Generalized Cylinder


A ruled surface is called a generalized cylinder if it can be parameterized by x(u,v)=vp+y(u), where p is a fixed point. A generalized cylinder is a regular surface wherever y^'×p!=0. The above surface is a generalized cylinder over a cardioid. A generalized cylinder is a developable surface and is sometimes called a "cylindrical surface" (Kern and Bland 1948, p. 32) or "cylinder surface" (Harris and Stocker 1998, p. 102).

A generalized cylinder need not be closed (Kern and Bland 1948, p. 32).

Kern and Bland (1948, p. 32) define a cylinder as a solid bounded by a generalized cylinder and two parallel planes. However, when used without qualification, the term "cylinder" generally refers to the particular case of a right circular cylinder.

See also

Cylinder, Ruled Surface

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Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 439-441, 1997.Harris, J. W. and Stocker, H. "General Cylinder." §4.6.1 in Handbook of Mathematics and Computational Science. New York: Springer-Verlag, p. 103, 1998.Kern, W. F. and Bland, J. R. "Cylindrical Surface." §14 in Solid Mensuration with Proofs, 2nd ed. New York: Wiley, pp. 32-36, 1948.

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Generalized Cylinder

Cite this as:

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

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