Pascal's Triangle

*To*: mathgroup at smc.vnet.net*Subject*: [mg37349] Pascal's Triangle*From*: "Al Mannon" <almannon at attbi.com>*Date*: Thu, 24 Oct 2002 02:56:20 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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

**Follow-Ups**:**Re: Pascal's Triangle***From:*Tomas Garza <tgarza01@prodigy.net.mx>