Jordan curve

9.9

A closed loop on a flat surface, like a circle, that does not cross itself

noun

Specialized

: curva de Jordan

In topology, a Jordan curve divides the plane into an inside and an outside region.

Examples

Every simple closed shape, such as a circle or triangle, qualifies as a Jordan curve.
Every simple closed polygonal path is an example of a Jordan curve.
The professor illustrated the concept of a Jordan curve on the whiteboard.
A Jordan curve is essential in topology.
The mathematician explained the concept of a Jordan curve.
In topology, a Jordan curve separates a plane into a bounded interior and an exterior region.
When learning about topology, students often create examples of a Jordan curve using string.

Synonyms

simple closed curve

vsJordan curve

Specialized

7.9

A curved line on a flat surface that makes a closed loop without crossing itself, like a circle

is the same loop idea phrased more simply without stressing continuity

Surface Forms

Jordan curve singular

Jordan curves plural

Morphology

Jordan + curve

This is an eponymous technical term: 'Jordan' is a proper name and provides no semantic information about the shape, while 'curve' only signals a general bent line. A B1 learner who knows the constituents might infer it's some kind of curve but would not be able to derive the precise topological sense ('simple closed curve that does not cross itself'), so the expression is opaque.

Etymology

Jordan curve is named after the French mathematician Camille Jordan. Imagine drawing one closed curve on paper that does not cross itself — that 'loop' makes an 'inside' and an 'outside', and that simple closed line is a Jordan curve.