Practical Uses for Pascal's Triangle

Date: 2/27/96 at 20:14:58
From: Andrew Cotton
Subject: Help with Pascal's Triangle

Hi,

I teach 7th grade math.  Some of my students are trying to find 
"practical uses" for Pascal's triangle.  All I have been able to find 
has been related to probability.  I remember hearing in the past 
of other uses, but I cannot remember them nor can I find any 
other info.  Can you help?

We will appreciate any help you can give us.

Date: 3/1/96 at 14:44:2
From: Doctor Ethan
Subject: Re: Help with Pascal's Triangle

Hey,

Great Question,

  Here are a few areas they can explore.

1. The triangular numbers
                              *
                      *      **
               *     **     ***
         *    **    ***    ****
    *   **   ***   ****   *****
*  **  ***  ****  *****  ******

1  3     6    10    15     21

First see if they can discover through examination what the 
pattern to the triangular numbers is (building triangles with 
pennies then, counting the pennies is a good way). 

Then see if they can draw a line through Pascal's triangle that 
will intersect the triangular numbers in sequence.

For a reference on this and much more check out 
_More Joy of Mathematics_,  p. 51.

2. This is in my opinion the clearest example of its usefulness:

I assume that if you talked about probabilities then you talked 
about binomial expansions.  A clear way to see this is by:

(x+y)^n

The coefficients for the terms will be the n+1 row of Pascal's 
triangle.

(x+y)^3  = x^3 + 3x^2 y  + 3xy^2 + y^3
           1       3       3       1

the 4th row.

In general I recommend the book I mentioned above.  It is awesome.

-Doctor Ethan,  The Math Forum