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Re: Pascal's triangle spacing is off. Need DigitCount?


I don't see what's more pretty with the vertex-in-center version, just 
that it's more familiar.

For actual manipulation of Pascal's triangle by computer or in formulas, 
the flush-left rows seems better suited. See, for example, the page:

   http://www.jsoftware.com/jwiki/Essays/Pascal's%20Triangle

That is based upon the insight of Ken Iverson many years ago.

On 9/5/11 7:05 AM, Helen Read wrote:
> There's certainly a case for that, but it's pretty with the symmetry
> about a vertical line, with the 1's going down the sides, and the
> interior entries being the sum of the two neighbors in the row above.
>
> HPR
>
> On 9/4/2011 6:07 PM, Murray Eisenberg wrote:
>> Why should Pascal's triangle be arranged so that it has symmetry around
>> a vertical line, and with its vertex at the center horizontally?
>>
>> Why not pad just to the right, so that each row starts flush left?
>>
>> The latter seems in a way more "natural" (if I may dare to use that
>> term), since each element of a row is then in its correct position
>> (indexing from 0 instead of 1, of course).
>>
>> On 9/4/11 4:12 AM, Heike Gramberg wrote:
>>> You could use Grid  in combination with ItemSize instead of Row to give
>>> all the entries the same width, e.g.
>>>
>>> pascalTrngl2[n_] :=
>>>     Module[{max, sp}, max = Max[Table[Binomial[n, j], {j, 0, n}]];
>>>      sp = Round[N[Log[10, max], 5]];
>>>      Column[Table[Grid[{Table[Binomial[i, j], {j, 0, i}]},
>>>         ItemSize ->    sp], {i, 0, n}], Center]]
>>>
>>> pascalTrngl2[10]
>>>
>>> Heike
>>>
>>> On 3 Sep 2011, at 14:04, Christopher O. Young wrote:
>>>
>>>> I'm trying to get the same spacing between the _center points_ of each of
>>>> the numbers in the Pascal triangle, so that each entry in a row is centered
>>>> properly underneath the corresponding two entries in the row above. Instead,
>>>> all the spacing options for Row[ ] seem to just apply to the spacings
>>>> between numbers.
>>>>
>>>> It looks like I would have to calculate the length (i.e., number of digits)
>>>> of each entry as I go through the table. Is DigitCount the best function to
>>>> use here? I.e., won't slow things down too much? Or is there a faster way?
>>>>
>>>> Thanks for any help.
>>>>
>>>> Chris Young
>>>> cy56 at comcast.net
>>>>
>>>> pascalTrngl2[n_] :=
>>>> Module[
>>>>     {max, sp},
>>>>
>>>>     max = Max[Table[Binomial[n, j], {j, 0, n}]];
>>>>     sp = Round[N[Log[10, max], 5]];
>>>>
>>>>     Column[
>>>>      Table[
>>>>       Row[
>>>>        Table[Binomial[i, j], {j, 0, i}],
>>>>        Invisible[sp]
>>>>        ],
>>>>       {i, 0, n}
>>>>       ],
>>>>      Center
>>>>     ]
>>>> ]
>>>>
>>>>
>>>>
>>>
>>>
>>
>
>
>

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305




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