Pascal's triangle
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In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.
Description
In the Western world, it is named after French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in India, Persia (Iran), China, Germany, and Italy.
The rows of Pascal's triangle (sequence A007318 in OEIS) are conventionally enumerated starting with row n = 0 at the top (the 0th row).
The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows.
Having the indices of both rows and columns start at zero makes it possible to state that the binomial coefficient \tbinom{n}{k} appears in the nth row and kth column of Pascal's triangle.
See also
- Bean machine, Francis Galton's "quincunx"
- Bell triangle
- Binomial coefficient
- Binomial expansion
- Euler triangle
- Floyd's triangle
- Leibniz harmonic triangle
- Mathematics
- Multiplicities of entries in Pascal's triangle (Singmaster's conjecture)
- Pascal matrix
- Pascal's pyramid
- Pascal's simplex
- Proton NMR, one application of Pascal's triangle
- (2,1)-Pascal triangle
- Star of David theorem
- Trinomial expansion
- Trinomial triangle
External links
- Pascal's triangle @ Wikipedia
