What does acnode mean?
Definitions for acnode
ac·n·ode
This dictionary definitions page includes all the possible meanings, example usage and translations of the word acnode.
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Wiktionary
acnodenoun
An isolated point not upon a curve, but whose coordinates satisfy the equation of the curve so that it is considered as belonging to the curve.
Etymology: acus + nodus
Wikipedia
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 f ( x , y ) = y 2 + x 2 − x 3 = 0 {\displaystyle f(x,y)=y^{2}+x^{2}-x^{3}=0} has an acnode at the origin, because it is equivalent to y 2 = x 2 ( x − 1 ) {\displaystyle y^{2}=x^{2}(x-1)} and x 2 ( x − 1 ) {\displaystyle x^{2}(x-1)} is non-negative only when x {\displaystyle x} ≥ 1 or x = 0 {\displaystyle x=0} . Thus, over the real numbers the equation has no solutions for x < 1 {\displaystyle x<1} 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, of the defining polynomial function, in the sense that both partial derivatives ∂ f ∂ x {\displaystyle \partial f \over \partial x} and ∂ f ∂ y {\displaystyle \partial f \over \partial y} 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.
Webster Dictionary
Acnodenoun
an isolated point not upon a curve, but whose coordinates satisfy the equation of the curve so that it is considered as belonging to the curve
Etymology: [L. acus needle + E. node.]
Wikidata
Acnode
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 non-negative when ≥ 1 and when . Thus, over the real numbers the equation has no solutions for except for. In contrast, over the complex numbers the origin is not isolated since square roots of negative real numbers exist. An acnode is a singularity of the function, where both partial derivatives and vanish. Further the Hessian matrix of second derivatives will be positive definite or negative definite. Hence the function has a local minimum or a local maximum.
Anagrams for acnode »
canoed
deacon
Numerology
Chaldean Numerology
The numerical value of acnode in Chaldean Numerology is: 7
Pythagorean Numerology
The numerical value of acnode in Pythagorean Numerology is: 6
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"acnode." Definitions.net. STANDS4 LLC, 2025. Web. 15 Feb. 2025. <https://www.definitions.net/definition/acnode>.
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