21 Jul
2012
21 Jul
'12
8:54 a.m.
I'd say that since a circle in R^2 is determined by its center and radius, the space of circles is naturally isometric to R^2 x (0,oo). For the general equation below to give a circle, it must hold that B^2 + C^2 > 4AD. So the space of coefficients (mod giving the same circle) isn't quite P^3. --Dan << . . . the general equation of a circle is: A(x^2 + y^2) + Bx + Cy + D = 0 which forms a projective 3-space of possible circles.
________________________________________________________________________________________ It goes without saying that .