Definition:Acnode

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This page is about Acnode. For other uses, see Node.

Definition

An acnode is a singular point of the locus of an equation describing a curve which is not actually on that curve.


Also known as

An acnode is also known as an isolated point, but the latter term has a wider application in the field of topology, of which the acnode is an example.


Examples

Policeman on Point Duty

Consider the locus of the equation:

$x^2 y^2 = a^2 \paren {x^2 + y^2}$

This is the classic quartic curve "policeman on point duty":


Policeman-on-point-duty.png


which has an acnode at $\tuple {0, 0}$.


Also see

  • Results about acnodes can be found here.


Sources