What does catenary mean?
A catenary is the distinctive curve that forms when a flexible chain or cable hangs freely between two points under its own weight. Unlike a parabola, which it superficially resembles, the catenary follows a hyperbolic cosine function — a distinction Galileo famously got wrong and later mathematicians proved rigorously. The word derives from the Latin 'catena,' meaning chain, and entered English usage in the seventeenth century. In engineering, the catenary describes the sagging shape of suspension-bridge cables, power lines, and overhead railway wires. Remarkably, when inverted, the same curve provides the strongest possible shape for an arch, which is why architects from Robert Hooke to Antoni Gaudí exploited it: Hooke observed that a hanging chain reveals the form a standing arch should take, and St. Louis's Gateway Arch is a monumental inverted catenary. The term appears mainly in technical writing but rewards general readers as a striking example of mathematics embedded in everyday structures.
nounA catenary is the curve formed by a flexible chain or cable of uniform density hanging freely between two fixed points under gravity. It is described mathematically by the hyperbolic cosine function.
- The curve assumed by a freely hanging chain or cable under its own weight.
- A structure or arch built in this curve's inverted form.
"The heavy chain between the two posts sagged into a perfect catenary."
"Power lines strung between pylons trace a natural catenary across the landscape."
"Gaudí used inverted catenary models to determine the ideal shape of his arches."
Standard English plural; used chiefly in technical and mathematical writing.
"The textbook compared several catenaries formed by chains of different lengths."
The Gateway Arch in St. Louis is an upside-down catenary — the exact shape a hanging chain would make if you flipped it over.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of catenary
The word 'catenary' comes from the Latin 'catena,' meaning 'chain,' via New Latin 'catenarius' — literally 'relating to a chain.' It was adopted into English scientific vocabulary in the seventeenth century as mathematicians studied the shape of a hanging chain. Its cognates include the English words 'catena,' 'concatenate,' and 'chain' itself, all tracing back to the same Latin root.
Related word forms
How catenary is actually used
Primarily technical or mathematical in register; common in engineering and architecture contexts. The adjective use ('a catenary curve') is more frequent than the standalone noun.
Easily confused with catenary
A parabola is a quadratic curve, while a catenary is the hyperbolic cosine shape of a hanging cable; they look similar but are mathematically distinct.