Introduction

Use the equation for a circle to create a product, in this instructable we will be making a bubble wand. Math has a number of applications for a variety of products but in class students are studying the circle. Two teachers (@ISBInventionCtr and @BeckyHall75) came up with a product that can be used as an interdisciplinary unit between maths and design.

Supplies / Materials / Equipment

Equation for Circle

Desmos Adobe Illustrator (or any other vector program)

Laser Cutter

3mm Acrylic

Additional Options:

Fusion 360

PLA filament

Ultimaker 3

Step 1: Circle Equations in Desmos

Using the equation for a circle use Desmos to create the circle.

The circle equation is (x-a)^2 + (y-b)^2 = r^2 where r is the radius of the circle and (a, b) are the coordinates of the centre of the circle.

There are a number of combinations and types of circle that you can draw.

Use the examples below as a guide that also include the bubble wand handle. Equations are in the desmos drawings.

Circle with small holes: https://www.desmos.com/calculator/jfnkxtn2ze

Different size holes: https://www.desmos.com/calculator/elgrwrieyr

Wand with elipse: https://www.desmos.com/calculator/gr20fsmmwl

Simple circle with spaces: https://www.desmos.com/calculator/vuwzmoyc8r

Simple Circle: https://www.desmos.com/calculator/d1b1euogyn

We found that the circles worked the best.

Step 2: Export Desmo File

In the top right corner of desmos there is a share Icon.

Click on the Share Icon

Go to Export Image (see photo)

Click on green "Download png"

This saves onto your computer. Keep it in a memorable place with a memorable name.

Step 3: Place Desmos Drawing to Vector Program

In this step you need to place/import the PNG from desmos into a vector drawings program. For our example we are using Adobe Illustrator. Inkscape would work fine as well. The important part is that you can export your as a vector drawing (SVG, DWG, DXF).

Make sure your canvas size is the appropriate size for your bubble wand. It's hard to get things precise, so be sure that you pay attention to sizes of the document.

Optional:

You can also import the file in Fusion 360 to create a 3D printed model of the bubble wand (see red wand in the photos).

Step 4: Trace the Bubble Wand

Unfortunately there's not a much better way to to do this from Desmos. It would be great if in Desmos we could export the vector files, but we have to do it ourself.

Use the circle tool and the pen tool to trace the image of your bubble wand.

Notes:

Pay attention the layers of your vector file. The image should be separate from the lines you are drawing.

Step 5: Export the Vector Lines

Now that you finished tracing the bubble wand you need to get the vector lines to the laser cutter. Note: The following steps depend based on your laser cutter.

File and then "Export"

Change the file format to DXF (or the vector type of your choice).

Step 6: Import to Laser Cutter Sofware

Now it's time to run it on the laser cutter. The power and speed settings depend on your laser cutter, but for the 3mm acrylic we used 30power and 20speed. Once your laster cutter is setup, run it and off you go...

Step 7: Blow Bubbles

You should have a laser cut bubble wand made with the equation for a circle now!

Get some soapy water or bubble blowing water and enjoy.

Note: you can follow a similar process but use a CAD software such as Fusion360 to create a 3D bubble wand and print the wand (see neon green in the photos).