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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 .
One has a hyperboloid of revolution if and only if =. Otherwise, the axes are uniquely defined (up to the exchange of the x-axis and the y-axis). There are two kinds of hyperboloids. In the first case (+1 in the right-hand side of the equation): a one-sheet hyperboloid, also called a hyperbolic hyperboloid.
Hyperboloid_Print.ogv (Ogg multiplexed audio/video file, Theora/Vorbis, length 3 min 31 s, 638 × 360 pixels, 1.47 Mbps overall, file size: 36.83 MB) This is a file from the Wikimedia Commons . Information from its description page there is shown below.
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.
Alternative to RCA for professional video electronics. Protocols: Serial digital interface (SDI) and HD-SDI. CoaXPress; 75 Ω for video signal (SDI and CoaXPress) on, for example, RG59 and RG6. 50 Ω for data link, like Ethernet on RG58. 93 Ω on RG62. 50 Ω (white/bottom row) and 75 Ω C connectors (red/top row) C connector (Concelman connector)
Hyperboloid structures are architectural structures designed using a hyperboloid in one sheet. Often these are tall structures, such as towers, where the hyperboloid geometry's structural strength is used to support an object high above the ground. Hyperboloid geometry is often used for decorative effect as well as structural economy.
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 ...