Catenoid

  A catenoid is a three-dimensional shape made by rotating a catenary curve around the x axis. Not counting the plane, it is the first minimal surface to be discovered. It was found by Leonhard Euler in 1744.

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Essential Laboratory Skills Guide

A physical model of a catenoid can be formed by dipping two circles into a soap solution and slowly drawing the circles apart.

One can bend a catenoid into the shape of a helicoid without stretching. In other words, one can make a continuous and isometric deformation of a catenoid to a helicoid such that every member of the deformation family is minimal. A parametrization of such a deformation is given by the system

for , with deformation parameter .