Introduction: The Tomahawk - an Angle Trisection Tool
While it is possible to bisect an arbitrary angle using only a compass and a straightedge, it is impossible to trisect an arbitrary angle with only a compass and straightedge. For more about this discussion, check out this Wikipedia post.
There are, however, a few tools that can be used to trisect an angle. One of those tools is called a Tomahawk. I stumbled upon a different Wikipedia post https://en.wikipedia.org/wiki/Tomahawk_(geometry) about this tool. I consider myself a proficient teacher and student of geometric constructions. So when I came across this interesting tool, I set out to make one and put together this Instructable.
Index card (or any paper, card stock or cardboard)
Scissors (or craft knife, circle cutting tool)
Step 1: How to Bisect an Angle - a Refresher
There are many ways to bisect an angle, using a compass and straightedge. Here are two of those ways. This will give you a little context before we make our Tomahawk.
Step 2: How to Make a Tomahawk
To make the Tomahawk, you will need some paper, card stock, or cardboard. I will demonstrate using a 3" x 5" index card. The dimensions work nicely for the design of the tool.
I based the design on the plans found in this article.
Step 3: How to Use the Tomahawk
Now that you've made your Tomahawk, draw some angles and try using the tool to trisect the angles. Verify the trisections using a protractor.
The tool should work for any angle less than 180°. You can also make the Tomahawk smaller or larger, depending on your angle needs.
Also, if you do a little searching, you can also find publicly-shared Tomahawk files for the 3-D printer.
Step 4: Final Thoughts
I love the simplicity of this tool and can't wait to have my students make it and try it out. I've also thought about renaming it an "Angle Axe".
I might even have students make one using compass and straightedge constructions. So even though the angle isn't trisected using a compass and straightedge, at least the tool was built using them.
I hope you've found this Instructable helpful and interesting. If you have any feedback, questions, or suggestions, please feel free to share them below. Thanks!
Step 5: 3D Printed Version
Since publishing the original post, I thought about making a 3D printed version of the tool. I started designing the tool in Tinkercad, using a composition of shapes. But I couldn't get it just right. So I designed the shape of the tool using this Desmos Calculator. This allowed me to make the proper vertex where the handle meets the curve of the blade.
I then exported the PNG from Desmos and converted it to an SVG, allowing it to be imported into Tinkercad. Here's the link to the Tinkercad model: https://www.tinkercad.com/things/8A1TV5hWxGm
Note: As of this update, I haven't yet printed the model. When I do, I will be sure to update this project.