Definition:Crunode

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

Definition

A crunode is a double point $P$ of the locus of an equation describing a curve which intersects itself in such a way that there are $2$ distinct tangents at $P$.

Examples

Folium of Descartes

Consider the folium of Descartes, given by the equation expressed in Cartesian coordinates as:

$x^3 + y^3 - 3 a x y = 0$

This has a crunode at $\tuple {0, 0}$.

Also known as

A crunode is also known as a node.

However, the term node has a number of different meanings, and hence its use in this context on $\mathsf{Pr} \infty \mathsf{fWiki}$ is deprecated.

Also see

• Definition:Acnode
• Definition:Double Point

• Results about crunodes can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): crunode
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): node: 1. (crunode)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): crunode
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): node: 1. (crunode)