The Tomahawk - an Angle Trisection Tool

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Introduction: The Tomahawk - an Angle Trisection Tool

About: I've been a teacher/learner/maker of Math since 1994. I am also a Milken National Educator & NYS Master Teacher Emeritus. Lover of family, music, DIYing, and the great outdoors. Life is good! Also please …

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.

Supplies

Index card (or any paper, card stock or cardboard)

Pencil

Ruler

Compass

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.

4 People Made This Project!

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6 Comments

0
charlessenf-gm
charlessenf-gm

7 months ago

Thanks, enjoyed watching that.
It appeared to me that the ratio was 3 x 4 rather than 3 x 5
You cut the top inch off the card, leaving 3 x 4 for the tommyhawk.
So Start with material where width = .75 Height and, then the radius Radius = Width/3 right?
Height = 4, width = 3, radius = 1

0
mkaercher
mkaercher

Reply 6 months ago

Correct! Thanks.

0
iamchrismoran
iamchrismoran

7 months ago

Oof... I didn't realize you couldn't trisect an angle, as I severely mistakenly let myself believe that trisecting a chord would let me trisect the central angle.
So, thanks for this instructable if for anything, to correct me.
Cool tool!

0
mkaercher
mkaercher

Reply 6 months ago

Thanks! It took a while for me to realize that same mistake.

Enjoy!

0
GoFish
GoFish

7 months ago

Looks like it will be a very handy addition to the toolbox. Thanks.

0
mkaercher
mkaercher

Reply 6 months ago

You're welcome! Enjoy!