A challenging, but fun, patty paper proof of the Pythagorean theorem

** I’m moving too slowly this morning and didn’t get a chance to edit this post before having to run the kids to various events. Sorry if the post is a bit sloppier than usual **

I was intending to do a project on the angle bisector theorem today, but when I opened up Patty Paper geometry I saw a really neat project on the Pythagorean theorem, so I switched topics on the fly!

This one didn’t go quite a smooth as I wanted – switching up on the fly sort of opens that door. I’m also a sick today . . . . oh well, don’t let our stumbles influence your thoughts on the project – the project itself is a great one for kids.

Here’s how we got started. Some of the folding parts gave the boys a little trouble. This project is at the end of the book and probably assumes a bit more folding experience than just diving in cold. An introductory folding exercise before we started probably would have been a good idea for us this morning.

So, we were struggling to fold a line meeting the edge of our paper at a specific point at the end of the last video, so we thought for a bit more about how to solve that problem.

Once we got over that hurdle, we made it through several more steps in the project. At the end of this video we are trying to make a fold through a specific point of a square that is perpendicular to a specific point on the hypotenuse of our right triangle.

In this part of the project we had two challenges:

(i) Make the perpendicular fold we were trying to make at the end of the last video, and

(ii) Make a fold through the center of the square parallel to the hypotenuse

My younger son’s ideas on the second part were really interesting to hear.

Finally, we had our 5 pieces that we needed to arrange into a square. This part was an interesting challenge. They initially thought the small square needed to be a corner of the larger square. After deciding that idea didn’t work, they produced the large square fairly quickly:

So, maybe not our best walk through a project ever, but a fun and interesting project for sure. As I mentioned at the beginning, a brief introduction with elementary folding ideas would have been a good idea.

Anyway, here’s the book in case you want to see many more incredible ways to approach geometry through folding:




2 Comments so far. Leave a comment below.
  1. What a great puzzle (to make and to solve!)
    I did this puzzle at MoMath. It gave me such a hard time that I had starting to think Pythagoras was wrong about his theorem after all.

    Watching the paper folding challenges, and seeing how the boys negotiated them, caught my attention, particularly using paper folding to make a square. There’s a really elegant way to create a custom square that I’ve never seen demonstrated anywhere: I’m thinking I’ll make a video of it today. Should take less than a minute…#famouslastwords.

    On your recommendation, I now own the Patty Paper book. Great book!

  2. ok, made a short video on a lovely way to make a square the size that you want using paper folding to first bisect an angle then make the square https://www.youtube.com/watch?v=_0EJoMp1rn0

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