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CYLINDER

Cartesian equation:
(for a cylinder with axis Oz).
Cartesian parametrization: . First fundamental quadratic form: . Second fundamental quadratic form: . |

The cylinders are the ruled surfaces the generatrices of which have a fixed direction .

A curve traced on the cylinder which meets all the generatrices is called a *directrix* of the cylinder; there exists a unique cylinder with given direction and directrix.

Necessary and sufficient condition: surface globally invariant under the action of any translation in the direction .

We can also consider that a cylinder is a cone the vertex of which is at infinity.

Cylinders are translation surfaces and developable surfaces.

The word cylinder is also used in a topological sense and refers to any surface homeomorphic to the cylinder of revolution, or, which amounts to the same thing, to a sphere minus two points. For example, an open strip with an even number of half-turns is topologically equivalent to a cylinder.

See also the cylindrical catenaries.

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© Robert FERRÉOL 2017