Definition

1. Noun:
   • A curve with no endpoints: A line that forms a complete loop, starting and ending at the same point, with no breaks or gaps. It encloses an area.

Usage

• The term "closed curve" is used in mathematics, geometry, and engineering to describe a continuous, unbroken loop.
• It is often contrasted with an "open curve," which has two distinct endpoints.

Examples

• Noun:
  • A circle is a simple example of a closed curve.
  • The artist drew a complex closed curve on the canvas.
  • In topology, a closed curve is also called a loop.

Advanced Usage

• "Simple closed curve" or "Jordan curve": A closed curve that does not cross itself. It divides the plane into an interior and an exterior region.
  • A square is a simple closed curve, while a figure-eight is a closed curve that is not simple.

Variants and Related Words

• Curve (n): A line that deviates from being straight.
• Open curve (n): A curve with two distinct endpoints.
• Loop (n): A shape produced by a curve that bends around and crosses itself, or a simple closed curve.

Synonyms

• Loop
• Circuit

Related Phrases

• Closed path: Often used interchangeably in some contexts, especially in vector calculus and physics.
• Closed contour: Used in fields like complex analysis and engineering.

Idioms

Noun

1. a curve (such as a circle) having no endpoints