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.

A STEM Project: Converting a Silhouette Studio File Into a 3D Print File In Tinkercad and Making a Slide Together Sports Car

 

Converting a Silhouette Studio File Into a 3D Print File In Tinkercad and Making a Slide Together Sports Car

In a previous blog posting I created a race car body using the Silhouette software. https://papercraftetc.blogspot.com/2023/12/a-stem-project-converting-silhouette.html In this blog posting, I created a sports car using similar principles.

I am only offering the SVG file of this model because Tinkercad requires an SVG file. (Silhouette Business edition is required.)

Here is the SVG. 

https://drive.google.com/file/d/1pDrdDaNmW_IEs3SywwThVthaYnLxBxSr/view?usp=sharing

Here are the three links in Tinkercad for the race car model.

https://www.tinkercad.com/things/5CHS4kq0aTB-sport-car-1-of-3

https://www.tinkercad.com/things/4f9WLBW5jee-sport-car-2-of-3

https://www.tinkercad.com/things/ej1VCM3A6UC-sport-car-3-of-3

Sport Car Part 1 of 3 and Sport Car Part 2 of 3 are parts that were copied from my Silhouette file and then converted to a 3D print file. I found that it is easier to print a file with a lot of space between the parts so I broke up the file into two files. 

Sports Car Part 3 of 3 are wheels for the race car which were designed by a Tinkercad user.  I also modified the hood of the race car to have a slant at the front edge of the hood. 

The model can be glued together if so desired.  I think it is more interesting to using Glue Dots so that the model can be taken apart later.

Slide the side pieces together onto the base platform with bumpers.

 Notice that the similar front (slit up) and back (slit down) pieces are in opposite directions.

Add the seat and steering wheel to the center chassis.

Attac the front of the chassis to the car body and then the back of the chassis.

Attach the spoiler back window, roof, mirrors and the hood of the car.

Attach the wheels to the axle and insert into the holes in the car. I used a glue dot on the axle to stop the wheels from moving.

A STEM Project: Coding an Oval Box in TurtleStitch

An Oval Box Coded In TurtleStitch and Embellished with Designs Created with the Silhouette For Mother's Day

I coded the oval box in TurtleStitch and then cut it out with a Silhouette

I love making boxes embellished with beautiful designs and this box fits that desire.  This is a lovely box which can be given for Mother's Day with its cheerful flowers and butterfly embellishments.

I designed the oval box in TurtleStitch and then copied it to the Silhouette software to be cut.  The flower and butterfly embellishments were made with the Silhouette software.

For my Silhouette friends and those of you who do not want to program, I have included all files to make the oval box with embellishments. The instructions to put the box together are at the end of this post.

Here is the PDF.  I used 65 lb. cardstock.

https://drive.google.com/file/d/1Y0Jhl1tPQc1w_X96eSHS4i1mzRv6PDSa/view?usp=sharing

Here is the .Studio file.

https://drive.google.com/file/d/1qMaP0vSwNeCl0-HfVWSInL_MX9d1_VKM/view?usp=sharing

Here is the SVG.  The file extends beyond the scope of the viewing field.  Zoom out to see the entire file.

https://drive.google.com/file/d/1LWXXBVRjPNwy2B-0DajhoVcOSCTQ8h1u/view?usp=sharing

Coding an Oval Box in TurtleStitch  

Here is the program in TurtleStitch where I made the oval box components. https://www.turtlestitch.org/users/Elaine/projects/Oval%20Box 

Coding the Box Top and Bottom 

Before I explain how I coded the box, I would like to talk about the thought process required when coding a TurtleStitch design.  Can the shape be broken down into manageable parts that are easily programmed? Draw a picture of the shape and break it into simple parts. The oval shape looks like two circles that are joined by a rectangle.  See photo below.

Looking at just the outer edge, there is a blue semicircle followed by a red straight line and then another blue semicircle with a straight red line that makes up the oval figure. 

Knowing this information, the coding is a simple task.  

Using the arc right block,  determine a radius that you want and then move the turtle 180 degrees to create the first semicircle.  Use a move block to get to the next semicircle, and then repeat these two instructions, arc right and move blocks, to finish the oval.

I repeated these instructions for the bottom of the box with a 98% reduction in size.  The bottom of the box needs to smaller so that the top can slide easily onto the bottom of the box.

Programming the Sides of the Box

The photo above shows the design for the side of the box. It is a strip of paper with tabs. The bottom tab adheres to the oval and the left side tab creates an oval strip when the tab is adhered to itself on the other end.

To calculate the circumference of the oval, two semicircles plus the two lengths of the rectangle need to be added together. 

Since the two semicircles equal the circumference of one circle, the circumference of one circle plus the two lengths of the rectangle is coded.

