Pascal's Triangle and Binomial Coefficients

This GeoGebra applet dynamically constructs Pascal's Triangle using Sequence and nCr (combinations) commands. It visually demonstrates the geometric arrangement of binomial coefficients, allowing users to observe their symmetry, the recursive addition rule (each number is the sum of the two above it), and combination calculations, serving as an excellent visualization tool for discrete mathematics and algebra. Students can interact with the triangle to see how each row corresponds to the coefficients of a binomial expansion (a + b)^n. By adjusting parameters, learners explore how the numbers grow row by row, reinforcing the connection between combinatorics and algebra. The applet highlights key mathematical properties including the symmetric nature of the triangle, the additive recurrence relation that defines every interior entry, and the direct computation of combinations through the nCr function. This interactive exploration helps learners build intuition for topics ranging from probability theory to polynomial expansion, making abstract combinatorial identities tangible and accessible.