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    Simple Double Point

    Definition

    An ordinary double point of a plane curve is point where a curve intersects itself such that two branches of the curve have distinct tangent lines. Ordinary double points of plane curves are commonly known as crunodes. Ordinary double points of a plane curves given by f(x, y) = 0 satisfy f = f_x = f_y = 0, where f_x denotes a partial derivative.

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