Generalized Cone


A ruled surface is called a generalized cone if it can be parameterized by x(u,v)=p+vy(u), where p is a fixed point which can be regarded as the vertex of the cone. A generalized cone is a regular surface wherever vy×y^'!=0. The above surface is a generalized cone over a cardioid. A generalized cone is a developable surface and is sometimes called "conical surface."

See also


Explore with Wolfram|Alpha


More things to try:


Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 439-441, 1997.Kern, W. F. and Bland, J. R. "Conical Surfaces." §23 in Solid Mensuration with Proofs, 2nd ed. New York: Wiley, p. 57, 1948.

Referenced on Wolfram|Alpha

Generalized Cone

Cite this as:

Weisstein, Eric W. "Generalized Cone." From MathWorld--A Wolfram Web Resource.

Subject classifications