Catenary curve

A catenary curve describes the shape formed by a flexible chain or rope hanging under its own weight when supported at its ends. Imagine a heavy chain draped between two points; it will create a smooth, U-shaped curve. This curve is important in engineering and architecture, as it appears in structures like bridges and arches. Mathematically, the catenary can be defined by a specific equation involving hyperbolic functions. Unlike a parabola, which is a similar U-shaped curve often described in physics, the catenary illustrates how the chain naturally settles into its most stable form.