Unduloid

In geometry, an unduloid, or onduloid, is a surface with constant nonzero mean curvature obtained as a surface of revolution of an elliptic catenary: that is, by rolling an ellipse along a fixed line, tracing the focus, and revolving the resulting curve around the line.

These are the plane, cylinder, sphere, the catenoid, the unduloid and nodoid.

In fact, the mean curvature across the entire surface is always the reciprocal of twice the major axis length: 1/(2a).

Also, geodesics on an unduloid obey the Clairaut relation, and their behavior is therefore predictable.

First documented in 1970, passing a strong electric current through a thin (0.16—1.0mm), horizontally mounted, hard-drawn (non-tempered) silver wire will result in unduloids forming along its length.