Pascal's Triangle

Pascal's Triangle was made famous by a French mathematician named Blaise Pascal. He did not necessarily invent this triangle of numbers, but he did contribute a lot when it comes to its uses. In fact, Indian, Iranian, and Chinese mathematicians discovered this well before Pascal was putting it to use. Ok, before going further let's explain and show how to create Pascal's Triangle.
Starting at the top of the triangle start with 1, followed by the next row which will have another 1 and 1. Take notice that 1's line the perimeter of this triangle. On the third row down the 2 is created by adding the 1's together from the second row. Each number is created by adding the numbers above it together. The triangle pictured is only 5 rows, but it can be built infinitely large.
What makes this triangle so interesting to those in the mathematics world are the patterns that it generates. Well we look at a few of those examples now.