Cylindrical

Cylindrical is an adjective describing anything related to a cylinder—a solid with two parallel circular bases connected by a curved surface. In geometry, a cylinder is defined by a fixed axis, a radius, and a height; its lateral surface is curved, while its ends are flat circles. Objects described as cylindrical have a circular cross-section when cut perpendicular to the axis and a constant radius along the length of the axis. The term also appears in more general contexts to describe surfaces and shapes that share this property.

A cylindrical surface is the set of points at a constant distance r from a given line, called the axis. Such surfaces exhibit cylindrical symmetry if they are invariant under rotations around that axis.

Cylindrical coordinates provide a convenient way to describe points in three-dimensional space when rotational symmetry about an axis is present. A point is given by (r, θ, z): r is the radial distance from the z-axis, θ is the angle around the axis, and z is the height along the axis. They relate to Cartesian coordinates by x = r cos θ, y = r sin θ. This system is common in physics and engineering, especially in problems involving pipes, cables, or circular tanks, as well as in computer graphics for textures and volumetric data.

Etymology traces the word to the shape of a cylinder; in practice, 'cylindrical' applies to objects, coordinates, and surfaces that reflect this geometry.