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  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.

 References 

Category:Geometry