[seqfan] Re: Another approximation of pi

[Alonso Del Arte]

That means that 0.148341471731... and 21.1781143663... are "divisors" of pi.

Al

On Wed, Oct 3, 2012 at 5:46 AM, Peter Luschny <peter.luschny at gmail.com>wrote:

> Alonso del Arte:
> >As far as I know, our own Daniel Forgues is the first to notice that
> >sqrt(9.87654321) = 3.1426968... which is about as good an approximation of
> >pi as 22/7. For some Sequences of the Day in September, to suggest that a
> >keyword:cons sequence ought to be chosen, I put in the number 9.87654321
> >purely as a placeholder. To my pleasant surprise, Dan added his
> observation
> >to the September 30 entry.
>
> Well, the problem here is that you did not stop your placeholder at 9.87.
> This would have given Daniel the chance to notice a much better
> approximation of Pi than 22/7.
>
> Alexander R. Povolotsky:
> >Also it might be worth noting that
> >7901234568/987654321*123456789=~987654312
> >and as a result
> >(79.01234568*1.23456789)^1/4
> >gives as well
> >3.142696798...
>
> Now this gives me the chance to point to my marvelous formula
>
> \pi=
> \left({\frac{\Gamma(\gamma)}{\Gamma(2\gamma)\Gamma(1/2-\gamma)}
> +\frac{2\Gamma(1-2\gamma)}{\Gamma(1-\gamma)\Gamma(1/2-\gamma)}}\right)^2
> \left(\frac{\Gamma(\gamma)\Gamma(1/2 - \gamma/ 2)}{\Gamma(\gamma
> /2)}\right)^4
>
> which you can see displayed on http://oeis.org/wiki/User:Peter_Luschny
>
> Peter (... sorry, could not resist.)
>
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>



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Alonso del Arte
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