What is the absolute simplest known formula /algorithm which
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What is the absolute simplest known formula /algorithm which approximates Pi? I don't care how slowly it converges, it just needs to be as simple as possible.
>>7728180
circumference/diameter
you're welcome
>>7728180
[math]
4*\sum_{n=0}^{\infty}\frac{(-1)^n}{2n+1}
[/math]
>>7728180
22/7
>>7728197
Was going to write this. The Greeks really hit a homerun.
4*atan(1)
>>7728272
They just wanted an approximation. I'd say that's pretty approximate.
>>7728180
Pi/2 + Pi/4 + ... + Pi / 2^n + ...
No problem
>>7728196
Shit latex didn't work
[math]
4 \sum_{n=0}^{\infty} \frac{(-1)^n}{2n+1}
[/math]
>>7728307
You realize that sum converges really fucking slowly, right? at n=100000, you have 4 accurate digits.
>>7728416
from op:
>I don't care how slowly it converges, it just needs to be as simple as possible.
>>7728416
>"I don't care how slowly it converges"
>>7728180
x^2+y^2=1
box of side 2
sample random points
the fraction of points inside the curve v outside is pi/4
>>7728416
>"I don't care how slowly it converges,"
[math]x_1=1[/math]
[math]x_{n+1}=x_n+sin(x_n)[/math]
Seems very fast and easy.
>>7728180
Might as well just make up your own symbols at this point to represent whatever formula for pi you want if we're picking one out based off of how "simple" it looks.
