A ruled surface is called a generalized cone if it can be parameterized by , where is a fixed point which can be regarded as the vertex of the cone. A generalized cone is a regular surface wherever . The above surface is a generalized cone over a cardioid. A generalized cone is a developable surface and is sometimes called "conical surface."

# Generalized Cone

## See also

Cone## Explore with Wolfram|Alpha

## References

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. https://mathworld.wolfram.com/GeneralizedCone.html