# 3D printing and negative space

As a follow up to yesterday’s blog post – Reacting to Dan Meyer’s “Developing the Question” post – I wanted to show the boys how the ideas we talked about can be used in 3D printing.  I planned to do a little more than we actually did, but our printer got up on the wrong side of bed and needed little tune up.  Despite learning more than I ever wanted to about printer maintenance, we did manage to get  in a pretty fun project.

Before we got started talking about math, I reminded them of our old “Prince Rupert Cube” project.   The question asked in this problem is whether you can pass a cube through another cube of equal size.  The math I used to create this shape (linear transformations)  is a little beyond what I wanted to show the boys today, but it still was a nice way to introduce the idea of intersecting shapes.

The slightly easier geometric shape I chose to look at in detail was the intersection of a sphere and some cylinders.  I began that conversation by talking about how you could get a computer to draw a circle and a cylinder:

Next, we went to the computer to see how to put the ideas from our talk to work. There’s a lot of just playing around with some of the commands to see what we get in this piece:

Having figured out a little bit about cylinders, we went back to the white board to talk about spheres. As usual, the intention wasn’t to be rigorous at all here, rather just to talk about the differences between cylinders and spheres. It was fun to hear the boys talk in a little bit of a hand waving way about what they thought the equation of a sphere would be.

For the last part of the talk we went back to the computer to draw some spheres and cylinders. Eventually we make a neat shape out of a sphere of radius 2 intersecting 3 mutually perpendicular cylinders of radius 1.

It was kind of fun to see the boys recognize that our final shape was pretty similar to Laura Taalman’s Coin Traps.  You should, of course check out her entire blog, too:  Makerhome Blog.

After we finished the last movie we made a slightly higher resolution version of our shape (150 plot points) and exported it to the Maker Bot.  Of course, we had to make it the right size to trap some coins!  Definitely a fun morning turning some of the math that we talked about yesterday into something that you can hold in your hand..