Evelyn Lamb’s latest article about tiling pentagons is incredible:
We used it for a fun project this morning with some 3d printed pentagons. That project is here:
Tonight I wanted to show the boys how I made those pentagons. Not the 3d printing commands in Mathematica, but rather just how I described the shape.
I stared by digging in to Wikipedia’s description of the kind of pentagon that Lamb found.
The Wikipedia page is here:
Kids will use a lot of nice introductory geometric ideas in simply describing the shape:
Next we talked about some of the basic properties of the pentagon. It was a bit of a tricky conversation since my older son knows quite a bit about equations of lines and my younger son really hasn’t seen equations of lines at all. So, for this part I let my younger so do most of the talking.
In this part we talk a bit about coordinates and equations of lines that are parallel to the x and y axis.
At the end we moved to the tricky part – how do we describe the final two lines. Describing these lines is even a little bit harder since we want the two line segments to have the same length. How do we do that?
At the end of the last movie we found a way to make the final two line segments have the same length. Now we needed to write down the equation of those two lines. This part took a while because my younger son was essentially seeing the math ideas here for the first time, but I’m glad we went slowly. He seemed to get a lot out of it.
If you are interested, the Mathematica code to make the pentagon looked like this:
I love using 3d printing to talk about 2d geometry ideas. The conversations that you have about making the shapes are really fun conversations about basic geometric and algebraic ideas. Since you either have the shape made already or are in the process of making the shapes, the conversations are really easy to get going 🙂