# Crunode

In mathematics, a **crunode** (archaic) or **node** is a point where a curve intersects itself so that both branches of the curve have distinct tangent lines at the point of intersection. A crunode is also known as an *ordinary double point*.^{[1]}

For a plane curve, defined as the locus of points *f*(*x*, *y*) = 0, where *f*(*x*, *y*) is a smooth function of variables *x* and *y* ranging over the real numbers, a crunode of the curve is a singularity of the function *f*, where both partial derivatives and vanish. Further the Hessian matrix of second derivatives will have both positive and negative eigenvalues.

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