Nth digit of PI
Kirby Urner
urner at alumni.princeton.edu
Mon Jun 5 15:34:50 EDT 2000
Here's another "math through programming" challenge:
Recent number theory breakthrough: you can get the
nth digit of PI without doing all the work needed
to compute all the digits up to the nth digit (same
with some other numbers -- not sure if we know all
the relevant criteria as to which).
The original algorithm worked for PI expressed as
a hexadecimal number, but I found a web page purporting
to give the algorithm for a base 10 PI, but I couldn't
figure out how to make it work in Python.[1][2]
Anyone?
Another question: does the algorithm for getting
the nth digit of PI actually do less work (in terms
of flipflops) than would an algorithm that gets
all digits up to n inclusive? I assume so, as I
read about someone getting a trillionth digit or
something -- but I don't think we've got PI to that
many places.
Kirby
[1] http://www.mathsoft.com/asolve/plouffe/plouffe.html
[2] http://www.lacim.uqam.ca/plouffe/Simon/articlepi.html
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