Linked from

The 15 pages that link to Catenary, each with the reason it gives.

• Suspension bridgeRelated: A hanging cable’s shape helps explain the geometry and forces of the main cables.

• Euler–Lagrange EquationBroader topic: Minimizing gravitational potential energy gives the catenary through a variational equation.

• Filippo BrunelleschiRelated: Its structural principles help explain how masonry arches and domes transmit forces.

• ArchCompared with: An inverted catenary carries its own weight in pure compression, unlike many loaded arches.

• ParabolaCompared with: It can resemble a parabola, but its equation and physical origin differ.

• Hyperbolic functionsBroader topic: Its profile is expressed using hyperbolic cosine.

• Johann BernoulliRelated: Johann studied the curve and its relation to the brachistochrone problem.

• Jakob BernoulliRelated: Bernoulli joined the debate that identified the catenary as a distinct curve.

• Roman archCompared with: An inverted catenary illustrates a shape whose compression forces can flow naturally toward its supports.

• Eero SaarinenRelated: The Gateway Arch’s profile derives from an inverted catenary adjusted for structural design.

• Main cableRelated: A freely hanging main cable approximates this curve, modified by loads from the deck.

• Overhead LinesBroader topic: A catenary system suspends the contact wire while keeping it near a consistent height.

• Gateway ArchRelated: The Arch’s profile approximates an inverted catenary, shaping its iconic outline.

• Brachistochrone curveCompared with: It resembles a cycloid but describes static balance rather than minimum travel time.

• Inverse hyperbolic functionsRelated: Its equation uses cosh, while solving for horizontal position naturally introduces arcosh.