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

A few weeks ago we got this book in the mail:

We used the book for one fun project already:

Playing with geometric transformations

Today we were really short on time in the morning, but I still wanted to do a project before we ran out the door. I’d been hoping print some of the shapes from the book, so today for a quick project we looked at one of the transformations.

Here’s the introduction to the shape and some of the thoughts that the boys had:

Next we tried to understand some of the details about the shapes – could we understand anything about the lengths of the sides or the angles?

I think that we now have enough information to make the tiles. It was nice that a little bit of trig came up since that’s what my older son is studying right now. Not sure if I’ll have time this weekend or not, but we’ll hopefully be able to do a project with the 3d printed tiles in the next week.

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

  1. Dear Mike,

    I enjoyed your videos in which you discussed Freese’s Plate 100 with your sons. That’s a really nice project, especially the way you posed questions to draw conclusions from your sons. And being able to 3D-print the pieces is the icing on the cake!

    I maintain a webpage for each of my books, where I supply tidbits about the books, including further information about people and things related the content of the book, including reviews, and new and improved dissections. I would like to link to your nonagon project via:

    Would that be all right with you? Please let me if there is anything that you would want corrected. The entry point for this page is through

    There isn’t a whole lot yet on that website, but you can get an idea what am intending by taking a look at:

    Could you please alert me if you make any further excursions into material from my Freese book? I’ve made animations of some of the hinged dissections from the book, as well as animations for a couple of translational dissections. (Those are part of a short powerpoint presentation that I gave at the recent Gathering for Gardner and will be part of longer presentation for a meeting in Chicago in September.) Yet there’s something really nice about having actual physical models that one can manipulate, as I’ve had done in the past out of wood with clear tape on the edges. I haven’t tried 3D-printed material yet.

    Sincerely yours,


    1. Greg –

      Great to hear from you! Of course it is ok to link to the project.

      We’ve done a total of three projects. The last one was just yesterday and has the remaining links:

      I’ve really enjoyed the book and plan to make more of the tiles. My older son is just learning a bit of trig now, and constructing the tiles is a fun little trig project.

      I’m happy to send the nonagon tiles to you for you to enjoy. I assume your webpage at Purdue has a good address, but if there is a better one feel free to drop me an e-mail at


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