3D Printing for the Math Classroom

George Hart

Below is a blurb for hands-on workshops I've been leading for high school and college math teachers.  Typically I've done this either as a full day course or as three two-hour sessions, which is preferable as it allows time for homework and practice in between sessions. I have mainly been giving these workshops using Mathematica (but also related workshops using Maya).  A site license or a trial version of the software would be needed for each participant to follow along.  This can be done in a school computer lab or by having everyone bring their own laptop with the software pre-installed.

3D printing is a valuable tool for engaging mathematics students and providing them with motivation to master many technical topics in the math classroom. As the technology becomes less expensive and more ubiquitous, teachers in K-12 and college environments are gaining easy access to 3D printers which can be used for education. Most teachers are not familiar with this technology and its possible uses, so I have been leading hands-on workshops for mathematics teachers across the US and internationally, introducing them to the techniques needed to use consumer-level 3D printers (such as the Makerbot Replicator) to enrich a math classroom.

Software packages such as Mathematica can translate algebraic expressions into 3D forms that are then created as tangible, low-cost, plastic objects that students can hold in their hands, take home, and/or pass around the class. Workshop participants are given a series of progressively more complex design challenges and are also asked to come up with their own individual objects of interest to create. Each class ends with something that has never existed before printing on the 3D printer. These techniques empower teachers and students to create physical versions of anything that can be described mathematically with algebraic, trigonometric, and Boolean functions. They introduce students to the creative side of mathematics and provide a powerful motivation for learning the details.

Participants will work through a series of design problems to learn the techniques and build up their skills. Here is an example of a Mathematica (version 10) notebook that resulted from one recent series of three classes for secondary school teachers at Math for America, but the details of what I cover vary depending on the interest, background, and ability of the participants:


A typical assignment is to create a Venn-diagram candy dish, which can be made by combining appropriately translated cylinders.  If you can write the equations, you can build one on an inexpensive 3D printer:

For many more examples of the kinds of objects that can be created through mathematical design and current 3D printing technology, see my RP page and the pages it cites:



George Hart is a sculptor and applied mathematician who demonstrates how mathematics is cool and creative in ways you might not have expected. Whether he is slicing a bagel into two linked halves or leading hundreds of participants in an intricate geometric sculpture barn raising, he always finds original ways to share the beauty of mathematical thinking.  An interdepartmental research professor at Stony Brook University, he holds a B.S. in Mathematics and a Ph.D. in Electrical Engineering and Computer Science from MIT.  Hart is an organizer of the annual Bridges Conference on mathematics and art and the editor for sculpture for the Journal of Mathematics and the Arts. His research explores innovative ways to use computer technology in the design and fabrication of his artwork, which has been exhibited widely around the world. Hart co-founded the Museum of Mathematics in New York City and developed its initial set of hands-on exhibits.  He also makes videos that show the fun and creative sides of mathematics.  See http://georgehart.com for examples of his work.