cylindrischen

Cylindrischen is the inflected form of the German adjective cylindrisch, used to describe things related to or shaped like a cylinder. In standard German, the typical equivalents are zylindrisch or zylinderförmig; "cylindrischen" appears mainly in contexts influenced by English technical vocabulary or in older texts. The word is commonly seen in phrases such as cylindrischen Koordinaten (cylindrical coordinates) or descriptions of cylindrical symmetry.

In mathematics and physics, cylindrical coordinates describe positions using three numbers: the radius r from a central axis, the angle φ around the axis, and the height z along the axis. The Cartesian conversions are x = r cos φ, y = r sin φ, z = z, and the volume element is dV = r dr dφ dz. Problems with axial symmetry—such as flow in pipes, long tubes, or circular drums—are often simpler in these coordinates.

In geometry, a cylinder is the set of points at a fixed distance from a given axis, formed by translating a circle along that axis. Cylindrical surfaces and shapes are common in engineering and design, including pipes, tanks, cans, and structural elements. Cylindrical forms are also studied in computer-aided design, architecture, and material science for their symmetry and structural properties.

Etymology and usage: Cylindrical derives from Latin cylindricus, via Greek kylindros, while German typically uses Zylinder as the noun for a cylinder and zylindrisch or zylinderförmig as adjectives. The form cylindrischen reflects loanword influence in German; readers may encounter it in German texts that adopt English terminology or in international technical contexts. See also cylindrical coordinates, cylinder, and cylindrical symmetry.