I had never been introduced to the axioms of plane geometry. I knew most of them, but I did not know that they had been formulated by Euclid. That's a handy thing to know.
Non-Euclidian geometry is still a little foreign to me. It's difficult to acknowledge that a triangle Might not have 180 degrees. It is possible for a triangle to have less than 180 degrees, or only more?
I like the idea that I could move to 4-space, re-orient myself, and become left-handed. Maybe that would improve my tennis game. Probably not.
The explanation of how Klein bottles are related to Mobius (yes, I know that has an umlaut, but I don't know how to do those) strips was very helpful.
I realize that this reaction is fairly short, but I felt that this chapter was very straightforward, and I don't really have any questions. This is the first math book that I've actually enjoyed and the first math class that I've liked in a long time. It's refreshing to have a class where mathematics isn't "just numbers."
Ignore the rest of this. I'm just writing it to confuse the machine in hopes that all of the important part will miraculously get transferred to the Web page.
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