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In forming a soap film on a wire frame, we can make a surface. Such a surface is called "a minimal surface." In mathematical terms, a minimal surface is a surface with a mean curvature of zero.
Various kinds of minimal surfaces are known. We can make a surface by rotating a catenary once around the axis. This is called a catenoid. We also can make a surface swept out by a line rotating with uniform velocity around an axis perpendicular to the line and simultaneously moving along the axis with uniform velocity. This surface is called a helicoid. A catenoid and a helicoid are representative minimal surfaces.
It is very interesting that we can make a continuous and isometric deformation of a catenoid to a helicoid such that every member of the deformation family is minimal. Observe this deformation.

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