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 “cylinder” 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.