Cylinder

Article By:

Frame, J. Sutherland Formerly, Department of Mathematics, Michigan State University, East Lansing, Michigan.

Last reviewed:2014

DOI:https://doi.org/10.1036/1097-8542.177500

The solid of revolution obtained by revolving a rectangle about a side is called a cylinder, or more precisely a right circular cylinder. More generally the word cylinder is used in solid geometry to describe any solid bounded by two parallel planes and a portion of a closed cylindrical surface. In analytic geometry, however, the word cylinder refers not to a solid but to a cylindrical surface (see illustration). This is a surface generated by a straight line which moves so that it always intersects a given plane curve called the directrix, and remains parallel to a fixed line that intersects the plane of the directrix. (Part or all of the directrix may consist of straight-line segments.) The generating line in each of its positions is called an element of the cylinder, and a section of the cylinder made by a plane perpendicular to the elements is called a right section. All right sections of a cylinder are congruent. A circular cylinder (cylindrical surface) is one whose right sections are circles. Its other sections made by planes cutting all the elements are ellipses. Cylinders whose right sections are ellipses, parabolas, or hyperbolas are called elliptic cylinders, parabolic cylinders, or hyperbolic cylinders, respectively. All these are quadric cylinders. The lateral surface of a prism is a special type of cylindrical surface whose directrix and right sections are polygons.

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