A135611

[Alexander Povolotsky]

>  could be modified/improved/transformed into the iterative formula
>   (again not the fastest one either ) for Pi calculation ?

Or is it impossible due to proven trancendentality of Pi ?
(does trancendentality rules out iterative root based formula ?)

On Wed, Mar 5, 2008 at 12:33 PM, Alexander Povolotsky
<apovolot at gmail.com> wrote:
> By the way (to be understood correctly)
>  I was not claiming that noted by me is
>  *the best Pi approximation possible*,
>  (not at all of course ! )
>  but instead I just noted that observed is relevant to A135611.
>
>  However I am wondering whether below formula
>
>  sqrt(e-x/2) + sqrt(e+x/2) - x = 0
>
>  could be modified/improved/transformed into the iterative formula
>   (again not the fastest one either ) for Pi calculation ?
>
>  Alexander R. Povolotsky
>
>
>
>  On Wed, Mar 5, 2008 at 11:40 AM, Alexander Povolotsky
>  <apovolot at gmail.com> wrote:
>  > below is even better ;-)
>  >
>  >  (11:44) gp > solve(x=3,4,sqrt(exp(1)-x/2) + sqrt(exp(1)+x/2) -x)
>  >  %11 = 3.142153292542580733700683505
>  >
>  >  2008/3/5 Alexander Povolotsky <apovolot at gmail.com>:
>  >
>  >
>  > > By the way is below known/interesting ?
>  >  >
>  >  >  sqrt(e-Pi/2) + sqrt(e+Pi/2) ~= 3.142216467362486483529141519 ~= Pi
>  >  >
>  >  >  gp > sqrt(exp(1)-Pi/2) + sqrt(exp(1)+Pi/2)
>  >  >  = 3.142216467362486483529141519
>  >  >
>  >  >  At least it gives better approximation of Pi than
>  >  >
>  >  >  sqrt(2) + sqrt(3) ~=  3.146264369941972342329135...
>  >  >
>  >  >  Alexander R. Povolotsky
>