Interesting Topic for Proofs Class I am teaching one of those university level classes where students learn enough proof theory to do their higher undergraduate courses.  In such a class, you need things for the students to prove.  What seems to be the norm in textbooks is a little bit of number theory (divisibility, odd/even numbers, etc.), some combinatory reasoning, and modular integers.  My question concerns finding a subject of a more geometric flavor.  It could be a subject from algebra, topology, or analysis, just as long as it is less discrete as the other subjects. Graph theory is taught in some books, but that boils down to combinatorics.
I understand if this question is removed for not meeting the standards of this site.  I'm just hoping that it is interesting enough to the community to remain.  Thanks.

Perhaps the Kissing Circles problem?
I will try to update the answer if I think of more.
