Introduction

Pascal's Triangle is a triangular presentation of binomial coefficients.  Each number is equal to the sum of the two numbers directly above it in the triangle. Although this triangle pattern has been credited to Blaise Pascal, a french scientist and mathematician, similar patterns had been discovered much earlier by several other mathematicians. For example, Yang Hui's Triangle from 13th century China (pictured below) and Al-Karaji studied something very similar to the triangle as early as the 10th century. The importance of Pascal's discovery was his proof of defining the numbers by recursion. He also discovered several useful patterns among the rows, columns, and diagonals of the triangle.