While all the real physics students are doing fantastic undergraduate research, I spend my summers as a TA in the physics courses at EPGY. The relativity students cohabitate with the non-euclidean geometry students, and so last year I was privileged to receive a hospital-waiting-room lecture on the nonexistence of rectangles in hyperbolic geometry. (You always get to take at least one trip to the hospital at 2am when you’re a camp counselor. In the same waiting room, I met an old anthropologist who told me about his thesis work on Korean traditional witchcraft just after the war.) You can’t build a rectangle on the surface of a sphere, but you can build a plot with two North-South fences and two East-West fences (the N-S and E-W directions are only perpendicular at the equator).
There’s also a puzzle 33 up on Wild About Math!