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Theory of plane curves by w van der woude communicated at the meeting of december 20 1947 i ntroduction in the development of conformal differential geometry several different lines of research were followed now it is remarkable that in all theories just in the beginning the introduction to the theory of plane curves is not. Quartic curves 1874 mathematische annalen vol 7 emphasized the dis tinction between odd and even circuits and proved the important theorem that in one and only one of the two regions f into which a plane is divided by a non singular even circuit odd circuits can lie he showed p 426 that a quartic. Review curves on the plane example i an ellipse centered at p 00 with radius a and b x2 a2 y2 b2 1 a sphere is the particular case a b r i a hyperbola with asymptotes y x x2 y2 1 i a hyperbola with asymptotes y b a x x2 a2 y2 b2 1 review curves on the plane example i a parabola with minimum at 00 y x2 i a parabola with minimum at ab