I found this chapter extremely satisfying. In my high school geometry textbook, the last chapter was on non-Euclidean geometry. Our teacher said that if we had enough time at the end of the year, we would study this topic, but alas, there wasn't time. Finally, after all these years of waiting, I get to learn about non-Euclidean geometry! (And with a much better text than that geometry book.)
I was sorry that there was no definition or explanation of a pseudosphere. In The Fourth Dimension, Rudy Rucker describes a true pseudosphere as a 2D surface which is bigger than a plane. He says that a shape like the one pictured on page 187 of B3D is actually "a sewed-together sector of the pseudosphere", and he calls it "Gabriel's Horn".
I have been intrigued by the Mobius band for as long as I can remember, and I am even more enchanted by the Klein bottle, which I only learned about a few years ago. I find the Klein bottle beautiful to look at and fascinating conceptually. Orientability, and its relation to flipping through higher dimensions, has been one of my favorite topics this semester.
Why are the followers of Immanuel Kant so uptight?
moocow@brown.edu