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
The formulas are derived from known mathematical relationships.
A example is drawn regular polygon with n sides inside and outside a circle with a diameter of 1. You know by definition the circumference is pi.
You know the circumference of the circle is larger then the one indide and smaller then the one on the outside. Add enough sides so the polygon are equal in length o the third decimal and you know pi also have the same decimal.
That is not in any way a efficient way to calculate pi but it is something that is easy to visualise and understand without a lot of mathematical knowledge
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