Here's the version which gets just the final ratio.
+`%/1x, 400#1
734544867157818093234908902110449296423351r453973694165307953197296969697410
619233826
734544867157818093234908902110449296423351%453973694165307953197296969697410
619233826
1.61803
(32#'O'),' ',32#'O'
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
If I have 32-bit numbers, when does this information become fiction. Also
how can I get the best possible and correct decimal approximation from these
rational numbers?
Linda
----Original Message-----
From: programming-boun...@forums.jsoftware.com
[mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Linda Alvord
Sent: Monday, March 10, 2014 9:32 PM
To: programm...@jsoftware.com
Subject: Re: [Jprogramming] Approximating e
Thanks for your hints. I always wanted to get rational approximations for
the Golden Section.
{.|.+`%/\1x, 300#1
26099748102093884802012313146549r16130531424904581415797907386349
32#'O'
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
{.|.+`%/\1x, 400#1
734544867157818093234908902110449296423351r453973694165307953197296969697410
619233826
734544867157818093234908902110449296423351%453973694165307953197296969697410
619233826
1.61803
How can I get the best possible decimal approximation (I have 32 bit
digits)?
Linda
-----Original Message-----
From: programming-boun...@forums.jsoftware.com
[mailto:programming-boun...@forums.jsoftware.com] On Behalf Of EelVex
Sent: Monday, March 10, 2014 7:12 PM
To: Programming forum
Subject: Re: [Jprogramming] Approximating e
* Summing infinite series
+/%!i.100x
+/^ t. i.100x NB. Taylor coefficients
%+/((_1&^)%!)i.100x
etc
* Taking an asymptotic
(-^~1-%) 100x
((^~%~^~@>:) - (^~%^~@<:))100x
etc
* Continued fractions
+`%/2 1,2#>:i.100x
+`%/2, 2#2+i.100x
(+%)/2 1, ,(1 1,~])"0 +:>:i.100x NB. canonical form
On Mon, Mar 10, 2014 at 6:38 PM, km <k...@math.uh.edu> wrote:
> The rational 2721r1001 approximates e to six, almost seven decimal
> places:
>
> 0j7 ": (^ 1) ,: 2721r1001
> 2.7182818
> 2.7182817
>
> I got 2721r1001 from a continued fraction. How would you look for
> rational approximations to e ?
>
> --Kip Murray
>
> Sent from my iPad
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