Make the Tabs for the Side of the Box

To create the tabs and dotted lines, two special blocks need to be used. The first special block is for the tabs. Here is the program in TurtleStitch if you would like to play with it functionality. https://www.turtlestitch.org/run#cloud:Username=Elaine&ProjectName=Edgefold%20Width%20With%20Multiple%20Teeth

The edgefold block can creates different types of tabs with a different number of teeth. 

Make the Dotted lines for the Side of the Box

The second special block is for the dotted lines. Here is the program in TurtleStitch if you would like to play with it functionality.

https://www.turtlestitch.org/run#cloud:Username=Elaine&ProjectName=Dashed%20Line%20Block

The move block can create different lengths of dotted lines.

Make the Strip Block For the Side of the Box

Here is the strip block that I created.  The turtle is moved for the length of the circumference and then turned at a right angle for the height of the top.  The turtle is moved again at a right angle and dotted lines are created with the move block. The turtle is turned around 180 degrees and the edgefold block creates the bottom tabs.

The turtle is turned around 180 degrees and aligned to create the side tab with the edgefold and move blocks

The instructions are repeated for the bottom side of the box with a 98% reduction in size. 

A one inch block is used to create a one inch square so that the image can be resized in the Silhouette software.  The design is then saved as a DXF file for the Silhouette.

Open the Oval Box in the Silhouette Software 

When a design is saved in TurtleStitch as a DXF file, the file measurements are not preserved and the file needs to be resized in the Silhouette software. Photo above shows the size of the one inch square in the Silhouette software.

The size of the entire file needs to be resized. Divide 1 by the size of the observed one inch square and then multiply by 100. 

1/0.618 x 100 = 161.81%

Transform the entire file with the calculated percentage amount. 

Check the one inch square to see if it is now one inch.  (The one inch square is no longer needed, and can be deleted.) Realign all of the components of the oval box on your Silhouette screen and cut as usual. In the file, I added another top and bottom oval to my Silhouette file, since I wanted the box to be two walled as this produces a sturdy box.

Make the Box 

The height of the top of the box is smaller than the bottom of the box. Repeat these instructions for each half of the box. Glue the strip together to form a loop as shown in photo above at the top. Fold the tabs of this strip at a right angle. 

Apply glue to the inside tabs as shown above. Adhere the corresponding oval to the tabs. 

Turn the piece over and apply glue to the tabs.  Adhere the corresponding oval to the tabs. 

Add embellishments to create a pretty oval box to give for Mother's Day.

A STEM Project: Making a Simple Microscope Using a Glass Marble

Image of an onion bulb epidermis as seen with an iPhone Magnifier

Simple Components of a Marble Microscope

Lens holder with glass marble inside, Slide carrier and a glass marble lens

Simple Microscope Assembly Using a Glass Marble

The microscopic world is an amazing environment to explore.  A drop of water placed on a piece of wax paper can begin your journey of magnifying objects.  The drop of water forms a round blob because of surface tension on the wax paper.  Using this water blob, you can magnify objects.

In this blog posting, I use a clear glass marble from the Dollar store to make a simple magnifying lens. 

Here are the files to make the lens holder and the slide holder.  I have three versions of the files.  The first is a PDF where you can cut out the pieces with scissors.  The second file is for the Silhouette and the third file is all other electronic paper cutting machines. 

Materials needed. - Glue Dots, Glass Marble and a Tea Light

Here is the PDF. I used 65 lb cardstock.

https://drive.google.com/file/d/1etHfDSnLN-BE9tSYH47d60gVbIy-cKnC/view?usp=sharing

Here is the .Studio file for the Silhouette.

https://drive.google.com/file/d/10pfceiCRgxA-Q0VvoHmQ9Cchk77-uBI6/view?usp=sharing

Here is the SVG. The file goes beyond the viewable area.  Zoom out to see the entire file.

https://drive.google.com/file/d/1sPCffoFfxJOxfiTgppDgNUQQDt6UXNVO/view?usp=sharing

Make the Box - The top and bottom construction is the same. The box top and bottom are two walled.  This produces a sturdy box. 

Crease the box top as shown above and apply glue to the two tabs on the sides.

Apply glue to the four tabs inside the box as shown above.  Adhere the box top.

Apply glue to the top of the box and adhere the second wall of the box top.

Repeat the construction for the bottom of the box.

I used a Glue Dot to center the tea light to the center of the bottom.

Put the cover on the box. Apply Glue Dots to the two tabs of the slide carrier.

Make the Lens Holder

Crease the tube and apply glue to the side tab.  Shape the tube into a hexagonal tube. Apply glue to the lens holder on the six tabs. 

Insert the lens holder into the tube.

Crease the two strips into a circle.

Apply glue to the two circle tabs and adhere.

Glue the two discs together.

Glue the circle onto the disc. Repeat for the second one.

Insert the glass marble into the smaller side. Apply glue to the top edge of the larger side.

Adhere the two sides together.

Assemble the Viewing Platform

Insert the slide into the slide carrier.

Place the slide carrier on top of the lite box.  Place the lens holder on top of the slide carrier.