I saw a really neat new video from Grant Sanderson this morning:

We’ve actually looked at the ideas Grant is sharing here before, but my son didn’t remember:

Grant Sanderson’s “Fair Division” video shows a great math project for kids

For today I asked my younger son (in 7th grade) to watch the video and take some notes. After he finished we started taking about what he saw. He was interested in the Borsukâ€“Ulam theorem and also he thought the “stolen necklace problem” was pretty neat:

Next we talked about the proof of the Borsuk-Ulam theorem. I was really happy that most of the main ideas that Grant shared in his video stuck in my son’s mind.

We wrapped up by talking about the “stolen necklace” problem. We did a few examples about that problem and then had a fun discussion about the equation for a sphere. My son was curious about the difference between the boundary of the sphere and the all of the points inside the sphere. In particular, he was wondering why the equation for a sphere Grant used was and not

From there we had an interesting discussion about dimension. I didn’t expect the conversation to go in that direction, but I guess you never know what a kid is going to take away from a video about some pretty advanced math ideas đź™‚