In a comment on a prior post my friend Amy told me about this Carl Sagan talk about the 4th dimension:

I decided to have the boys watch the video and then talk to start our Family Math project for today. After they watched it we discussed the parts they found interesting.

My younger son thought these two things were interesting:

(1) How the apple appeared as it fell through “Flatland”, and also how the creatures in Flatland interacted with the apple.

(2) The other 2D world that was curved.

My older son found these parts interesting:

(1) The discussion of projecting images from one dimension to a lower dimension, and

(2) The idea that lower dimensional things would have a hard time, but not an impossible time, noticing higher dimensions.

Right at the end we talked about the similarity between Carl Sagan walking around the sphere and (i) Vi Hart’s “Wind and Mr. Ug” video and (ii) a bicycle trip around a Klein Bottle. These are two of my all time favorite videos – sadly, though, the Klein Bottle video is no longer on youtube ðŸ˜¦ Luckily Wind and Mr. Ug remains:

Definitely a fun little project today – always fun to hear the boys’ ideas about complicated math topics ðŸ™‚