Crunode

Point where a curve intersects itself at an angle From Wikipedia, the free encyclopedia

Crunode

In mathematics, a crunode[1] (archaic; from Latin crux "cross" + node[2]) or node of an algebraic curve is a type of singular point at which the 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.[3][4]

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A crunode at the origin of the curve defined by

In the case of a smooth real plane curve f(x, y) = 0, a point is a crunode provided that both first partial derivatives vanish

and the Hessian determinant is negative:

[5]

See also

References

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