So I've been accepted into a research program at my school, and I'm to come up with a research topic to work on over the school year. My mathematics is limited to geometry, though after this year will encompass trig and pre-calc. Anyway, I'm interested in pure mathematics, but obviously my knowledge limits what I can do. Any original research is surely out of the question, so I've been thinking something along the lines of analyzing a conflicted area of study and coming to my own judgement. Some one suggested the concept of infinity, which certainly could be interesting. Any suggestions? and remember this has to be a YEAR of research.