How to calculate Pi

How do I calculate Pi accurately with scratch blocks?

I am making a Pi game where the digits go on forever

There are many ways to do this. For your example, try just downloading and saving the digits, however, if a script is what you need, you can try the long script from this project.

lgrov44 wrote:

There are many ways to do this. For your example, try just downloading and saving the digits, however, if a script is what you need, you can try the long script from this project.

Thanks!

-MePix- wrote:

lgrov44 wrote:

There are many ways to do this. For your example, try just downloading and saving the digits, however, if a script is what you need, you can try the long script from this project.

Thanks!

No worries.

This topic should probably be closed since it looks resolved

-MePix- wrote:

(#3)

lgrov44 wrote:

There are many ways to do this. For your example, try just downloading and saving the digits, however, if a script is what you need, you can try the long script from this project.

Thanks!

That doesn't compute pi. It renders a fixed list of digits. Scratch isn't precise enough to hold more than 9 or 10 digits of pi.

Even though Scratch isn't precise enough, you can try this algorithm:

set [pi v] to [3]
set [i v] to [2]
forever
    change [pi v] by ((4) * (((i) * (((i) + (1)) * ((i) + (2)))) - (((i) + (2)) * (((i) + (3)) * ((i) + (4))))))
    change [i v] by (4)
end

here's a funny approach
https://scratch.mit.edu/projects/682780554/

circumference / diameter

mumu245 wrote:

-MePix- wrote:

(#3)

lgrov44 wrote:

There are many ways to do this. For your example, try just downloading and saving the digits, however, if a script is what you need, you can try the long script from this project.

Thanks!

That doesn't compute pi. It renders a fixed list of digits. Scratch isn't precise enough to hold more than 9 or 10 digits of pi.

What do you mean? You can store that many digits. You would, at most, save it as an item of a list, but you can definitely store all of those digits, specifically, you can definitely store more than the mentioned 9 or 10 digits.

There's a pretty cool infinite sum that can be used to calculate pi:

However, it's pretty slow. You have to sum like the first thousand terms of the terms to get like the first four places of pi.

There's a faster one called the Machin formula, but it requires a little more math:

You can find the arctangent block from the operators section:

([atan v] of ())

mumu245 wrote:

Even though Scratch isn't precise enough, you can try this algorithm:

set [pi v] to [3]
set [i v] to [2]
forever
    change [pi v] by ((4) * (((i) * (((i) + (1)) * ((i) + (2)))) - (((i) + (2)) * (((i) + (3)) * ((i) + (4))))))
    change [i v] by (4)
end

Can you make a project with the script? It is kinda hard to tell what it is through forums

Shrek_em wrote:

circumference / diameter

The issue with that is to know both the circumference and diameter you have to know Pi and all of its digits, and Pi is indefinitely long…

https://scratch.mit.edu/projects/47680290/ is the fastest Scratch pi calculator I know of.
If you really wanted to you could even use mine: https://scratch.mit.edu/projects/991482978/

2000 digits in ~3 seconds on @DadOfMrLog's ~112 seconds on mine, so mine is 40x slower. Mine also scales worse. I hope I can make mine better.

Basically the idea behind both it is Machin-like formulas, of the form
pi/4=a*arctan(1/x)+b*arctan(1/y)…etc…

Using infinite series to calculate each arctan term.

The hard part is figuring out how to make custom blocks to do your arithmetic with thousands of digits of precision.

This is a wikipedia article on different formulae that can be used to approximate pi. Here is a list of just the formulas (ignore the integrals part). You can implement any of these into scratch, although the more efficient ones take more computing power or are prone to floating point errors, and the less efficient ones just take more time to get there.

Floating point numbers aren't precise enough for any of these formulas. So, I recommend you store the numbers as a string and make your own digit-by-digit addition, subtraction, long multiplication and long division functions for strings. Using strings can hold way more numbers than floating point can I think.

22/7 = (edit) roughly pi

You can also check out @DadOfMrLog 's super pi calculator
https://scratch.mit.edu/projects/47680290

london11gm wrote:

22/7 = pi

That is a terrible estimation of pi compared to what OP's asking for.

Vaibhs11 wrote:

london11gm wrote:

22/7 = pi

That is a terrible estimation of pi compared to what OP's asking for.

but my teacher said to use that

did my teacher lie to me?

TheUltimateHoodie wrote:

but my teacher said to use that

did my teacher lie to me?

The OP wants an approximation of pi that goes on as long as they can. 22/7 comes out to about 3.1428. That's a 0.0403% error from the actual value of pi, so it's fine to use in calculations. However, it's 3rd decimal place is already wrong.

PhiPhenomenon wrote:

TheUltimateHoodie wrote:

but my teacher said to use that

did my teacher lie to me?

The OP wants an approximation of pi that goes on as long as they can. 22/7 comes out to about 3.1428. That's a 0.0403% error from the actual value of pi, so it's fine to use in calculations. However, it's 3rd decimal place is already wrong.

so…my teacher lied…she said 22/7 WAS pi