Associated Topics || Dr. Math Home || Search Dr. Math

### 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?

```

```
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

```
Associated Topics: