# Cylindrical Surface

## cylindrical surface

[sə′lin·drə·kəl ′sər·fəs] (mathematics)

A surface consisting of each of the straight lines which are parallel to a given straight line and pass through a given curve. Also known as cylinder.

## Cylindrical Surface

(or cylinder), a surface traced by a line moving parallel to a given fixed line and intersecting a given curve. The fixed line is called the generatrix, and the curve is called the directrix.

If the generatrix of a cylindrical surface is parallel to the *z*-axis of a rectangular coordinate system, the equation of the surface is *F*(*x*, *y*) = 0. If the generatrix of a cylindrical surface is parallel to the line *ax* + *by* + *c* = 0 in the *xy*-plane, the equation of the surface has the form *z* = *f*(*ax* + *by*). If a circle, ellipse, hyperbola, or parabola is the directrix, the resulting cylindrical surface is said to be circular, elliptical, hyperbolic, or parabolic, respectively.