An acnode is an isolated point not on a
curve, but whose
coordinates satisfy the equation of the curve. The term "isolated point" or "hermit point" is an equivalent term. Acnodes commonly occur when studying
algebraic curves over
fields which are not
algebraically closed, defined as the zero set of a polynomial of two variables. For example the equation has an acnode at the origin of , because it is equivalent to and is positive for , except when . Thus, over the real numbers the equation has no solutions for except for (0, 0). In contrast, over the complex numbers the origin is not isolated since square roots of negative real numbers exist.
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NODO ISOLATO [MATEMATICA]. PUNTO DOPPIO ISOLATO [MATEMATICA]