A comment on yesterday’s blog pointed me to some fun problems from the Julia Robinson Math Festival:
Julia Robinson math festival problems
It was exciting to see these problems and I really enjoyed played around with them a little bit yesterday afternoon. With nothing specific planned for our Family Math today I thought picking two of them to work through with the boys would make for a fun project this morning. Since my younger son is just starting to learn some basic geometry, I picked two of the problems that didn’t require any advanced geometry, but I’ll definitely keep the complete list in mind when I’m looking for other geometry projects in the future.
The first problem we looked at was problem #5 in the link above:
A circle of radius 15” intersects another circle, radius 20”, at right angles (see below). What is the difference of the areas of the non-overlapping portions.
On thing that made this problem attractive is that had some similarities with the problem we looked at yesterday. The boys found a nice solution and also avoided the trap set by the problem writers!
The second problem I picked from the above link was #8 – a neat Pythagorean identity that I’d not seen before.
This problem gave them a bit more difficulty, though the did remember a few things from Numberphile’s Blob Pythagorean Theorem video, so that was nice to hear. After struggling to figure out how to get started, they eventually decided to check out what would happen in a 3-4-5 triangle – a great way to get started!
The interesting thing about this video, though, is just listening to the kids trying to get their arms around the problem. Similar to many previous examples, the path to the solution isn’t a straight line.
We paused the last video because we’d gone over 5 minutes, but we just turned the camera on and off. The next video just picks up on the calculation we were doing for the 6-8-10 triangle. At the end of the last video there was a bit of confusion between the radius and the diameter of the circles. With that confusion out of the way we get to the solution of the problem without too much trouble:
So, thanks to Ben for pointing out this great list of problems from the Julia Robinson Math Festival. Can’t wait to use a few more of these problems in future math projects!
Mike's Math Page 
Wow that was fast and fun to watch in the videos. Btw: you should have your sons prove that any triangle circumscribed in the circle is a right triangle. That’s more fundamental than these problems and also a cool proof.