Sharing an idea from Experiencing Geometry with kids

This week learned about the book Experiencing Geometry by David Henderson and Diana Taimina. Unfortunately I learned about the book through people sharing news about David Henderson’s death. But despite the terrible circumstances, the book was captivating.

This morning I picked an idea from the book to share with the boys. The idea is from chapter 16 and is about drawing a circle through three points in a plane chosen at random.

Here’s the introduction to the problem. My younger son struggled a bit in the beginning to remember the ideas, but they did come to him eventually. That little struggle made me happy that we were looking at these geometric ideas today:

After we’d talked through some of the introductory ideas, I had the boys talk about their thoughts on the geometry in a bit more detail. I was especially happy that my younger son was able to sketch a proof that the perpendicular bisector was equidistant from the two endpoints of a line segment:

I had the boys work through the constructions off camera and then explain what they did. My older son approached the problem through folding:

My younger son worked for about 15 min on his construction – he works in a way that is so much more detailed than me! Here’s his work and his explanation which includes a nice discussion of why the center of the circle is outside of the triangle he drew: