The Unduloid

a

1.6

b

1.

u

15.

First studied by Delaunay [1], the unduloid (or onduloid) is a surface of revolution of an elliptic catenary with constant nonzero mean curvature (in this case, the reciprocal of twice the major axis length,

1/2a

). It can be obtained by tracing the focus of a rolling ellipse along a fixed line. This surface appears in fields like string theory [2] and carbon nanotubes [3].