What is the use of knowing more than 20 digits of pi?

I thought about it a lot last night and came up with some possible applications:

1) You can check your arbitrary precision integration software.  The integral of Sqrt(1-x^2) from x=-1 to x=1 should be pi/2.  The more digits of pi you know, the more precisely you can check your integration algorithm.

2) Similarly, you can check an arbitrary precision ODE solver.  If you get a numeric solution to y''+y=0 with y(0)=0 and y'(0)=1, then the solution at t=pi should be 0.  The more digits of pi you know, the more precisely you can check your solution.

3) You might conjecture that exp(i pi) = -1.  The more digits of pi that you know, the more precisely you can check your conjectures.


 

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