Cartesian and parametric equations
The Cartesian equation for the catenary is:
where is a parameter determining how much the catenary opens up.
The catenary is described as follows: it is the shape taken by a hanging flexible wire under the influence of uniform gravitational force, when supported at the ends. Here, the downward direction gravitationally corresponds to the negative -axis, and the parameter is related to the extent of gravitational force.
A surface of revolution corresponding to this planar curve is: catenoid