I’ve been enjoying getting familiar with our new 3D printer. I’m not sure these parametric surfaces were the best pieces to start out with, but I have learned a lot!
From left to right, we have a figure eight torus, a Fresnel surface, and a cyclide. Not pictured: the many, many failures.
I’m looking forward to exploring 3D printing in Calculus class this year. We don’t have a printer in our classroom (yet!), but some students have enough experience and access to work on modest projects outside of class.
Here’s a print of an interesting surface in xyz-coordinate space.
It’s always exciting to find a new way to represent or experience a mathematical idea, and physical representations can be especially powerful.
And perhaps more importantly, 3D printing gives students an opportunity to use mathematics to create. Mathematics is a creative endeavor, and whatever helps promote this idea will ultimately help change attitudes about math.
My students and I experimented a bit with 3D printing at the end of the year (as part of my always-do-something-new strategy). This (5,3) Torus knot was one of our successes.
I see a lot of possibility for 3D printing in my classrooms next year, and I’m looking forward to thinking and learning more about it.
The NYT has an interesting article about the increased use of 3D printers in commercial applications. Nowadays, companies are using the technology to build custom furniture, low-cost prosthetic limbs, and even housing components.
Basically, the geometry of the object is laid-out in software (like Autodesk), and the “printer” then translates the design into reality by extruding layers of hot plastic, one after another, building the object up essentially by printing one cross section at a time.
It seems that the process is becoming more commonplace and less expensive, opening the door for a wider array of commercial uses. I’ve seen students using this technology, and it is a pretty remarkable advance. I believe you can even have a custom-designed plastic guitar built!