Elliptic cylinder

ELLIPTICAL CYLINDER

Cartesian equation:

(of revolution if and only if a = b).
Developable quadric.

The elliptical cylinders are the cylinders with an ellipse as directrix.

Contrary to appearances, every elliptical cylinder contains circles, intersections between the cylinder and the planes forming an angle with the horizontal. Hence the other name: oblique circular cylinder.
It can therefore be constructed by hanging strings between two circles, the strings being parallel to the line joining the two centers.

Two circular sections of an elliptical cylinder

The arches of the cupola of the Duomo in Florence are arcs of circles. The cupola is therefore composed of 8 portions of elliptical cylinders. See this page for more explanations.
See also the echo room at Chaise-Dieu, on this page.

See also the spherical ellipses, and the focal cubics.

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Contrary to appearances, every elliptical cylinder contains circles, intersections between the cylinder and the planes forming an angle with the horizontal. Hence the other name: oblique circular cylinder. It can therefore be constructed by hanging strings between two circles, the strings being parallel to the line joining the two centers.	Two circular sections of an elliptical cylinder
The arches of the cupola of the Duomo in Florence are arcs of circles. The cupola is therefore composed of 8 portions of elliptical cylinders. See this page for more explanations. See also the echo room at Chaise-Dieu, on this page.