What is a Galton board?
A Galton board is also known as a quincunx or bean machine. The board is named after the English statistician Sir Francis Galton who invented the board. Sir Francis Galton was fascinated by how the apparent chaotic looking movement of beads bouncing off of pegs in the Galton Board results every time in the same pattern. He described in his book “Natural Inheritance” as follow: Whenever a large sample of chaotic elements are taken in hand and marshalled in the order of their magnitude, an unsuspected and most beautiful form of regularity proves to have been latent all along.
How to build a Galton board?
The board consists out of two main parts. The upper parts consists out of evenly spaced pegs. The pegs are arranged in staggered order. The lower part consist out of equally distributed slots.
Balls are dropped in at the top in the centre of the board just above a peg. Each time the ball hits a beg it has a 50/50 percent change to go left or right. The board is created so that each time the ball hits the next peg there is again a 50/50 percent change to go left or right. The ball continues falling down until the ball falls into a slot at the lower part.
Creating a board by your own can be a challenge since you have to make certain that there is every time a 50/50 percent change that the ball goes left or right. This means you have to take into account the elasticity of the balls, the radius of the pegs the distance between pegs and the offset of the ball over the funnel’s opening.
We have programmed an online Galton board below which fulfils the above design principles. Make sure to check it out!
Galton board and math
The Galton Board is math in motion! The board is created in such a way that each falling ball follows a Bernoulli trial. This means if a large enough number of balls will fall the height of the balls in the different slots will approximate a normal distribution. Also know as the gaussian distribution or bell curve.
The Galton board demonstrates the central limit theorem which states When you add identically distributed independent random variables, their sum tends toward a normal distribution.
You can create boards for other distributions by changing the shape of the pegs or biasing them towards one direction.
Where to find a Galton board?
You can simply buy an awesome Galton board.
It is a nice desktop gadget and conversation starter!
If you want you can create your own Galton board by printing it with a 3D printer
Or you can make it yourself with some easy to find materials. This build is a good STEM project to do with kids.
Online Galton board simulation
If you do not want to buy a Galton board or have time to create one by your own, you can check out the working principle of the Galton board below with our online Galton board.