Using 3d printing to review properties of lines

As a follow up to our last two projects with 3d printed triangles, I thought it would be fun to try out a similar project. The point of the 2nd project wasn’t the geometry, though, it was to use the process of making the shapes as a way to review some basic ideas about lines.

So, I started by showing my older son the basic idea – we wanted to write down the equations of the three lines that border a 5-12-13 triangle. Since we have a right triangle the equations aren’t too difficult, but are still useful for a simple review:

Next we went upstairs to Mathematica to make our 3d template using the function RegionPlot3d:

After the prints finished we played around with them a bit to see which triangles we could make with the same area:

I think that making little shapes like this might be one of the best educational uses of 3d printing. Kids get an opportunity to apply some basic math knowledge and create some fun shapes!