Studying inscribed circles with Patty Paper Geometry

It has been a while since we did a project inspired by Patty Paper Geometry:

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This morning I thought it would be fun to revisit an old project and study inscribed circles via folding. One of the most difficult parts of this project was finding our box of patty paper!

We started by reviewing inscribed and circumscribed circles and I told the boys some basic properties about the shapes:

Next we moved on to trying to construct the inscribed circle via folding patty paper. It wasn’t too hard to find the center of the circle by creating the angle bisectors, but finding the length of the radius was challenging. The difficulty was that they knew how to find the perpendicular bisector of a side by folding, but couldn’t quite figure out how to find a perpendicular line passing through a specific point (the center of the circle).

The boys couldn’t figure out how to find the radius, so I cut the last video short and we discussed that problem in this video. The figured out how to do it after a few hints, and the circle that we drew with our compass was actually almost perfect – always a nice surprise given how the little folding errors can add up over the project.

I love Patty Paper Geometry’s approach to studying geometry. All of the complexity and computations completely seem to melt away when you approach problems through folding.

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