A Galton Board

Tuesday 10 March 2015

Some day I'm going to build my very own Galton Board (also known as a quincunx). It's a fantastic device for experimentally demonstrating a binomial distribution or binomical coefficients. Without a real one in my hands, I use 'electronic' ones that I can run on my computer for class demonstrations.

My favorite is the Galton Board on the Math is Fun website - click here or on the image to open a page showing it. I've used it often in class - and it never fails to get students' attention. It has some nice features - including: (1) easily increase or decrease the number of rows of 'pegs' that the balls bounce off of; (2) possible to change the probability of bouncing left (obviously also affecting probability of bouncing right); (3) fast forward button is a very nice feature because it allows one to quickly get a result for a very large number of trials (# of balls). The image at left shows the result for 5000 balls having bounced through the triangular arrangement of 'pegs'.

There are some decent youtube videos showing physical Galton Boards made from various materials (I will make one some day - or maybe I'll get a student to make one as part of their Exploration (IA) ...now there's personal engagement).  Below is a short (19 sec) youtube video of a Galton Board in action. The device appears to have been constructed with a fairly simple design (yeah, I could definitely make that).

And, finally, I have come across two or three digital animations of Galton Boards that have been very cleverly made with Geogebra.  The one below, called Bino Stat by its creator, is my favorite with Geogebra.

Tags: probability, binomial coefficients, quincunx, galton, binomial distribution


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