[VA] SRC #016 - Pi Day 2024 Special

[J-F Garnier]

(03-14-2024 06:20 PM)Valentin Albillo Wrote:  Solve this equation for x, where \(\phi\) is the Golden Ratio = (1+√5)/2. Post both result and code or keystroke sequence:

     

This is my take with 10^5 terms:
>P=1 @ FOR N=1 TO 1E5 @ P=P*(1-1/N/N/100) @ NEXT N @ DISP 5*2/(1+SQR(5))/P
3.14159235271

Using more terms takes too long, even in Emu71, and doesn't improve the result so much.

While experimenting a bit, I found a few interesting similar expressions:

>P=1 @ FOR N=1 TO 1E5 @ P=P*(1-1/N/N/4) @ NEXT N @ DISP 2/P
3.14158479717

>P=1 @ FOR N=1 TO 1E5 @ P=P*(1-1/N/N/36) @ NEXT N @ DISP 3/P
3.14159181273

J-F