In the last couple of weeks I’ve started to get a better understanding of how to use our 3D printer to help teach the boys about both algebra and 2d geometry. The project that got me thinking about this particular application of 3d printing was based on a problem that Patrick Honner shared on his blog back in November:

Inequalities and Mr. Honner’s Triangles

Then, just last week Tina Cardone shared a neat problem on Twitter:

A Cool Geometry Problem Shared by Tina Cardone

Then, by lucky coincidence, my son struggled with a challenge problem in his Geometry book just a couple of days later:

A Follow Up to Our Tina Cardone Geometry Project

All of that background left me with 3D printing on my mind when my older son stumbled on this problem at the end of last week:

Problem 12 from the 2005 AMC 10a

I wanted to try something a little different for this problem, though, so when my wife and older son were out at an art class, I tried using this problem as a 3d printing project with my younger son. He’s not had much geometry or algebra, and certainly nothing about lines. The goal for this project was to see how 3D printing would work out as an introduction to those topics.

We started by talking through the problem:

Next we drew the two shapes in Mathematica in three steps. The first of the three steps was to make a 3D version of an equilateral triangle:

The next step was making the little circle parts. Unfortunately we drew the wrong shape:

The last step was correcting the mistake in step two so that we draw only the little circular arc. This time we got it right:

It took about two hours to print all of the pieces. I hadn’t really thought about how big they were going to be, but probably 4 cm sides would have been plenty big instead of the 6 cm sides I made for the triangles. Once they were all printed I revisited the challenge problem from “A follow up to our Tina Cardone Geometry Project” and the new geometry problem from the AMC10 with my younger son. Without the printed puzzle pieces, I wouldn’t even consider giving him these problems. With the manipulatives, though, he is able to talk through the problems and test out some ideas. I especially liked his ideas to try to make circles out of the shapes and seeing that the first couple of attempts were not circles:

Finally, I showed the shapes to my older son. We spent probably 15 minutes talking about the problem yesterday since there are several different ways to solve it. Having the shapes in your hand helps you see one of the geometric solutions pretty quickly:

Although it may seem like a strange application of 3D printing, getting Mathematica to draw some 2D shapes and then printing them is a fun exercise in both algebra and geometry. I think it is also an educational exercise, too, as getting the shapes from the board to the computer and then to the printer involves some math that might be interesting and challenging for kids. I’m excited to try out a few more projects like this one.