Jimmy, a further note (this does not reproduce your actual diagram, but does
present a J algorithm to produce the square matrix of same pattern as your
diagram …
>./~ i.5
0 1 2 3 4
1 1 2 3 4
2 2 2 3 4
3 3 3 3 4
4 4 4 4 4
|. '.oO*&' {~ >./~ i.5
&&&&&
****&
OOO*&
ooO*&
.oO*&
Rob
> On 15 May 2018, at 9:21 am, Raul Miller <[email protected]> wrote:
>
> Are you looking for something like this for "figure 2.1"?
>
> o=: _1 1 }. ":@<@(,~ 'o ' $~ {:@$)@(,. ' o' $~ #)
> o o o o _1 1 }.":<'o'
> ─────────┐
> o o o o o│
> ───────┐ │
> o o o o│o│
> ─────┐ │ │
> o o o│o│o│
> ───┐ │ │ │
> o o│o│o│o│
> ─┐ │ │ │ │
> o│o│o│o│o│
>
> Thanks,
>
> --
> Raul
>
> On Tue, May 15, 2018 at 9:42 AM, Jimmy Gauvin <[email protected]> wrote:
>> Hi all,
>>
>> In "Makers of Mathematics" by Stuart Hollingdale there is a reference about
>> Pythagoreans who where in the habit of representing numbers by pebbles in
>> the sand.
>>
>> Figure 2.1 illustrates how square numbers can be generated by adding
>> successive odd numbers.
>>
>> ───────┐
>> o o o o│
>> ─────┐ │
>> o o o│o│
>> ───┐ │ │
>> o o│o│o│
>> ─┐ │ │ │
>> o│o│o│o│
>>
>>
>> The sum of first n odd numbers is simply n^2.
>>
>> How about some J code to generate figure 2.1 ?
>>
>>
>>
>>
>>
>> On Tue, May 15, 2018 at 5:22 AM, 'Jon Hough' via Programming <
>> [email protected]> wrote:
>>
>>> Try this:
>>>
>>> smodd1=:+/@:>:@:+:@:i.
>>>
>>> Your tacit verb was creating forks, as can be seen with dissect:
>>> load 'debug/dissect'
>>> dissect '+/1+2*i. 5'
>>>
>>>
>>> But since the sum of the first N odd numbers is N^2
>>> it is easiest to write
>>> smodd=: *:
>>>
>>>
>>> --------------------------------------------
>>> On Tue, 5/15/18, Skip Cave <[email protected]> wrote:
>>>
>>> Subject: [Jprogramming] Summing odd numbers
>>> To: "[email protected]" <[email protected]>
>>> Date: Tuesday, May 15, 2018, 5:29 PM
>>>
>>> A simple Quora question wants to know the
>>> formula to sum the first n odd
>>> numbers.
>>>
>>> I can write an explicit verb:
>>>
>>> smodd =.3 :'+/1+2*i.y'
>>>
>>> smodd 5
>>>
>>> 25
>>>
>>> I want to write a tacit verb:
>>>
>>> smodd1=:+/1+2*i.
>>>
>>> smodd1 5
>>>
>>> 6 8 10 12 14
>>>
>>> What am I doing wrong?
>>>
>>>
>>> Skip Cave
>>> Cave Consulting LLC
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>>>
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