achille
Posts:
575
Registered:
2/10/09
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Re: The unit interval covered by a set of intervals with measure < 1
leaves no determinable gaps.
Posted:
Jun 14, 2011 4:44 AM
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On Jun 14, 4:38 pm, Tim Little <t...@little-possums.net> wrote:
> On 2011-06-14, achille <achille_...@yahoo.com.hk> wrote:
>
> > Isn't we have an upper bound for the irrationality measure
> > of Pi too (current record ~7.6063 (Salikhov 2008)). ie. a
> > bound of the form | Pi - p/q | > const. 1/q^(7.6063).
>
> Ah yes, that would suffice. I was not aware that an upper bound had
> been proved.
>
> > If an multiple for e is easy to find (whose irrationality measure is
> > known to be 2), why is it much more difficult to find one for
> > Pi?????
>
> You may not have seen e's continued fraction sequence. If you had, it
> would be fairly obvious why various properties are much more easily
> proved for it than for pi.
>
> --
> Tim
Oh, I see it now, the continued fraction of e is indeed very simple.
Thanks for the info.
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