PureBasic Forums - English

Hi all

I like the math so I do my own of discovering as alternative from the PI (may be at wrong so possible)

All of you know PI is equal as approximate at 3.14, right ?

Very simple, the true limited transcendent decimal is 3.14159265358979323846 on the C programming the macro that defined, ok ?

If you read from the Wikipedia of PI : https://en.wikipedia.org/wiki/Pi and you will understand more thing ...

If you see the circle is exactly more than at 3.14... A question arise is if the circle stop at more than 3.14... so it move at infinity very small in zoom, right ? The line move very small at size too, thus for me maybe is not correct maybe ...

My approach is a bit different maybe more correct in theory, just a thought

If we are agreed the PI stop at exactly 3.14 but with infinity, so my theory is simple too :

We can calculate at first the number :
Which give in PB : But in reality is more correct at the same as 3.14 with a calculator.

Ok ?

So I am adding some very simple number is to make as multPI = 9.42 (Even is not correct in PB) by this multPI =9.421 then it gives at : with a calculator and not by PB is error thought i don't know as here : Ok the circle stops at the line to 3.14033333333 as it does not move in very small at size but in infinity ...

Voilà

What do you think of my theory? ^^

That's where my avatar came from

threedslider wrote: Sun Jun 01, 2025 9:48 pmWhat do you think of my theory? ^^

I don't understand your theory. Did you use Google Translate for that? It's not very comprehensible for me as a German where English is only the fourth language I learned.
In case you wanna understand floating point inaccuracies, just read this chapter: https://en.wikipedia.org/wiki/Floating- ... y_problems

Pi is an interesting number, recently I watched this Mathtologer video about the Powell's Pi paradox https://youtu.be/ypxKzWi-Bwg?si=JpGYCbrGyO2vnzGh
I think that most people know about this series for Pi, Pi/4 = 1 - 1/3 + 1/5 - 1/7 ..., if you multiply the series by 4 you get Pi = 4 - 4/3 + 4/5 - 4/7 ...
if you add 1000000 terms of the last series you get an interesting result
for comparison here's the true value of PI to 60 digits and below that the sum of 1000000 terms
3.14159265358979323846264338327950288419716939937510582097494...
3.14159165358979323871264338327919038419717035250010581556479...

using PARI/GP https://pari.math.u-bordeaux.fr/
\p60
p=0;s=4.0;for(i=1,1000000,p=p+s/(2*i-1);s=-s)
Pi
p

@Piero : Nice to your avatar !

@NicTheQuick : Sorry my English is not my first language but yeah thanks for link about of accuracy with floating

@jack : Thanks a lot for sharing and link, it is nice too

I am not a mathematician but I think Mr. Mathologer made a mistake in his presentation of the last correction term
1/(N+1/(4*N+4/(N+9/N))) it should be 1/(N+1/(4*N+4/(N+9/4/N)))
with N=10 we have
Pi = 4 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - 4/15 + 4/17 - 4/19 = 44257352/14549535 = 3.041839618929402
correction = 16520/165609 = 0.09975303274580488, Pi = 3.14159265167520688 that's 9 correct digits

threedslider wrote: Sun Jun 01, 2025 9:48 pmtranscendent

https://www.youtube.com/watch?v=_cr46G2K5Fo

@Piero : Thanks for YT !

BTW,
π in "quantum physics":
https://www.youtube.com/watch?v=t1ZnptSEPI8