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

• To: mathgroup at smc.vnet.net
• Subject: [mg121217] Re: Pascal's triangle spacing is off. Need DigitCount?
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 4 Sep 2011 18:05:37 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201109031204.IAA05249@smc.vnet.net> <201109040812.EAA14904@smc.vnet.net>

```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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