An acnode is an isolated point in the solution set of a polynomial equation in two real variables. Equivalent terms are isolated point and hermit point.

For example the equation

has an acnode at the origin, because it is equivalent to

. Thus, over the real except for (0, 0).

In contrast, over the complex numbers the origin is not isolated since square roots of negative real numbers exist. In fact, the complex solution set of a polynomial equation in two complex variables can never have an isolated point.

An acnode is a critical point, or singularity vanish. Further the Hessian matrix of second derivatives will be positive definite or negative definite, since the function must have a local minimum or a local maximum at the singularity.

See also

• Singular point of a curve

• Crunode

• Cusp

• Tacnode

References

es:Punto singular de una curva#Acnodos