“What would you print if you had a 3D printer in your home?” James Madison University math professor Laura Taalman is printing a thing a day and blogging about it at MakerHome. Her family has a MakerBot Replicator 2 and an Afinia H-Series, and each post includes an .stl file of the project and some information about which printer they used, how long it took, and other pertinent details in case you want to play along at home.
Taalman’s project started last August, I assume to coincide with the beginning of school. Her university JMU has embraced 3D printing. They have a MakerLab where math students can learn about 3D printing (their blog is here) and a 3D printer-equipped general education classroom with its own website and blogs.
I’m impressed with the wide range of things Taalman prints at home. In addition to cool math stuff (more on that in a moment), she makes toys such as Daleks and polyhedral bears and useful household objects such as a coin-operated bottle opener, dietary restriction toothpicks, and a strainer funnel for hibiscus tea. She even 3D printed a grate to keep fingers safe from the 3D printer’s fan. (I like to think that if I had a 3D printer, my headboard would now be attached to my bed instead of propped against the wall because I don’t have the right sized bolts.)
The math-based designs are great. Some of my favorites are an icosahedron into which jawbreakers were dropped while it printed, a chain of interlocking rhombic dodecahedra, rocking knots that only touch the table in two places, a Hilbert curve, a tetrahedron puzzle, an icosiodecahedron, and a stereographic projection model. She even printed a knot without knowing what knot it is, or even whether it’s the unknot!
Some things, like the Menger sponge coasters, and cosine-based cookie plate, are part math and part practical. Why a cosine-based cookie plate? Taalman writes, “I need a small cookie plate for a reception. And maybe PLA [polylactic acid, a plastic used in some 3D printing] isn’t FDA-approved but frankly I think most people would probably eat a cookie that was sitting on the table with no plate at all, so a PLA plate is probably okay. Just in case, however, here is a plate the minimizes cookie/PLA contact, because of the waviness of the plate – based off the cosine curve.”
I don’t have a 3D printer yet, but I am increasingly impressed with how professional their outputs look and how easy they seem to be to use. From Taalman’s blog, it looks like she has occasional frustrations with the printers, and I’m sure there’s a learning curve for figuring out what shapes work and what settings to use, but projects like hers make me think that maybe I could do this. The ability to print out exotic mathematical shapes could certainly make a big difference in a class like multivariable calculus or complex analysis in which concrete visualizations can be incredibly helpful. I don’t know if I’ll take the plunge anytime soon, but it’s very tempting. There are so many freely available projects already and endless ways to tweak them or make entirely new things.
I first got interested in 3D-printed math when Saul Schleimer brought a 3D printed puzzle he and Henry Segerman had designed to a conference I attended, and I learned about Taalman’s blog from Segerman. I recently ordered a model of the hyperbolic plane from his Shapeways store to use in an upcoming talk. I can hardly wait for it to get here!