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An interesting example is the modular group = (): it acts on the tree given by the 1-skeleton of the associated tessellation of the hyperbolic plane and it has a finite index free subgroup (on two generators) of index 6 (for example the set of matrices in which reduce to the identity modulo 2 is such a group).
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 .
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 .
The Weierstrass coordinates of a point are the Cartesian coordinates of the point when the point is mapped in the hyperboloid model of the hyperbolic plane, the x-axis is mapped to the (half) hyperbola ( , , +) and the origin is mapped to the point (0,0,1). [1]
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 .
Pages in category "Hyperboloid structures" The following 35 pages are in this category, out of 35 total. This list may not reflect recent changes. ...
[7]: 40 By definition, each end of this "adapter" has a different connection method – e.g. the solder tabs on a male phone connector, and the male phone connector itself. [3] In this example, the solder tabs connected to the cable represent the permanent connection, whilst the male connector portion interfaces with a female socket forming a ...
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 ...