User:Jim.belk/Draft:Cylinder

A cylinder is a three-dimensional geometric shape obtained by translating a circle along a perpendicular axis. The two ends of a cylinder are congruent circles, and the side is a single curved surface. The shape of a cylinder is determined by the radius of the circle as well as the length or height of the cylinder along its axis.

An infinite cylinder is a cylinder without ends, having infinite length or height. Such a cylinder may be defined as the the locus of points within a given distance of a given line. A finite cylinder may be obtained from an infinite one by cutting along two planes perpendicular to the axis.

As with many three-dimensional shapes, the word &ldquo;cylinder&rdquo; may refer to either the surface of the cylinder or the solid object inside. In addition, the word is sometimes used to refer only to the lateral surface of a finite cylinder, with the two ends excluded.

In differential geometry, a generalized cylinder is any surface obtained by translating a plane curve along a perpendicular axis. This results in a ruled surface spanned by a one-parameter family of parallel lines. For example, a prism is a cylinder obtained by translating a polygon. In this context, a standard cylinder is referred to as a circular cylinder

If the original plane curve is a conic section, the resulting generalized cylinder is a quadric surface. A cylinder whose cross section is an ellipse, parabola, or hyperbola is called an elliptic cylinder, parabolic cylinder, or hyperbolic cylinder.

An oblique cylinder is a cylinder whose two ends are not perpendicular to the axis. The two ends are still required to to be parallel to each other. In the context of oblique cylinders, a standard cylinder is referred to as a right cylinder, since the two ends make right angles with the axis.