Re: Pascal's triangle spacing is off. Need

*To*: mathgroup at smc.vnet.net*Subject*: [mg121294] Re: Pascal's triangle spacing is off. Need*From*: Tomas Garza <tgarza10 at msn.com>*Date*: Wed, 7 Sep 2011 08:29:25 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201109031204.IAA05249@smc.vnet.net>

It seems the link is outdated... -Tomas > Date: Tue, 6 Sep 2011 03:55:56 -0400 > From: murray at math.umass.edu > Subject: Re: Pascal's triangle spacing is off. Need DigitCount? > To: mathgroup at smc.vnet.net > > 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 >

**References**:**Pascal's triangle spacing is off. Need DigitCount?***From:*"Christopher O. Young" <cy56@comcast.net>

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

**Pascal's triangle fixed. Have to use Grid[ ].**