Four Pines Publishing – Galton Board Desktop Probability Machine

• The Galton Board is a probability machine that brings the statistical concept of normal distribution to life.

The Galton Board is mathematics in motion and demonstrates centuries-old mathematical concepts in an innovative desktop device. It relates to the presentation of the binomial distribution by Sir Francis Galtons (1822-1911), which represents the normal distribution for a large number of balls. It also shows a superimposed Pascal Triangle (Blaise Pascal, 1623-1662), a triangle of numbers that follows the rule to add the two upper numbers to get the lower number. The number on each pin indicates the number of different paths that a ball can go through from the upper pin to the respective pin. The Fibonacci numbers (Leonardo Fibonacci, 1175-1250) can also be found as a sum of the specific diagonals in the triangle. When turned around the axis, the 3,000 balls in the table size fall through the rows of symmetrically placed pins on the Galton board. When the device is straight, every ball jumps from the pins, with the same chance to be distracted to the left or right. When the balls collect in the compartments under the board, they form an approximate bell curve. The bell curve as well as the average and standard deviation lines are printed on the board. The bell curve, also known as Gaussian distribution (Carl Friedrich Gauss, 1777-1855), is important in statistics and probability theory. It is used in the natural and social sciences to portray random variables like the balls in the Galton board. The Galton Board is reminiscent of the groundbreaking “probability machine” by Charles and Ray Eames, which was presented in 1961 at the Mathematica exhibition. An even larger EAMES probability machine was exhibited at the 1964 World’s Fair in New York in the IBM Pavilion. Both the Galton Board and the superimposed Pascal triangle contain numerous related mathematical, statistical and probability concepts.