Pascal's pyramid
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In mathematics, Pascal's pyramid is a three dimensional generalization of Pascal's triangle. Just as Pascal's triangle gives coefficients for the terms of a binomial expansion, so Pascal's pyramid gives coefficients for a trinomial expansion.
Pascal's pyramid is also called Pascal's tetrahedron. A generalization to arbitrary dimension is sometimes called a Pascal's simplex.
The pyramid is constructed layer by layer, starting with the apex and working downward. The first few layers are as follows.
1 1 1 1 1
1 1 2 2 3 3 4 4
1 2 1 3 6 3 6 12 6
1 3 3 1 4 12 12 4
1 4 6 4 1
External links
- Beyond Flatland: Geometry for the 21st Century. PART I: Pascal's Tetrahedron (http://www.4dsolutions.net/ocn/urner.html)
- Pascal's Simplices (http://people.ucsc.edu/~erowland/pascal.html) (discusses Pascal's triangle, Pascal's pyramid, and more)de:Pascalsche Pyramide