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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. A hyperboloid is a quadric surface , that is, a surface defined as the zero set of a polynomial of degree two in three variables.
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For example, a cone is formed by keeping one point of a line fixed whilst moving another point along a circle. A surface is doubly ruled if through every one of its points there are two distinct lines that lie on the surface. The hyperbolic paraboloid and the hyperboloid of one sheet are doubly ruled surfaces.
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This page is a list of hyperboloid structures. These were first applied in architecture by Russian engineer Vladimir Shukhov (1853–1939). Shukhov built his first example as a water tower ( hyperbolic shell ) for the 1896 All-Russian Exposition .
This list is of songs that have been interpolated by other songs. Songs that are cover versions, parodies, or use samples of other songs are not "interpolations". The list is organized under the name of the artist whose song is interpolated followed by the title of the song, and then the interpolating artist and their song.
The pseudosphere and its relation to three other models of hyperbolic geometry. The half pseudosphere of curvature −1 is covered by the interior of a horocycle.In the Poincaré half-plane model one convenient choice is the portion of the half-plane with y ≥ 1. [7]
In geometry, the hyperboloid model, also known as the Minkowski model after Hermann Minkowski, is a model of n-dimensional hyperbolic geometry in which points are represented by points on the forward sheet S + of a two-sheeted hyperboloid in (n+1)-dimensional Minkowski space or by the displacement vectors from the origin to those points, and m ...