I wondered if this really was a table or just a bunch of lines, but it really is a table.
]M=:(h"0) 1+i.7 1 0 0 0 0 0 0 1 2 0 0 0 0 0 1 2 1.5 0 0 0 0 1 2 1.5 1.66667 0 0 0 1 2 1.5 1.66667 1.6 0 0 1 2 1.5 1.66667 1.6 1.625 0 1 2 1.5 1.66667 1.6 1.625 1.61538 $M 7 7 Linda -----Original Message----- From: programming-boun...@forums.jsoftware.com [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Linda Alvord Sent: Friday, February 21, 2014 1:55 AM To: programm...@jsoftware.com Subject: Re: [Jprogramming] What does this do? The tables show what is happening quite nicely. g=: 13 :'(+%)/\ y $ 1x' (g"0) 1+i.7 1 0 0 0 0 0 0 1 2 0 0 0 0 0 1 2 3r2 0 0 0 0 1 2 3r2 5r3 0 0 0 1 2 3r2 5r3 8r5 0 0 1 2 3r2 5r3 8r5 13r8 0 1 2 3r2 5r3 8r5 13r8 21r13 h=: 13 :'(+%)/\ y $ 1' (h"0) 1+i.7 1 0 0 0 0 0 0 1 2 0 0 0 0 0 1 2 1.5 0 0 0 0 1 2 1.5 1.66667 0 0 0 1 2 1.5 1.66667 1.6 0 0 1 2 1.5 1.66667 1.6 1.625 0 1 2 1.5 1.66667 1.6 1.625 1.61538 Linda -----Original Message----- From: programming-boun...@forums.jsoftware.com [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Linda Alvord Sent: Friday, February 21, 2014 1:01 AM To: programm...@jsoftware.com Subject: Re: [Jprogramming] What does this do? WOW! This is quite impressive! {|.(+%)/\100$1x 573147844013817084101r354224848179261915075 0{|.(+%)/\200$1x 453973694165307953197296969697410619233826r280571172992510140037611932413038 677189525 Linda -----Original Message----- From: programming-boun...@forums.jsoftware.com [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Roger Hui Sent: Thursday, February 20, 2014 10:07 PM To: Programming forum Subject: Re: [Jprogramming] What does this do? If you want just the n-th term, you can do as follows, (+%)/ instead of (+%)/\ % 1 +. (+%)/ 100$1x 354224848179261915075 On Thu, Feb 20, 2014 at 6:48 PM, Linda Alvord <lindaalv...@verizon.net>wrote: > It allows you to find the 100th term in a Fibonacci series. > > 0}|.% 1 +. (+%)/\ 100 $ 1x > 354224848179261915075 > > Linda > > -----Original Message----- > From: programming-boun...@forums.jsoftware.com > [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Roger Hui > Sent: Thursday, February 20, 2014 5:14 PM > To: Programming forum > Subject: Re: [Jprogramming] What does this do? > > See also http://www.jsoftware.com/jwiki/Essays/Fibonacci%20Sequence > > It is another way to the "Why J?" (or "Why APL?") question. Because it > allows, encourages, assists, ... you to think of 10 different ways of > generating the Fibonacci numbers and other similar questions. Several > factors come into play in such thinking. See section 1 of Ken Iversons' > Turing lecture <http://www.jsoftware.com/papers/tot.htm>. Do you get the > same with another language? > > More direct answers to the questions you posed: > > - It's known both in conventional mathematics and in APL that the > continued fraction (+%)/n$1 has the golden ratio phi as the limit. > - Therefore, (+%)/\n$1 are convergents to phi. > - It's known but perhaps less so that (+%)/\n$1x provides rational > approximations to phi. > - It is known (?) that these rational approximations to phi are of the > form x%y where x and y are successive Fibonacci numbers. If you didn't > know it and you stare at the result of (+%)/\n$1x, the answer comes > pretty > quickly. > - It is known that 1+.r is the reciprocal of the denominator of the > rational number (I learned it in my I.P. Sharp days circa 1980). > > Hope this helps. I am not sure exactly what is "that way" of thinking that > you refer to. (Array thinking? Mathematical thinking? Sideways > thinking?) > > > > > On Thu, Feb 20, 2014 at 1:27 PM, Peter B. Kessler < > peter.b.kess...@oracle.com> wrote: > > > A more interesting question is: Why did you think of doing it that way? > > The really interesting question is: How can I learn to think that way? > > > > ... peter > > > > > > On 02/20/14 12:42, Roger Hui wrote: > > > >> % 1 +. (+%)/\ 100 $ 1x > >> > > ---------------------------------------------------------------------- > > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
