Catenary

A catenary is a type of curve. An ideal chain hanging between two supports and acted on by a uniform gravitational force makes the shape of a catenary. (An ideal chain is one that can bend perfectly, cannot be stretched and has the same density throughout.) The supports can be at different heights and the shape will still be a catenary. A catenary looks a bit like a parabola, but they are different.
The equation for a catenary in Cartesian coordinates is
where formula_2 is a parameter that determines the shape of the catenary and is the hyperbolic cosine function, which is defined as
Hence, we can also write the catenary equation as
The word "catenary" comes from the Latin word "catena", which means "chain". A catenary is also called called an alysoid and a chainette.