Do We Need the Digits of $\pi$?
I was reading today that someone found $\pi$ to the ten trillionth digit. Whenever I read that $\pi$ has been calculated to more digits, I ask myself whether this is useful. I know that there are conjectures out there about distributions of numbers in $\pi$ and such. So, I supposed knowing more digits helps us test conjectures. But, are there more reasons that we would want to know the digits? Anything really cool I'm ignoring or forgetting?
Solution 1:
Not for any real-life calculations according to wikipedia
Practically, one needs only 39 digits of π to make a circle the size of the observable universe accurate to the size of a hydrogen atom.
It is however useful to test supercomputers for accuracy and as a memory intensive number-crunching benchmark.
Today the high precision calculation of $\pi$ finds practical use in testing the "global integrity" of a supercomputer. "A large scale calculation of pi is entirely unforgiving; it soaks into all parts of the machine and a single bit awry leaves detectable consequences.
Solution 2:
A less mathematical reason for calculating more and more decimal places is because we know they are there. Man is inherently curious and always wants to see what's over the next hill, round the next bend etc.