The surface generated by a twisted curve 
when rotated about a fixed axis 
and, at the same time, displaced parallel
to 
so that the velocity of displacement is always proportional to the angular
velocity of rotation.
Generalized Helicoid
See also
Generalized Helix, Helicoid, HelixExplore with Wolfram|Alpha
References
do Carmo, M. P.; Fischer, G.; Pinkall, U.; and Reckziegel, H. "General Helicoids." §3.4.3 in Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 36-37, 1986.Fischer, G. (Ed.). Plate 89 in Mathematische Modelle aus den Sammlungen von Universitäten und Museen, Bildband. Braunschweig, Germany: Vieweg, p. 85, 1986.Kreyszig, E. Differential Geometry. New York: Dover, p. 88, 1991.Referenced on Wolfram|Alpha
Generalized HelicoidCite this as:
Weisstein, Eric W. "Generalized Helicoid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GeneralizedHelicoid.html