+26400 This identity, when calculated correctly, is a very familiar constant. The question is this: how many accurate digits are there in its decimal expansion? {nl} Ln{[640,320^3 + 744]^2 - 393,768} / sqrt(652)=?
"\(\dots\) one example on Mathworld's Pi Approximations page.
The same formula from Ramanujan that I have used was extended in a different way by Warda (2004) with the result:
π ≈ ln [ ( 6403203 + 744 )2 - 2 · 196884 ] / ( 2 · \(\sqrt{163}\) ) [ Heureka: \(\pi \approx \frac{ \ln{ [~ ( 640320^3 + 744 )^2 - 2 \cdot 196884 ~]} } { 2 \cdot \sqrt{163}} \) ]
giving the resulting approximation to π :
π ≈ 3.1415926535897932384626433832795028841971693992820...
that is accurate to 46 digits past the decimal point \(\dots \)".
( From http://members.bex.net/jtcullen515/math7.htm )
see: http://members.bex.net/jtcullen515/math7.htm
and see: http://mathworld.wolfram.com/PiApproximations.html
