Ran across an interesting problem in our Introduction to Geometry book today that reminded me of an old Numberphile video. My son didn’t make the connection right away, but he did have some interesting observations about the problem so I thought it would make a fun little project.

I wanted to do a quick review of the problem first, but an accidental mistake sent us down the wrong path at the start. We sort of start over about 2 minutes in to the video below. Solving problems isn’t always a straight line . . .

Now that we were on the right path, we finished up the calculation and talked about the geometric situation. He recognized that the Pythagorean theorem was hanging around somewhere, and that there might be an analogous theorem for half circles:

After we finished up I had him watch Numberphile’s excellent “blob Pythagorean theorem” video featuring Harvard’s Barry Mazur:

So, a fun morning project (even with the little false start). Nice to see some of the ideas in Numberphile’s videos coming up when we study geometry.

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