- Acnode
An acnode is an isolated point not on a
curve , but whosecoordinates satisfy the equation of the curve. The term "isolated point " or "hermit point " is an equivalent term. [ [http://eom.springer.de/I/i052770.htm Encyclopaedia of Mathematics, Springer Online Reference Works.] ] [ [http://eom.springer.de/A/a130100.htm Encyclopaedia of Mathematics, Springer Online Reference Works] ]Acnodes commonly occur when studying
algebraic curve s over fields which are notalgebraically 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.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. Hence the function has a local minimum or local maximum.ee also
*
Singular point of a curve
*Crunode
*Cusp
*Tacnode References
*cite book |last=Porteous |first=Ian |title=Geometric Differentation |year=1994 |publisher=
Cambridge University Press |id=ISBN 0-521-39063-X
Wikimedia Foundation. 2010.