       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
>
>
>

```

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