The Galton Board is math in motion, demonstrating centuries-old mathematical concepts in a modern compact device. It incorporates Sir Francis Galton’s (1822-1911) illustration of the binomial distribution, which for a large number of beads approximates the normal distribution. It also has a superimposed Pascal’s Triangle (Blaise Pascal, 1623-1662), which is a triangle of numbers that follow the rule of adding the two numbers above to get the number below. The number at each peg represents the number of different paths a bead could travel from the top peg to that peg. The Fibonacci numbers (Leonardo Fibonacci, 1175-1250) can also be found as the sums of certain diagonals in the triangle.
When you rotate the small desktop-sized Galton Board on its axis, 3,000 beads cascade through rows of symmetrically placed pegs. When the device is level, each bead bounces off the pegs with equal probability of moving to the left or right. As the beads settle into the narrow bins at the bottom of the board, they accumulate to approximate the bell curve, or normal distribution, shown on the board. The normal distribution, also known as the Gaussian (Carl Friedrich Gauss, 1777-1855) distribution, is important in statistics and probability and is used in the natural and social sciences to represent random variables, like the beads in the Galton Board.
The Galton Board is reminiscent of Charles and Ray Eames’ groundbreaking 11-foot tall “Probability Machine”, featured at the 1961 Mathematica exhibit. An even larger Eames probability machine was showcased at IBM’s Pavilion for the 1964 World’s Fair in New York.