/sci/ - Science & Math » Thread #14000954

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Anonymous Thu 23 Dec 17:06:21 2021 No.14000954 View Reply Original Report

Quoted By: >>14000975 >>14002222

what's the least-complex sieve to calculate digits of pi?
pi is the most popsci topic and yet i have literally never seen any piece of media describe calculating digits instead of just memorizing them

Anonymous

Anonymous Thu 23 Dec 2021 17:09:13 No.14000968 Report

Quoted By: >>14000977

https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80

Anonymous

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Anonymous Thu 23 Dec 2021 17:10:18 No.14000975 Report

Quoted By:

>>14000954
bbp spigot algo

Anonymous

Anonymous Thu 23 Dec 2021 17:11:18 No.14000977 Report

Quoted By: >>14001001 >>14001009

>>14000968
jesus fuck i feel like a retard if that's the easiest one

Anonymous

Anonymous Thu 23 Dec 2021 17:19:46 No.14001001 Report

Quoted By:

>>14000977
Convergence speed is shit

You can literally just google for custom handmade series with awful looking fractions for faster convergence

Anonymous

Anonymous Thu 23 Dec 2021 17:22:01 No.14001009 Report

Quoted By:

>>14000977
There are a bunch of ways to do it. It's probably easiest to write a quick program for Leibniz formula because you can just use a for loop up to some term n and return an approximation of pi up to that accuracy. Quick python example:

>def Pi(n):
>>p = 0
>> for i in range(n+1):
>>>p += 4*(-1)**i/(2i+1)
>>return p

Just look at the wiki for pi, it's filled with different methods of approximating pi.

Anonymous

Anonymous Thu 23 Dec 2021 22:39:05 No.14002222 Report

Quoted By: >>14002233 >>14002261

>>14000954
If you're going to be doing it by hand try 16 atan(1/5) - 4 atan(1/239) with the Taylor series for atan. There was a guy who calculated it to hundreds of digits that way long before electronic computers existed.

Anonymous

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Anonymous Thu 23 Dec 2021 22:41:59 No.14002233 Report

Quoted By:

>>14002222
https://en.wikipedia.org/wiki/William_Shanks

Anonymous

Anonymous Thu 23 Dec 2021 22:48:39 No.14002261 Report

Quoted By:

>>14002222
By hand it takes on the order of an hour to get 10 digits. Tips from my experience trying it:
>Do repeated long division by 239. Don't try to work out the exponent first and then divide, it's just extra work with more opportunity for error.
>Write out a table of 239 multiplied by each digit to make long division easier.
>The final addition step is more prone to error than you might think, double check it.
>It's less confusing and thus less error prone to add the positive terms and negative terms separately then subtract them.

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