SHAWORDS

A surface which may be generated by a moving straight line is called a — Hyperboloid

Home›Hyperboloid›Quote
"A surface which may be generated by a moving straight line is called a . The plane, the cone, and the cylinder are simple examples... the hyperbolic paraboloid is a . ...[T]he unparted hyperboloid \frac{x^2}{a^2} + \frac{y^2}{b^2} - \frac{z^2}{ c^2} = 1 is a ruled surface having two sets of rectilinear generators, i.e., ...through every point of it two straight lines may be drawn, each of which shall lie entirely on the surface."
H
Hyperboloid
H
Hyperboloid
Hyperboloid
author11 quotes

In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by deforming it by means of directional scalings, or more generally, of an affine transformation.

More by Hyperboloid

View all →
Quote
"The hyperboloid of revolution (generated as a surface of revolution) is a special case of the elliptical hyperboloid... The shape of a small portion of the hyperboloid of revolution around the equator is similar to that of the , but larger portions are quite different, as are the s. The image of the Gauss map of the whole hyperboloid of revolution omits disks around the north and south poles, whereas the image of the Gauss map of the whole catenoid omits only the north and south poles."
H
Hyperboloid