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Pascal's pyramid : ウィキペディア英語版 | Pascal's pyramid
In mathematics, Pascal's pyramid is a three-dimensional arrangement of the trinomial numbers, which are the coefficients of the trinomial expansion and the trinomial distribution. Pascal's Pyramid is the three-dimensional analog of the two-dimensional Pascal's triangle, which contains the binomial numbers and relates to the binomial expansion and the binomial distribution. The binomial and trinomial numbers, coefficients, expansions, and distributions are subsets of the multinomial constructs with the same names. Pascal's Pyramid is more precisely called "Pascal's tetrahedron", since it has four triangular surfaces. (The pyramids of ancient Egypt had five surfaces: a square base and four triangular sides.) ==Structure of the tetrahedron== Because the tetrahedron is a three-dimensional object it is difficult to display it on a piece of paper or a computer screen. Assume the tetrahedron is divided into a number of levels, or floors, or slices, or layers. The top layer (the apex) is labelled "Layer 0". Other layers can be thought of as overhead views of the Tetrahedron with the previous layers removed. The first six layers are as follows:
The layers of the Tetrahedron have been deliberately displayed with the point down so that the Tetrahedron is not confused with Pascal's triangle.
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