Re: Representations of Pi, etc.

[Peter Monta <pmonta@qualcomm.com>]

Tim May writes:

> > [ individual bits of pi ]
>
> I didn't see this result you mention, but it surprises me. The part about
> how it works in some bases, but not in decimal.

It's an open question as to whether there's a version that works
in base 10.  There's a nice summary at
"http://www.mathsoft.com/asolve/plouffe/plouffe.html".

> In summary, I would be surprised to find that a method for calculating the
> Nth digit of pi works for base N but not for base M (modulo some minor
> efficiency factors related to machine architecture, etc.).

It does seem strange, but radix conversion can be much more expensive
than the baseline algorithm.  I vaguely remember hearing that
the billion-digit pi computations done with AGM techniques haven't
dealt with base 10 recently.

Cheers,
Peter Monta   pmonta@qualcomm.com
Qualcomm, Inc./Globalstar