Right Conoid

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 xy-plane and the line to be the x-axis gives the parametric equations


(Gray 1997). Taking h(u)=2u and theta(u)=u gives the helicoid.

See also

Conoid, Helicoid, Plücker's Conoid, Right Circular Conoid, Wallis's Conical Edge

Explore with Wolfram|Alpha


Dixon, R. Mathographics. New York: Dover, p. 20, 1991.Ferréol, R. "Conoid.", 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.

Subject classifications