Pascal's Triangle

Pascal's triangle is an infinite triangular array of the binomial coefficients, in which each entry is the sum of the two entries directly above it and the outermost entries of every row equal 1. Long before Blaise Pascal's own 17th-century treatise gave the array its name in the West, equivalent constructions were described by the Indian mathematician Piṅgala around the 3rd to 2nd century BC, by Persian mathematicians including al-Karaji, and by the Chinese mathematician Yang Hui in the 13th century, who is still credited with it in China today. Each entry C(n, k) gives the number of ways to choose k items from a set of n, so the triangle's rows recover the coefficients of a binomial expansion and appear throughout combinatorics and probability.