The best rational approximation to the golden ratio is the ratio of two consecutive Fibonacci numbers.
On Mon, Mar 10, 2014 at 6:31 PM, Linda Alvord <[email protected]>wrote: > 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: [email protected] > [mailto:[email protected]] 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 <[email protected]> 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 > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
