I'm looking for a good topic to base my presentation on (length: 15-20 mins). I'm a freshman mathematics student, and my audience won't be skilled in mathematics beyond high-school maths. I've been looking all over, but I can't seem to find an inspirational subject - most are quite worn out. I'd love for it to be something related to topology or non-euclidean geometry. It doesn't matter if it gets somewhat abstract; I'll be able to tackle the pedagogy part. I'm just mostly out to make my audience see some interesting things in mathematics and make them think about it.
I'd love it if somebody would be so kind as to help me out here!
Knot Theory should be a winner. Here are some notes by a colleague, although you'll probably want to look at the chapter before this one to see where it's coming from.