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Hyperbolic groups have a solvable word problem. They are biautomatic and automatic. [9] Indeed, they are strongly geodesically automatic, that is, there is an automatic structure on the group, where the language accepted by the word acceptor is the set of all geodesic words.
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.
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One can take the hyperboloid to represent the events (positions in spacetime) that various inertially moving observers, starting from a common event, will reach in a fixed proper time. The hyperbolic distance between two points on the hyperboloid can then be identified with the relative rapidity between the two corresponding observers.
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 ...
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Connectors on this cable would be designated: 1A1W35P1; 1A1W35P2; ASME Y14.44-2008 continues the convention of Plug P and Jack J when assigning references for electrical connectors in assemblies where a J (or jack) is the more fixed and P (or plug) is the less fixed of a connector pair, without regard to the gender of the connector contacts.