({17 + 15 \sqrt 5}\right) \left({7 + 15 \sqrt 5}\right)$

$\pi \approx \dfrac {63 } {25 } \dfrac {\paren {17 + 15 \sqrt 5} } {\paren {7 + 15 \sqrt 5} }$

Approximation involving $\dfrac {99^2} {1103}$

$2 \pi \sqrt 2 \approx \dfrac {99^2} {1103}$

Source of Name

This entry was named for Srinivasa Ramanujan.