# B3D Chapter 9

## Lisa Eckstein

*Please read my tardy (tsk tsk ) chapter 8 response.*
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?

Prof. Banchoff's response

*moocow@brown.edu*