Surface of revolution

Surface of revolution are in the geometry of known surfaces that are generated by rotation about the axis of an in - plane ( and, for example, defined by an equation of the form) curve.

In formulas: Be a regular plane curve with for all, then

The surface of revolution generated by. It can be shown that a regular surface.

As well as the surfaces of rotation bodies such as the cylinder for the surface of the ball for the paraboloid of revolution, or can be generated for.

The area of calculated according to the formula

Are surfaces of revolution, for example, for cooling towers ( Rotationshyperboloide ) used.

Surfaces of revolution of constant Gaussian curvature were classified by Gaussian and Ferdinand Minding. Surfaces of revolution with vanishing Gaussian curvature, the plane of the cylinder and cone. Surfaces of revolution with positive Gaussian curvature are the sphere surface, the surfaces of the spindle type and the surfaces ridge type. Surfaces of rotation with a negative Gaussian curvature, the pseudo- sphere, which is also known as Mindingsche surface area of the cone type, and the surfaces of the fillet type. ( The surface of the sphere and the pseudosphere have constant Gaussian curvature. )