in like a LION >:3

Bet you thought I'd forget didn't you, my non-existent audience? Well, more or less I did. Between McNairs, homework, my neglected research and upcoming poster presentation at the ACS meeting, not to mention taxes/FAFSA, community service and my newest charge: the backyard garden; yeah, I'm a bit frazzled.
So here's a short post... which should probably have some content besides my lame excuses. How about this:You may be able to guess what I'm getting at from the picture alone. I'm not sure if it's been done before or if this is some geometry thing that everyone thought was too obvious to ever point out to me but:
Placing a certain number of points equidistant on a circle and then drawing lines from each point to the others generates a certain number of equilateral polygons with that same number of sides. Using an even number of points will generate the same number of polygons as the odd number before it. Example, five points generate two pentagons, six points also generates two of its corresponding polygons. This is because the number of N-sided polygons that can be made is directly proportional to how many *pairs* of lines can be drawn from each point (note, the paired lines are at equal angles).
Something else that's kinda interesting: when drawing all these lines, it becomes apparent that even numbers of points generate symmetric forms, while odds generate centered forms. Anyway, I thought it was spiffy.
I don't know if all this is completely true because I haven't proven/disproven it. Someone else probably has, but I'd like to try it on my own as I figured this out on my own. It'll probably require some sort of inductive proof... though it seems pretty intuitive, so maybe observation alone is enough?... or ya know I could just ask a professor. That's what they're there for, right? :P

Whew, not so short after all. OK, I'm done being a math nerd now. Hopefully Spring Break won't be completely used up with poster prep and I'll be able to relax. I'm starting to fall apart...

Time to stay up all night to finish my art project. 'night.