Tracy Harms wrote:
> Recently I enjoyed producing the sequence of
> triangular numbers through the following code:
>
> +/\}.i.>:
Just curious and always trying to understand.
Following the e-mail thread you started about triangular numbers
triggered me in trying to understand what's going on in the result of
your experiment.
What I noticed is the following;
,/\i.>: 4
0 0 0 0 0
0 1 0 0 0
0 1 2 0 0
0 1 2 3 0
0 1 2 3 4
What I see is a redundant first row and first column compared to
,/\>:i. 4
1 0 0 0
1 2 0 0
1 2 3 0
1 2 3 4
leading to
+/\>:i. 4
1 3 6 10
So by swapping i. and >: you may omit }. if I'm right?
Or is it just a matter of: there are several ways to compose this sentence.
A single number will be given by:
triN=: +/\>:@:i.
triN 3
6
Here are some variants
trigonNum=: -:@:(*>:)
or
trigonNum=: [:-:(*>:)
[: by following the e-mail thread ;-)
And how about all the other xxx-gon numbers?
f.i.
pentagons=: [:+/\ >:@:(3*])@:i.
hexagons=: [:+/\ >:@:(4*])@:i.
pentagons 5
1 5 12 22 35
hexagons 5
1 6 15 28 45
I translated this more or less from the Haskell functions:
pentagons = scanl1 (+) [1,4..] :: [Int]
hexagons = scanl (+) [1,5..] :: [Int]
Your experiment in some way did remind me to what
T.S. Elliot said:
"poetry can communicate before it is understood" ;-)
...hoping you don't bother this comment,
@@i<=>arie
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
