cylinder, in mathematics, surface generated by a line moving parallel to a given fixed line and continually intersecting a given fixed curve called the directrix; each line of the family of lines forming the cylinder is called a ruling, or generator. If the directrix is a conic section (e.g., a circle or a parabola), the cylinder is called a quadric cylinder. The commonest type of cylinder is the right circular cylinder, in which the directrix is a circle and the lines forming the cylinder are all perpendicular to the plane of the circle. The solid bounded by a cylindrical surface and two parallel planes intersecting the surface in closed curves is also called a cylinder. The perpendicular distance between the planes is the altitude of the cylinder. The volume of the cylinder is equal to the product of the altitude and the area of the base (the area enclosed by either closed curve).

Small stone cylinder engraved in intaglio on its surface to leave impressions when rolled on wet clay. It first appeared circa 3400–2900 BC and is considered to be one of the finest artistic achievements of Mesopotamia. The earliest examples used geometric or animal patterns; later seals incorporated the owner's name and depicted a variety of motifs. They were used to mark personal property and make documents legally binding. The seals were adopted in Egypt and the Indus civilization.

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