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CYLINDER

Cylinder directed by a Fermat spiral

Cartesian equation of a cylinder with axis orthogonal
to (a, b, c) and (a', b', c') : .
For a cylinder with axis Oz :
Cartesian equation: . Cartesian parametrization: . First fundamental quadratic form: . Second fundamental quadratic form: . |

The cylinders (or cylindrical surfaces) 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, developable
surfaces and moulding surfaces.

The lines of curvature are the generatrices and their normal sections.

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.

Cylindrical balconies of the First Nations University of Canada.

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© Robert FERRÉOL 2020