A catenoid

A catenoid is a three-dimensional shape made by rotating a catenary curve around the x axis. Image File history File links Catenoid. ... Image File history File links Catenoid. ... 2-dimensional renderings (ie. ... In geometry, two objects are of the same shape if one can be transformed to another (ignoring color) by dilating (that is, by multiplying all distances by the same factor) and then, if necessary, rotating and translating. ... In mathematics, the catenary is the shape of a hanging flexible chain or cable when supported at its ends and acted upon by a uniform gravitational force (its own weight). ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ...

A catenoid is one of several types of minimal surfaces. Verrill Minimal Surface In mathematics, a minimal surface is a surface with a mean curvature of zero. ...

A physical model of a catenoid can be formed by dipping 2 circles into a soap solution, (popping any film in the center of the circle), and slowly drawing the circles apart. A circle, in Euclidean geometry, is the set of all points at a fixed distance, called the radius, from a fixed point, the centre. ...

One can make a continuous and isometric deformation of a catenoid to a helicoid such that every member of the deformation family is minimal. In mathematics, a continuous function is a function in which arbitrarily small changes in the input produce arbitrarily small changes in the output. ... The helicoid is one of the first minimal surfaces discovered. ...