Π day

[Gerson W. Barbosa]

(03-14-2022 03:35 AM)robve Wrote:  Happy \( \pi\ {\cal D}\alpha\gamma ! \)

Sharp's series

Sharp's series

\( \frac{\pi}{6} = \frac{1}{\sqrt3}\left(1-\frac{1}{3^1\cdot3}+\frac{1}{3^2\cdot5}-\frac{1}{3^3\cdot7}+\cdots\right) \)

on a Sharp:

10 S=0,P=1
20 FOR N=0 TO 16
30 S=S+P/(3^N*(2*N+1)),P=-P
40 NEXT N
50 PRINT "?=";6*S/√3
RUN
?=3.141592654

That’s a nice one. Interestingly, it was first derived in India by Madhava some three centuries earlier:

https://en.wikipedia.org/wiki/Madhava_of..._of_π_(pi)


Happy \(\pi\) Day you all!