3D Printed Math and Science

by Joan Horvath & Rich Cameron

Teachers have always explained abstract concepts using impromptu models made with whatever was handy. How does learning math concepts change if every student can have (or, even better, make) models to learn concepts? And how can teachers take advantage of 3D printing to make that happen?

For the last few years, we have been exploring the benefits and challenges of creating 3D printable models for both K-12 math and science concepts as well as and higher-level math visualization.We have been using the open-source 3D CAD program OpenSCAD to create models that students can vary based on the inherent science or math to create interactive learning experiences.

We have learned a lot from these early experiences. First we’ve noticed that almost every graph of a 2D projection of a 3D phenomenon is the same. When you take the third dimension into account, it can give new insights. For example, in our 2016 3D Printed Science Projects book, we developed a model of Kepler’s Laws of planetary motion. In particular, there is a law that says that a line connecting one body orbiting another will sweep out equal areas in equal time. So if you have a very elliptical orbit (like that of Halley’s comet around the sun) it will go fast near the sun and then much slower farther away.



We made that concept into a model (shown here) with the orbit as the base of the model and the height representing how fast the planet was going at that point in the orbit. The long ellipse is the orbit of Halley’s comet. The three concentric orbits are those of Mercury, Venus and Earth. We never realized how elliptical Mercury’s orbit was until we printed this model.

If you want to hear more about this directly, we will be teaching a workshop about their lesson learned developing 3D printed math models at Bay Area Maker Faire at 3 PM on Saturday, May 18. Pre-registration and a small fee (in addition to Maker Faire admission) is required. You can sign up at this link.

About the Author

Joan Horvath & Rich Cameron are the co-founders of Nonscriptum LLC. Their Pasadena, California consulting and training firm was founded in early 2015 and focuses on teaching educators and scientists how to use maker tech, and teaching online for LinkedIn Learning/ Lynda.com and others. They have collaborated on 8 books (so far!) Joan is a recovering rocket scientist and alumna of MIT and UCLA. Rich is a 3D printing innovator, and the designer of the RepRap Wallace and Bukito 3D printers. Joan and Rich’s Apress books can be found at this link. Joan and Rich photo by Michelle Lowman.

This article was contributed by Joan Horvath & Rich Cameron, authors of Mastering 3D Printing in the Classroom, Library, and Lab.