Acnode

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

For example the equation

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

and ${\displaystyle x^{2}(x-1)}$ is non-negative only when ${\displaystyle x}$ ≥ 1 or ${\displaystyle x=0}$. Thus, over the real numbers the equation has no solutions for ${\displaystyle x<1}$ except for (0, 0).

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