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

• To: mathgroup at smc.vnet.net
• Subject: [mg121224] Re: Pascal's triangle spacing is off. Need DigitCount?
• From: Helen Read <readhpr at gmail.com>
• Date: Mon, 5 Sep 2011 07:05:36 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201109031204.IAA05249@smc.vnet.net> <201109040812.EAA14904@smc.vnet.net> <j40srf$l1e$1@smc.vnet.net>

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
>>>    ]
>>> ]
>>>
>>>
>>>
>>
>>
>

• Follow-Ups:
  • Re: Pascal's triangle spacing is off. Need DigitCount?
    • From: Murray Eisenberg <murray@math.umass.edu>

• References:
  • Pascal's triangle spacing is off. Need DigitCount?
    • From: "Christopher O. Young" <cy56@comcast.net>
  • Re: Pascal's triangle spacing is off. Need DigitCount?
    • From: Heike Gramberg <heike.gramberg@gmail.com>