Wiktionary
n. (context geometry English) A three-dimensional surface formed by rotation of a catenary
Wikipedia
A catenoid is a surface in 3-dimensional Euclidean space arising by rotating a catenary curve about its directrix (see animation on the right). Not counting the plane, it is the first minimal surface to be discovered. It was found and proved to be minimal by Leonhard Euler in 1744.
Early work on the subject was published also by Jean Baptiste Meusnier. There are only two minimal surfaces of revolution ( surfaces of revolution which are also minimal surfaces): the plane and the catenoid.
The catenoid may be defined by the following parametric equations:
$$x=c \cosh \frac{v}{c} \cos u$$
$$y=c \cosh \frac{v}{c} \sin u$$
z = v
In cylindrical coordinates:
$$\rho =c \cosh \frac{z}{c}$$
A physical model of a catenoid can be formed by dipping two circles into a soap solution and slowly drawing the circles apart.
The catenoid may be also defined approximately by the Stretched grid method as a facet 3D model.
Usage examples of "catenoid".
Various combinations of conic sections and the six surfaces of revolution symmetrical around an axis, the plane, the sphere, the cylinder, the catenoid, the unduloid, and the nodoid.
He could imagine the beautiful latticework of the gamma titanium aluminum, patterned in a tapestry of nodoids and catenoids like hooks and eyes, vibrating madly with the heat.
The circle and the globe began to stretch and distort, became unduloid and catenoid, and folded back Klein-bottle fashion into a nodoid surface.