A catenary curve is the shape that a flexible chain or cable assumes when it is hung between two points and allowed to sag under its own weight. This curve is mathematically defined by the hyperbolic cosine function, which describes how the curve forms a smooth, U-shaped line. The catenary is often seen in structures like bridges and power lines. The term "catenary" comes from the Latin word "catena," meaning "chain." This curve is distinct from a parabola, which is often mistakenly used to describe similar shapes. Notable examples of catenary curves can be found in the design of the Gateway Arch in St. Louis and the Sagrada Família in Barcelona.