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Pi Calculator (without using imports, Circles, Pi, or non-terminating numbers!)
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Pi Calculator

So, I wanted to make a Pi calculator without imports. I figured I could just use circles, but I would have to use Pi to render the circles in Python without imports (to my knowledge)... So, in search of calculating Pi, I came upon the Leibniz formula. My script started out about 100 lines long but I got it down real small; however, though, this formula was very inefficient, and I ended up with the Nilakantha formula. It's really fast and generates a lot of digits. I'm kinda proud of it, so I hope you guys like it too. If anyone knows how I could make it faster or more accurate, I'm open to any suggestions!

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glad you asked! let me break it down:

The range

The range is set to count up to n plus one (the number that the user inputs) from two, by four...

For example, if the user were to put in 10, the range would count up like so:

2, 6, 10

The formula

The formula used in this one is the Nilakantha sequence, or in this, 4/(i*(i+1)*(i+2)) - 4/((i+2)*(i+3)*(i+4)).

Here's what the formula looks like:



Sadly, none of the formulas I've tried exceed 14 digits, and not just because a decimal in a string is that long by default.

Even if I were to extend the digits with a module or using this:

'%.100f' % n

...the digits aren't accurate after 14, no matter how many iterations you push into it [, sadly].

I don't know what the problem is with it but I'm aiming to fix it :/