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.

See also

Generalized Helix, Helicoid, Helix

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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.

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Generalized Helicoid

Cite this as:

Weisstein, Eric W. "Generalized Helicoid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GeneralizedHelicoid.html

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