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

*To*: mathgroup at smc.vnet.net*Subject*: [mg121245] Re: Pascal's triangle spacing is off. Need DigitCount?*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Tue, 6 Sep 2011 03:55:56 -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> <201109051105.HAA28340@smc.vnet.net>*Reply-to*: murray at math.umass.edu

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>

**Re: Pascal's triangle spacing is off. Need DigitCount?***From:*Heike Gramberg <heike.gramberg@gmail.com>

**Re: Pascal's triangle spacing is off. Need DigitCount?***From:*Helen Read <readhpr@gmail.com>

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

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