Introduction:
The helicoid is the only known ruled minimal surface,
other than a plane. It also has the interesting
property that, while its topology is finite, its Gaussian curvature is
infinite (when v = 0).
Definition:
Geometrically, the helicoid is defined by simultaneously rotating and
translating a line at constant speed about an axis to which it is perpendicular.
Properties:
Tangent Planes:
At u = u_{0}, v = v_{0},
the tangent plane to the surface is parameterized by:

Infinitesimal Area:
The infinitesimal area of a patch on the surface is given by

Gaussian Curvature:


Gaussian curvature of the surface.

Surface colored by Gaussian curvature.


Mean Curvature:


Mean curvature of the surface.

Surface colored by Mean curvature.


