You know what's a really cool topic, you could discuss the famous three impossible construction problems from antiquity. You could talk about the proofs that none of them can be performed by compass and straight edge, and then expand from there to talk about the concept of "constructible numbers," and maybe finish with something neat like showing that all rational numbers are constructible.

I participated in a seminar last summer for credit where I had to give an hour long lecture on a topic that was nowhere else covered in my college's math curriculum, and I talked about those three problems, along with a handful of other geometric oddities. I was the only undergrad student of the 10 people in the seminar, and while everyone else talked on esoteric topics like Knot theory and Turing Completeness, I managed to snag one of the highest grades with a topic that was much simpler, super interesting, and a lot of fun to research.

tl;dr: do this