Re: Base 8 counting in Gevey

Dennis Paul Himes wrote:
>
>Andreas Johansson <and_yo@...> wrote:
> >
> > While the concept of base pi have always attracted me, it should be
> > possible to find a base in which pi is 3.11111111 for the n first
>digits.
>
>     Sure, base 10.  n is 1.  This is assuming you mean, "there exists a
>base
>and an n such that pi is ...".  If you mean, "for every n there exists a
>base such that pi is ..." then you're wrong.  0.11111... in base b is the
>expansion of 1/(b-1).  Pi minus 3 is approximately 1/7, so base eight is
>going to give you the closest expansion to 3.11111....
I don't really see how I'm wrong. Are you assuming we stick to integer
bases?

Given that pi minus 3 is EXACTLY pi-3, it seems to me that pi is EXACTLY
3.11111... in base (pi-3)^(-1)+1. If I'm wrong, I'd like to know why.

                                                Andreas

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