How do mathematicians know that they have the correct Nth digit of pi calculated?

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I’m not sure if I worded this correctly but I’ll try to elaborate more. I know that there are formulas that can calculate pi to the Nth digit. But my question is how can we be certain that the formulas accurately calculate the Nth digit of pi when we have nothing to compare it to since pi is an irrational number that keeps on going?

For example if I discovered a new formula than can calculate pi to 1 higher digit than what we currently know and the value I got was 4. How do I confirm that it is indeed 4 and not any other number? I have nothing else to compare it to?

I hope this makes sense

In: Mathematics

11 Answers

Anonymous 0 Comments

There’s a algorithm called the BBP algorithm which can calculate only a certain part of pi without having to do the whole thing. They can use that to just check the ending digits.

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