A plane curve can often be represented in Cartesian coordinates by an implicit equation of the form $${\displaystyle f(x,y)=0}$$ for some specific function f. If this equation can be … See more

An algebraic plane curve is a curve in an affine or projective plane given by one polynomial equation $${\displaystyle f(x,y)=0}$$ (or $${\displaystyle F(x,y,z)=0,}$$ where F is a homogeneous polynomial, in the projective case.)
Algebraic curves … See more

A smooth plane curve is a curve in a real Euclidean plane $${\displaystyle \mathbb {R} ^{2}}$$ and is a one-dimensional smooth manifold. … See more

• Algebraic geometry
• Convex curve
• Differential geometry
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• Weisstein, Eric W. "Plane Curve". MathWorld. See more