# Nonagon tiles

Last week we did a fun project using a pattern we say in “Ernest Irving Freese’s Geometric Transformations” by Greg N. Frederickson:

Using “Ernest Irving Freese’s Geometric Transformations” with kids

I thought it would be fun to make some of the tiles – especially since my older son is studying trig right now. The tiles finished printing overnight:

Last night my son and I talked about how you could make these tiles, with a focus on the trig and algebra required to define the shapes.

Here’s the introduction to the topic:

Now we talked about how to define the kite shape in the tiling. This involves talking about 40 and 50 degree angles:

Finally, we talked through the last part – finding the final point is pretty challenging. Turns out, though, that we don’t have to find the coordinates of the point because we can write down the equation of the top line pretty easily:

I’ve been happily surprised that 3d printing is a fun way to help kids explore 2d geometry. I’m excited to have my son try to make some other tiles from the book on his own for our next project.