I have already asked myself (and been asked) a couple of times what would be possible topics for undergraduate seminars. In such a seminar students are given passages of a book (or even paper) which they have to present to their fellow students.
As an analysist I sometimes feel that the topics get very advanced quickly, making it hard to include second year students (that have seen pointset topology, calculus, measure theory, a bit of abstract algebra and an intro to numerics). The one time I run a seminar, I picked Devaney's book "An introduction to chaotic dynamical systems", which gives a down-to-earth intro to chaotic systems and does not use much, still is a very fun topic also interesting for more advanced students. My question would be:
Do you know other such "easy" (not many prerequisites) and "non-technical" topics that would be suitable for an undergraduate seminar?
I am not sure this is a suitable question as it quite open and has no definitive answer. If you feel I should change it in some way or ask it somewhere else, please let me know (I mostly answer questions and have not asked many so far).
I think that arithmetic billiards can fit your requirements. Wikipedia has the article Arithmetic billiards and Wolfram MathWorld has the article Billiards.