What Is Pascal's Triangle?


Quick Answer

Pascal's triangle is a geometric arrangement of binomial coefficients in a triangle. Its construction is related to the binomial coefficients by Pascal's rule. This intricate number pattern was named after Blaise Pascal, a French mathematician, although it was known about by the Chinese and studied for 500 years before Pascal.

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What Is Pascal's Triangle?
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Full Answer

Even though other mathematicians studied these numbers before him, it was Pascal who developed the uses for the triangle and arranged the numbers in this fashion. Two main functions of Pascal's triangle are to find coefficients in binomial expansions and to calculate combinations. There are also many patterns present. The patterns arise in diagonals, in odds and evens (that resemble the Sierpinski triangle), horizontal sums, exponents of 11, squares and the Fibonacci Sequence.

Pascal's triangle is also a symmetrical mirror image. Sir Francis Galton created a machine based off of Pascal's triangle called the quincunx. It is made up of many pegs in the shape of Pascal's triangle, and balls are dropped down onto the first peg at the top. The balls do not drop randomly but rather in a pattern. This pattern is known as a normal distribution. Pascal is also credited for the Pascaline, the wrist watch, the roulette table and more.

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