I was just thinking about the expression "square the circle", and I realize I'm not totally sure about what it means. People were trying to construct a square with an area identical to a given circle...using only a compass and a straight-edge, maybe? Must be, because otherwise...hm. But you really can do so in non-Euclidean geometry, IIRC? But can your straight-edge be getting a lot of play in the non-Euclidean world, or do you have an infinite series of curved-edges to use? That could take up a lot of room. Someone help me out here.
This just reminds me that one of the things I have looked forward to in having school-age children is that I will very slowly get to re-learn all of math, at a painless pace. All the worries I'll have when Zoë and Violet are teenagers will surely be compensated by the fun of re-learning the calculus, right? That was the only part of HS math I liked. That, and graphing imaginary numbers on those wonky polar graph things.
John has sucessfully explained zero to Zoë. She was counting the people in the elevator as they left, until only she and I were on, and when we got out, she said "and now there's zero people in the elevator!" Right on for the null set, baby! I ran into a little trouble trying to explain infinity the other day, however. All in good time, I guess.