I saw a really neat post from Jordan Ellenberg last week:

Jordan Ellenberg’s “The Quarter Circle Game” blog post

It looked like something that the boys might enjoy playing with, so we gave it a shot this morning. Thankfully Ellenberg included some code in his blog post which made it really easy to implement this game in Mathematica. We’ll get to the computer simulations in the last video, but I started out by just explaining the game:

Now we tried to solve the game for a circle of radius 3. I started out with this extra small version of the game to make sure that the kids understood the rules and also to be sure that they knew what “winning position” and “losing position” meant:

Now we moved on to a circle of radius 6. This example was a little harder, but it really helped both kids get to the finish line on understanding how the game worked. I definitely think anyone exploring this game with kids should run through a few small examples first since there are a few potential areas of confusion that probably aren’t obvious to adults.

Here’s how this next case went:

Finally, we moved to the computer program. Roughly speaking the first 3 min of this video are me explaining the code, and the last 5 are playing around with different cases. It was fun to see the kids describe the different patterns they were seeing.

Also, my older son wanted to explore the ratio of winning points to losing points inside the circle. We’ll either tackle that off line or maybe for a project tomorrow.

It is always super fun to be able to share ideas that are both accessible to kids interesting to professional mathematicians. I really like this game since it gives kids a nice opportunity to think through a pretty complex problem and also because the game is so easy to play with on a computer.

Thanks to Jordan Ellenberg for writing up his thoughts (and sharing his code!).