Using 3d printing to explore some basic ideas from calculus.

A few days ago we did a short project with some shapes that the boys and I had made using the F3 program:

Using 3d printing to talk math with kids

My older son made a “twisted octahedron” based on one of the examples that comes with the program. When we talked about the shape he wondered how you would calculate the volume of the shape. Today I made some slicing models that you might see in a calculus class to help him see the answer to that question.

I’m still 3 steps below a novice at using F3 but am learning a bit more every day. The program I wrote to make the slicing models is pretty easy (and pretty short) and didn’t take that long to figure out. The code is below – I show it not because it will make sense to everyone, but rather to show how easy it is to make really cool shapes with the F3 program. The code is a very slight modification of F3’s twisted tetrahedron example that caught my son’s eye the other day, and running this code allowed me to make the three sliced examples in the second video below.

So, for our project tonight we first revisited the twisted octahedron and talked about the volume:

Next we looked at the sliced models I made. Unfortunately I made the models way too small. By luck they showed up ok on camera (though sorry for going off screen a few times) and the boys were able to see how the smaller slices converged to the shape we had originally:

I’m not teaching the boys calculus – don’t worry! It still is really neat to be able to show them some of the ideas from calculus using 3d printed models. Can’t wait to play with more shapes this week!