# Catenary

From Diffgeom

## Definition

### Cartesian and parametric equations

The Cartesian equation for the catenary is:

where is a parameter determining how much the catenary opens up.

### Physical definition

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.

## Constructs

*A surface of revolution corresponding to this planar curve is:* catenoid