Definition

1. Noun:
   • A specific mathematical curve: The curve that a perfectly flexible, uniform chain or cable forms when it is supported only at its ends and hangs freely under its own weight. This curve is described by a hyperbolic cosine function.

Examples of Usage

• Noun:
  • The shape of the hanging power line follows a catenary.
  • Engineers must calculate the catenary of the suspension bridge's main cable to ensure its stability.

Advanced Usage

• "Catenary arch": An arch that has the shape of an inverted catenary curve, which is a structurally efficient form for supporting its own weight.
  • The Gateway Arch in St. Louis is a famous example of a catenary arch.
• "Catenary system": In railways, the overhead wire system that supplies electricity to trains, named for its curved, hanging shape.
  • The train's pantograph maintains contact with the catenary to draw power.

Variants and Related Words

• Catenarian (adj): Relating to or having the form of a catenary. (Less common variant of as an adjective).
• Catenate (v): To connect in a series like links in a chain. (Shares the Latin root , meaning "chain").
• Catenoid (n): The surface generated by rotating a catenary curve around its axis.

Synonyms

• Chain curve: A direct descriptive synonym.
• Hanging chain curve: A descriptive phrase for the same shape.

Related Phrases

• To form a catenary: Describes the action of a cable or chain assuming this specific curve.
  • When suspended, the necklace will form a perfect catenary.

Related Idioms

(No common idioms are directly based on the word "catenary" due to its technical nature.)

Noun

1. the curve theoretically assumed by a perfectly flexible and inextensible cord of uniform density and cross section hanging freely from two fixed points