A STEM Project: 3D Printing a Galton Board To Demonstrate The Concept of a Binomial Distribution

3D Printing a Galton Board To Demonstrate The Concept of a Binomial Distribution

Here is a video of the Galton Board in action.

There are a lot of outside forces that prevent the candy balls from falling accurately - such as friction, the inconsistent size of the candy balls, the acetate is flexible and causes the flat surface to buckle. Even with these inconsistencies the concept of the binomial distribution is still shown. 

The mathematical concept of a binomial distribution can be visually displayed using a Galton Board. A Galton Board was invented by Sir Francis Galton (1822-1911).  It is a rectangular board with evenly spaced pegs.  A small opening at the top of the pegs funnels the small balls.  The small balls bounce from peg to peg.  The ball can either fall to the left or to the right once it hits a particular peg. Each movement has the probability of fifty percent. The small balls continue bouncing from one peg to the other and then are funneled into rectangular slots.  Once in these slots, the small balls are observed. with a sufficient sample size, the observed formation demonstrates the shape of a binomial distribution.

I will now explain how I made the Galton Board.

Using the Silhouette software, I created a copy of the Galton Board from an image that I observed in Wikipedia https://en.wikipedia.org/wiki/Galton_board#/media/File:Galton_box.jpg  I saved this image as an SVG file.

I then created the outside border of the box by deleting the interior design and saving this image as an SVG file.

I imported the base layer and made the base 2 mm thick.

I imported the pegged layer and made this layer 4 mm thick. When copying the image from Silhouette software, the image must be at the same exact location.  This ensures that the two images will stack on top of one another.  Once they are stacked, the pegged layer must be moved upwards 2 mm to account for the base layer.

The layers are then grouped together to complete the design for exporting to the 3D printer.

Here is my design in Tinkercad

 https://www.tinkercad.com/things/90k9Tbxcr0s-galton-board

Once the Galton Board has been 3D printed, make the paper and acetate cover for it using an electronic paper cutter machine.

Here is the PDF. I used 65 lb cardstock and acetate for the cover of the Galton Board.

https://drive.google.com/file/d/1MKNQfMTIW7ApsiAL7F3IoEOEPArLVDZo/view?usp=sharing

Here is the .Studio file for the Silhouette.

https://drive.google.com/file/d/1YU1axS4WDdbpJCNLQ1g2hhFI_AKLA5Sy/view?usp=sharing

Here is the SVG for all other cutting machines. The file goes beyond the viewable area.  Zoom out to see the entire file.

https://drive.google.com/file/d/1k7cCQMSIZ_rdeIiWmDeSSGRnvM01Vjh2/view?usp=sharing

Make the paper frame by creasing the sides and gluing the corners. 

Use a 1/4 tsp. of Snow Cap candy balls.  The white candy balls are the residue at the bottom of the Snow Caps candy.  Attach the acetate and then the paper cover. I used Scotch tape to fix the paper cover to the Galton Board.