A135611

[Alexander Povolotsky]

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