# Pascal's Triangle - History, Binomial Numbers Or Coefficients, Pascal, Probability Theory

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equals represent expansion

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) × (a+b) × (a+b) which equals (a^{2}+2ab+b^{2}) × (a+b) which equals (a^{3} + 3ab^{2} + 3ba^{2} + b^{3}). The coefficients are 1,3,3,1. These are listed in the third row of Pascal's triangle.

## Additional Topics

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.
The combination of numbers that form Pascal's triangle were w…

A number of unsolved problems in Pascal's days encouraged the formation of probability theory. The Gambler's Ruin and the Problem of Point are two examples of such problems. The Gambler's Ruin was a problem Pascal challenged the great mathematician, Pierre de Fermat, to solve. The problem, according to one explanation, was determining what the chances of winning were for each …

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## User Comments

almost 8 years ago

opra winfrey

suck a duck :) Gaaaaaaaay.