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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.
Hyperboloid structures are superior in stability against outside forces compared with "straight" buildings, but have shapes often creating large amounts of unusable volume (low space efficiency). Hence they are more commonly used in purpose-driven structures, such as water towers (to support a large mass), cooling towers, and aesthetic features.
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 ...
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 .
The world's first diagrid hyperboloid 37-meter water tower by Vladimir Shukhov, All-Russian Exposition, Nizhny Novgorod, Russia, 1896 The world's first hyperboloid structure in Polibino, 2009. The Shukhov Tower in Polibino, designed in 1896 by Russian engineer and architect Vladimir Shukhov, is the world's first diagrid hyperboloid structure.
The hyperbolic paraboloid and the hyperboloid of one sheet are doubly ruled surfaces. The plane is the only surface which contains at least three distinct lines through each of its points ( Fuchs & Tabachnikov 2007 ).
The primary reflector is a paraboloid, while the shape of the convex secondary reflector is a hyperboloid.The geometrical condition for radiating a collimated, plane wave beam is that the feed antenna is located at the far focus of the hyperboloid, while the focus of the primary reflector coincides with the near focus of the hyperboloid. [1]
In mathematical physics, global hyperbolicity is a certain condition on the causal structure of a spacetime manifold (that is, a Lorentzian manifold). It is called hyperbolic in analogy with the linear theory of wave propagation, where the future state of a system is specified by initial conditions.