Acnode
From Wikipedia, the free encyclopedia
An acnode is an isolated point not on an curve, but whose coordinates satisfy the equation of the curve.
Acnodes commonly occur when studying algebraic curves, which are defined as the zero set of a function of two variables. For example the equation
- <math>f(x,y)=y^2-x^2(1-x)=0\;</math>
has an acnode at the origin.
An acnode is a singularity of the function, where both partial derivatives <math>\partial f\over \partial x</math> and <math>\partial f\over \partial y</math> vanish. Further the Hessian matrix of second derivatives will be positive definite. Hence the function has a local minimum or local maximum.
[edit] See also
- Singular point of a curve
- Crunode
- Cusp or Spinode
- Tacnode
[edit] References
- Porteous, Ian (1994). Geometric Differentation. Cambridge University Press. ISBN 0521-39063-X.zh:孤立点
