Π day

[robve]

Happy \( \pi\ {\cal D}\alpha\gamma ! \)

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 "Π=";6*S/√3
RUN
Π=3.141592654

and on a very nice non-Sharp:

10 DESTROY ALL @ S=0 @ P=1
20 FOR N=0 TO 20
30 S=S+P/(3^N*(2*N+1)) @ P=-P
40 NEXT N
50 DISP "PI=";6*S/SQR(3)
RUN
PI=3.14159265359

What's your favorite pi series?

- Rob