Catenary curve

Description

In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends. The curve has a U-like shape, superficially similar in appearance to a parabola, but it is not a parabola; it is a (scaled, rotated) graph of the hyperbolic cosine. . All catenary curves are similar to each other, having eccentricity equal to √2. Changing the parameter “a” is equivalent to a uniform scaling of the curve.