The Galton board, invented by Francis Galton (1822-1911), is a nice device visualizing the binomial distribution. Small beads start their travel at the apex of the lattice and trickle down the lattice by deciding, at each branch point, with equal probability whether to take the left or right path. Thus, to find the final distribution of balls after K branch points along the horizontal line, one considers the polynomial (x/2+ y/2)^K , where x symbolizes a left turn and y a right turn, and 1/2 is the equal probability to take either a left or right turn. The probability to find a bead at position m is then given by the coefficient in front of x^(K-m)/2 y^(K+m)/2 in the above polynomial, corresponding to (K-m)/2 steps to the left and (K+m)/2 steps to the right, summing to a total of K steps ending at position m. The result is a binomial distribution, K!/[(K-m)/2]!/[(K+m)/2]! (1/2)^K.  For large K, this approaches a Gaussian distribution.