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CYLINDER OF REVOLUTION

Equation of the cylinder with radius R and axis (O, )
with : .
Cylindrical equation: . Cartesian equation: . Cartesian parametrizations: or (cf figure on the right). Developable quadric. First fundamental quadratic form: . Surface element: . Second fundamental quadratic form: . |
Parametrization the coordinate lines of which form a double lattice of orthogonal circular helices, which are also the rhumb lines at 45° of this cylinder (be it placed horizontally or vertically). |

The cylinder of
revolution is the surface generated by the revolution of a line parallel to an axis, around this axis.

The cylinder can be developed by mapping a point *M* to the point of the plane with Cartesian coordinates
.

Remarkable curves traced on the cylinder of revolution:

- curvature lines: the circles *z* = constant and the generatrices.

- geodesics, helices and rhumb lines: the circles *z* = constant, the generatrices, and the circular helices.

See also the cylindrical curves, and the equidomoids.

Intersection between 3 orthogonal cylinders, by Alain Esculier

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© Robert FERRÉOL 2017