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Pascal's Triangle

Pascal's triangle is a well known set of numbers aligned in the shape of a pyramid. The numbers represent the binomial coefficients. Binomial coefficients represent the number of subsets of a given size. The numbers in Pascal's triangle are also the coefficients of the expansion of (a+b)n, (a+b) raised to the n-th power. So for n equals to three, the expansion is (a+b) x (a+b) x (a+b) which equals (a2+2ab+b2) x (a+b) which equals (a3 + 3ab2 + 3ba2 + b3). The coefficients are 1,3,3,1. These are listed in the third row of Pascal's triangle.

Pascal's triangle was also known as the Figurate Triangle, the Combinatorial Triangle, and the Binomial Triangle. The triangle was first given the name, "Pascal's triangle," by a mathematician named Montmort in 1708. Montmort wrote the numbers in the form below known as the combinatorial triangle.

1 1 1 1 1 1 2 3 4 1 3 6 1 4 1

The combination...

This section contains 1,096 words(approx. 4 pages at 300 words per page) |