Re: [Jprogramming] Approximating e

2014-03-11 Thread km
Look at the small denominators in Roger's first way (here slightly modified): how do your denominators compare? vv =: 2 1 , [: , 1 ,.~ 1 ,.~ 2 + 2 * i. ]v =: vv 3x 2 1 2 1 1 4 1 1 6 1 1 ,. (+%)/\ v 2 3 8r3 11r4 19r7 87r32 106r39

Re: [Jprogramming] Approximating e

2014-03-11 Thread Linda Alvord
0j1100 ": +`%/1x, 1100#1' 0.722473 Linda -Original Message- From: programming-boun...@forums.jsoftware.com [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Bo Jacoby Sent: Tuesday, March 11, 2014 4:30 AM To: programm...@jsoftware.com Subject: Re: [Jprogramming

Re: [Jprogramming] Approximating e

2014-03-11 Thread Linda Alvord
0j1100 ": +`%/1x, 1100#1' 0.722473 Linda -Original Message- From: programming-boun...@forums.jsoftware.com [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Bo Jacoby Sent: Tuesday, March 11, 2014 4:30 AM To: programm...@jsoftware.com Subject: Re: [Jprogramming] Approximating e

Re: [Jprogramming] Approximating e

2014-03-11 Thread Bo Jacoby
s 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...@for

Re: [Jprogramming] Approximating e

2014-03-10 Thread Roger Hui
3826 > > > > 734544867157818093234908902110449296423351%453973694165307953197296969697410 > 619233826 > 1.61803 > > How can I get the best possible decimal approximation (I have 32 bit > digits)? > > Linda > > > > -Original Message- > From: progr

Re: [Jprogramming] Approximating e

2014-03-10 Thread Devon McCormick
on 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

Re: [Jprogramming] Approximating e

2014-03-10 Thread Linda Alvord
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 ap

Re: [Jprogramming] Approximating e

2014-03-10 Thread Roger Hui
449296423351r453973694165307953197296969697410 > > > 619233826 > > > > > > > > > > > > > > > 734544867157818093234908902110449296423351%453973694165307953197296969697410 > > > 619233826 > > > 1.61803 > > > > > >

Re: [Jprogramming] Approximating e

2014-03-10 Thread Devon McCormick
t; > > -----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

Re: [Jprogramming] Approximating e

2014-03-10 Thread Roger Hui
ftware.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

Re: [Jprogramming] Approximating e

2014-03-10 Thread Linda Alvord
mming-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&^

Re: [Jprogramming] Approximating e

2014-03-10 Thread EelVex
* 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

Re: [Jprogramming] Approximating e

2014-03-10 Thread Roger Hui
Two of a large number of ways: n=: 20x v=: 2 , ,1,.(2+2*i.n),.1 v 2 1 2 1 1 4 1 1 6 1 1 8 1 1 10 1 1 12 1 1 14 1 1 16 1 1 18 1 1 20 1 1 22 1 1 24 1 1 26 1 1 28 1 1 30 1 1 32 1 1 34 1 1 36 1 1 38 1 1 40 1 (+%)/v 22876575111522797753057490407482r8415821667943532643424692161961 0j20 "

[Jprogramming] Approximating e

2014-03-10 Thread km
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