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plane curve
In mathematics, a plane curve is a curve in a plane, that may be either a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves.
==Smooth plane curve==
A smooth plane curve is a curve in a real Euclidean plane R2 and is a one-dimensional smooth manifold.
Equivalently, a smooth plane curve can be given locally by an equation , where is a smooth function, and the partial derivatives and are never both 0. In other words, a smooth plane curve is a plane curve which "locally looks like a line" with respect to a smooth change of coordinates.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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