hopefully we all know x^2 + y^2 =1 and x=cost y=sint, t between 0 and 2pi. There's also one with slope; x= (1-t^2)/(1+t^2) y= (2t)/(1+t^2) I was wondering if this counts as a separate one x+iy=e^it, t also between 0 and 2pi or if this is analogous to the trig parameterization. I don't know a whole lot of trig(I'm not really a math man per se), but something in my gut tells me these two aren't really different... Anyway, I was just curious. I'd also be interested in any other ones. I don't know much about hyperbolic geometry, can there be a unit circle for that? I'm also starting to work through something as a set of ratios, but does anyone else have any other ideas?