Central Limits

Short answer: The Galton board, also called the quincunx or bean machine, has interleaved rows of pegs above a row of bins. Each bead that falls through bounces left or right at each peg.

The number of paths to each bin follows Pascal's triangle, so the bead counts follow a binomial distribution. With many rows and many beads, that binomial distribution approaches the normal distribution, the bell curve. That's a special case of the central limit theorem known as the de Moivre–Laplace theorem. Francis Galton designed the board for a Royal Institution discourse on February 27, 1874. He described a two-stage version in an 1877 letter to George Darwin and celebrated the 'Law of Frequency of Error' in his 1889 book Natural Inheritance. He used it to illustrate his ideas about heredity and regression toward the mean ('reversion to mediocrity'), ideas that were part of his eugenics. The bell shape isn't automatic. A tilted board or biased pegs shift and skew it, and other peg shapes give other distributions: Jacobus Kapteyn built a board that produces a log-normal curve. Large Galton boards designed by Charles and Ray Eames appeared in the IBM Pavilion at the 1964–65 New York World's Fair. The footage shows a modern desktop Galton board with a printed bell curve, its beads settling into the shape.

In collections:Everyday Physics