I saw a couple of tweets from Steven Strogatz yesterday that got me thinking about how you might use 3d printing in the college classroom:

The last tweet, in particular, made me think that having the 3d print versions of the two shapes would be useful. Before I get too far in to this post, though, I had to throw this post together pretty quickly to be able to fit in an hour of shovelling prior to heading to work! Sorry if it isn’t the most well-written or well-argued post. The main takeaway I want is that I think there are many great uses for 3d printing in the college math classroom.

The topic of 3d printing and calculus is one that I’ve thought about briefly before – see these old posts:

3d Printing and Calculus Concepts for kids

Using 3d printing to explore some basic ideas from calculus

Here are the shapes from the first post linked above – I think they would help students understand ideas like Riemann sums and volume by slicing:

Here are the two 3d shapes from the second Strogatz tweet from yesterday. Unfortunately we lost power in the middle of the night before the print project was complete, but you’ll get the idea. One of the things that comes through immediately in the prints is the difference in size of the two shapes:

Finally, an important shape from advanced algebra – a cube inside of a dodecahedron. This shape appears (and plays an important role) in Mike Artin’s Algebra book:

I found it hard as a student to understand the shape solely from the picture. Holding the shape in my hand, though, makes it much easier to see what is going on (I have made the cube slightly larger to highlight it):

So, while I’m sure it is true that learning to draw some of these shapes by hand is useful, I also think that 3d printing can be an important tool to help students see, understand, and experience the same shapes.