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I wanna tell you about a really lovely problem. Suppose you have a circle, how many ways can you draw it? Well, theres only one way. I mean, we could make it bigger, we could make it smaller, we could move it around the paper, but theres only one way. So, the answer for one circle is 1. What if you have two cicrles? They could be inside each other. They could cross each other. Well, they could be separated. So for two circles - 3 ways. And I better tell you what the rules are. We dont allow this kind of thing, we dont allow two circles to just kiss. Theyve gotta make up their mind, theyve gotta overlap or theyve gotta be separate. No, thats not allowed. And when we get to more circles, youre not allowed to have three going through a point. Thats not allowed either. Whats more, were doing this on a piece of paper. Were doing it in - technically were doing it in the affine plane were not doing it on the projective plane. If we were doing projective geometry we could take a