A ruled surface is called a right conoid if it can be generated by moving a straight line intersecting
a fixed straight line such that the lines
are always perpendicular (Kreyszig 1991, p. 87).
Taking the perpendicular plane as the 
-plane and the line to be the x-axis
gives the parametric equations
(Gray 1997). Taking 
and 
gives the helicoid.
See also
Conoid,
Helicoid,
Plücker's Conoid,
Right
Circular Conoid,
Wallis's Conical Edge
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References
Dixon, R. Mathographics. New York: Dover, p. 20, 1991.Ferréol, R. "Conoid."
https://mathcurve.com/surfaces.gb/conoid/conoid.shtml.Gray,
A. Modern
Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca
Raton, FL: CRC Press, pp. 450-452, 1997.Kreyszig, E. Differential
Geometry. New York: Dover, 1991.Referenced on Wolfram|Alpha
Right Conoid
Cite this as:
Weisstein, Eric W. "Right Conoid." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RightConoid.html
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