Seeing Math and Art in New Ways Through 3D Printing

Teachers often tell us that being in our 3D ThinkLink class helps students do better in math. At the same time, many students say learning about 3D design and printing brings out their artistic creativity.

That’s part of the magic of 3D printing as a teaching tool. It combines mathematics and art in ways that appeal to all sorts of students, especially those who are visual or tactile learners. It’s easier for them to understand an abstract concept when they have the ability to transform it into a physical object they can hold and examine from every angle. And in the process, they sometimes discover there’s beauty in the numbers and formulas.

This idea predates 3D printing by at least a century, as WIRED magazine reported in an article about 19^th-century mathematician Felix Klein. He pioneered the idea of turning equations into three-dimensional models.

“… workers in Klein’s laboratory painstakingly drew the horizontal sections solving a planar version of the equation. Each cross-section was cast separately, in a plaster made from powdered chalk, bone glue, double varnish, essence of lavender and essence of clove. Then the layers were carefully stacked, glued together, and sanded smooth.”

The process is strikingly similar to what’s done by today’s powder-bed 3D printers like the Z450 in our 3D ThinkLink Creativity Lab. They build objects using layers of engineered gypsum powder and liquid binder. 

“The models were part of a program to make algebra palpable. It’s one thing to check that the derivatives of a function are zero and another to feel the plaster taper to a sharp point. … By making models you can hold in your hands, Klein hoped to keep mathematics anchored to the physical world. ‘Collections of mathematical models and courses in drawing are calculated to disarm, in part at least, the hostility directed against the excessive abstractness of the university instruction,’ Klein said at the 1893 Evanston colloquium. An image or an object does more than ease fear of the unseen, it makes the equation real.”

As WIRED notes, artists and architects were sometimes inspired by the models they saw on display in university math departments. Today, “mathematical artists” such as Paul Nylander and Henry Segerman are producing wondrous creations, thanks to 3D printing.

Others are using additive manufacturing technology to visualize the invisible. They’re turning audio waveforms into 3D-printed art. For example, here’s a keychain charm in the shape of the soundwave of a person saying “I love you.”

One thing we know about our 3D ThinkLink students is that they love to make things that are personalized and unique. While some of the "math art" calculations may be too advanced for our students, making things like rings and bracelets in the shapes of their own voiceprints is well within their abilities.

And those who want to think way outside the box can try to wrap their minds around projects like these 3D-printed optical illusions.