>:@*/%>:i.20 2.71828 This speeds up the series.
Den 7:11 tirsdag den 11. marts 2014 skrev Roger Hui <rogerhui.can...@gmail.com>: > 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? > >32-bits give you about 10 decimal digits. (0 j. n) ": x displays x to n >decimal places. Where the following two outputs agree tells you how many >digits for +`%/401#1x can be trusted. > > _100]\(98$' '),0j200 ": +`%/1x, 400#1 > > 1. >6180339887498948482045868343656381177203091798057628621354486227052604628189024497050372347293136948 >1774505251856655015609156645743553332885289608910521042249892203715062899055972967323443765486133617 > > _100]\(98$' '),0j200 ": +`%/1x, 500#1 > > 1. >6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374 >8475134846000035278501181299327946966700279337151010482725318315024081083474561817534485930797695298 > > > > > >On Mon, Mar 10, 2014 at 7:07 PM, Linda Alvord <lindaalv...@verizon.net>wrote: > >> 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 >> > ---------------------------------------------------------------------- >> > 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 >> >---------------------------------------------------------------------- >For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
