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Vladimir Grigoryevich Shukhov (Russian: Влади́мир Григо́рьевич Шу́хов; 28 August [O.S. 16 August] 1853 – 2 February 1939) was a Russian and Soviet engineer-polymath, scientist and architect renowned for his pioneering works on new methods of analysis for structural engineering that led to breakthroughs in industrial design of the world's first hyperboloid ...
Unlike the real hyperbolic space, the complex projective space cannot be defined as a sheet of the hyperboloid , =, because the projection of this hyperboloid onto the projective model has connected fiber (the fiber being / in the real case).
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 isometry to the previous models can be realised by stereographic projection from the hyperboloid to the plane {+ =}, taking the vertex from which to project to be (, …,,) for the ball and a point at infinity in the cone () = inside projective space for the half-space.
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 ...
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.
Hyperbolic motions can also be described on the hyperboloid model of hyperbolic geometry. [ 1 ] This article exhibits these examples of the use of hyperbolic motions: the extension of the metric d ( a , b ) = | log ( b / a ) | {\displaystyle d(a,b)=\vert \log(b/a)\vert } to the half-plane and the unit disk .
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 .