Helicoid

[Gr. helikoeidéo. See HELIX.) ( Geom.) There are two surfaces of this name: the developable helicoid or screw-surface, whose generators are the tangents to a common helix: and the skew helicoid, generated by a line which moves so as always to rest on the helix and cut its axis perpendicularly. The former is simply the developable osculatrix of the helix - a leve lop able surface, therefore, of which the helix is the cuspidal edge; the latter is a conoid having the helix for its directing curve; it is, in fact, the focus of the principal normals of the helix. The developable helicoid is circumscribed to the skew helicoid, the helix itself being the curve of contact. Every plane perpendicular to the axis of the helix cuts the developable helicoid in the involute of the circular section of the cylinder on which that helix is traced. The developable helicoid is also the cyclifying surface of the helix; that is to say, when the surface is unfolded into a plane, the helix becomes a circle.