Re: Pascal's Triangle

*To*: mathgroup at smc.vnet.net*Subject*: [mg37370] Re: [mg37349] Pascal's Triangle*From*: Tomas Garza <tgarza01 at prodigy.net.mx>*Date*: Fri, 25 Oct 2002 02:48:08 -0400 (EDT)*References*: <200210240656.CAA05165@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

It looks as if you might profit enormously by taking a look at Stephen Wolfram's recent book, "A New Kind of Science", where this and similar problems are painstakingly discussed. In particular, in p. 611 of the book you have a plot of the Pascal triangle. The code used by Wolfram illustrates the way Mathematica programming is used by the great gurus. Tomas Garza Mexico City ----- Original Message ----- From: "Al Mannon" <almannon at attbi.com> To: mathgroup at smc.vnet.net Subject: [mg37370] [mg37349] Pascal's Triangle > I want to write a program that will create an array of equilateral triangles > such that in the first row there is 1 triangle, in the second row there is 3 > triangles, in the third row there will be 5 triangles...in the nth row there > will be 2n - 1 triangles. Putting all of these triangles together and > calling the first row, row 0, we would have a large triangle with n + 1 rows > along the side of the large triangle and 2n - 1 columns along the base of > the triangle. > > This would be phase one of the project. > > Phase 2: Fill in the binomial coefficients into the triangle. > Phase 3: Color all odd numbered triangles blue. > Phase 4: Color all even numbered triangles red. > Phase 5: Any triangle that shares an edge with a red triangle, color red. > > The result is Zierpinski's Triangle! I have done this by hand for a triangle > with 16 rows. Needless to say the work was tedious. The result, however, is > quite satisfying and remarkable. I would like to be able to use this as a > tool to teach some of the other derivations that are possible from Pascal's > triangle other than binomial coefficients and combinations. Therefore it > would be beneficial to be able to reproduce this work at will. > > Since my Mathematica programming skills are practically nil, any help would > be appreciated. > > I can be reached directly by electronic mail by deleting "the" in the > following: > > althemannon at attbi.com > > >

**References**:**Pascal's Triangle***From:*"Al Mannon" <almannon@attbi.com>