Pascal's Triangle

Recently in my math class we were taught about a thing called Pascal's triangle. I am not sure if this is my synesthesia kicking in (post on that coming soon!) or if its something else but I find Pascal's triangle to be one of the most amazing things, like ever...

I am writing this post to raise awareness to Pascal's triangle since many people I have talked to have no idea what it is. According to Wikipedia, "Pascal's triangle is a triangular array of the binomial coefficients in a triangle." This here is Pascal's Triangle (and it goes on forever.)

See a pattern?

One of the cool things about our friend's triangle is that it is simple to write. All you do is start with 1 at the very top and then go down and put 2 1s. The rows are created by adding the two numbers above it. Say you want to create row 3 (#1 is the zero row so we are talking about row 1 3 3 1) then you just look at row two and see, "Oh, 1+0=1 (the first digit), 1+2=3 (the second digit)..."

Don't think its neat yet?

Well! Prepare for blastoff Elwood, because I am about to make you think this is so neat that...I dunno... but its neat.

So say, your teacher gives you the problem, (a + b)^4

You would find the 4th row in the triangle, (1 4 6 4 1)

Then you would write

1 4 6 4 1

Then put in 1a 4ab 6ab 4ab 1b

and add the exponents starting at 4 for a on the left and 4 for b on the right

and you would get:

a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4

I just think this is really neat and my apologies for bursting into geek mode...