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":
which has an acnode at $\tuple {0, 0}$.
Example: $y^2 = x^3 - x^2$
Consider the locus of the equation:
- $y^2 = x^3 - x^2$
This has an acnode at $\tuple {0, 0}$.
Also see
- Results about acnodes can be found here.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): acnode
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): acnode
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): isolated point (acnode)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): acnode
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): isolated point (acnode)
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): acnode