Pascal's triangle reveals hidden mathematical patterns

Pascal's Triangle is a simple yet powerful mathematical structure that generates binomial coefficients, which are numbers used in algebra and probability. Each number in the triangle is the sum of the two directly above it, starting with a single '1' at the top. The rows correspond to the coefficients for expanding expressions like (a + b) to a power. For example, row 3 (1 3 3 1) gives the coefficients for (a + b)³.