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

Because whatever method is being used to calculate pi has a rigorous proof proving its accuracy. AFAIK, for pi specifically, it’s not so much about developing new methods to calculate new digits, but about producing more computing power to actually be able to calculate new digits using the same methods.

Theoretically, I suppose the new digits could be wrong somehow, but it’s actually totally irrelevant. You only need 15 digits or something to calculate the size of the Universe with a margin of error the width of a single atom. Or something preposterous like that. Knowing an extra trillion digits of pi is meaningless. Again, if you something about this in a headline, it’s not really about pi; it’s about the computer.

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