THE WORLD'S CRAZIEST KITE... and COMBINATIONS.

Pascal's Triangle is a really neat pattern of numbers.  The numbers in Pascal's Triangle represent mathematical combinations, given by the formula:

nCr =  n! / (r!)(n-r!)

For example, if I have 10 people in a room, and I need to choose 3 people to join my team on a GCE scavenger hunt, there are 10C3 = 10! / 3! x 7! = 120 ways to choose 3 people.

Look at Pascal's Triangle:

The numbers in this triangle relate to the value in the formula above.

Now, here's a very interesting kite picture.  From more than 100 years ago!
What is that crazy thing??  It's a kite created by Alexander Graham Bell (do you know who he is?  You probably own something he invented!!) based on a geometric shape called a Sierpenski Triangle.  I think it's incredibly cool.  I like how the person is holding the kite with what looks like a fishing pole in the bottom of the picture.

And you know what, Sierpenski Triangles 'live' inside of the Pascal Triangle, too.  What if you made a Pascal triangle but colored each even number with one particular color (blue) and each odd number with another color (red)?  Look at the result!

That resembles the 100-year old kite!  What came first?  The kite, or the math? 

I think the math involved in Pascal's Triangle provides a lot of room to investigate new topics.  And it has very interesting applications.


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