Why can't it be both a table and "just a bunch of lines"? I know that when you are teaching a large set of students you need to address the intersection of their abilities. And I understand that once we set up ways of thinking for ourselves we tend to like following those patterns in other contexts. But we also tend to like discovery and learning new things and if we adhere *too* strictly to our old habits we miss some of the joys of discovery.
That said, these questions are not actual programming and I do not know if you are subscribed to the chat forum, so I am going to Cc you directly. I also decided to clean up the subject line, since I am not sure I like the way the mail forum software handles these things. Thanks, -- Raul On Fri, Feb 21, 2014 at 2:35 AM, Linda Alvord <[email protected]>wrote: > 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: [email protected] > [mailto:[email protected]] On Behalf Of Linda > Alvord > Sent: Friday, February 21, 2014 1:55 AM > To: [email protected] > 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: [email protected] > [mailto:[email protected]] On Behalf Of Linda > Alvord > Sent: Friday, February 21, 2014 1:01 AM > To: [email protected] > Subject: Re: [Jprogramming] What does this do? > > WOW! > > This is quite impressive! > > {|.(+%)/\100$1x > 573147844013817084101r354224848179261915075 > > 0{|.(+%)/\200$1x > > 453973694165307953197296969697410619233826r280571172992510140037611932413038 > 677189525 > > > Linda > > -----Original Message----- > From: [email protected] > [mailto:[email protected]] 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 > <[email protected]>wrote: > > > It allows you to find the 100th term in a Fibonacci series. > > > > 0}|.% 1 +. (+%)/\ 100 $ 1x > > 354224848179261915075 > > > > Linda > > > > -----Original Message----- > > From: [email protected] > > [mailto:[email protected]] 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 < > > [email protected]> 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 > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
