[VA] SRC #016 - Pi Day 2024 Special

[J-F Garnier]

(03-14-2024 06:20 PM)Valentin Albillo Wrote:  what do I consider a rare \(\pi\) appearance ? Well, broadly speaking mostly any unexpected appearances of \(\pi\) having nothing to do with circles or other geometric matters (including arc lengths, areas, volumes, etc.,)

The most memorable unexpected appearance of pi for me was with the expression: sum(n=1 to Inf,1/n²) = \(\pi\)²/6.
So simple ...

Quote:let's begin with the first appearance:

Solve this equation for x in [1, 6]. Post both result and code or keystroke sequence.

      

Here is my keystroke sequence on the 71B, with my Math 2B to save a few keystrokes:

>A=INTEG(0,1,1E-10,ATAN(ATANH(IX))/IX)
>FROOT(1,6,FX*(LN(GAMMA(1/FX))-LN(GAMMA(1/2+1/FX))-LN(FX)/2)-A)
3.14159265358

J-F