# Learning math by studying 3d printing

My son spent the last couple of months preparing for the AMC 10. Now that the test is behind him I’m going to spend some time with him studying 3d printing.

Today we looked at some simple code in the F3 program:

The details of the code don’t matter that munch – all the code is doing is testing whether or not a point is inside of a sphere by checking whether or not the distance from that point to the center is greater than or less than the radius.

Immediately two ideas come to mind:

(i) how do we compute distance in 3 dimensions?

(ii) is that distance measure unique.

So, after 1 minute of looking at code we went to the whiteboard ðŸ™‚

Our previous 3d prints of the sphere and torus in different L^p metrics were still on the table, so I used those as props.

The first topic was distance in two dimensions:

The second topic was distance in three dimensions:

The last topic was how the L^p metrics vary as p varies – it was lucky we had the spheres handy ðŸ™‚

Today’s conversation was actually a nice surprise – I think there’s going to be quite a lot of fun math review that comes from studying 3d printing more carefully.