In geometry, the hyperboloid model, also known as the Minkowski model after Hermann Minkowski, is a model of n-dimensional hyperbolic geometry in which...

 xn] on the upper sheet of the hyperboloid of the hyperboloid model, thereby defining a point in the hyperboloid model, we may project it onto the hyperplane...

the hyperboloid model, the Beltrami–Klein model's relation to the Poincaré disk model, and the Poincaré disk model's relation to the hyperboloid model. Every...

cases of Apollonius' problem. In the hyperboloid model they are represented by intersections of the hyperboloid with planes whose normal lies on the asymptotic...

the hyperboloid model (Hy) with as center the center of the hyperboloid (O) and the projection plane tangent to the nearest point of the hyperboloid. Given...

In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal...

hyperboloid model is immediate through the action of the connected component of S O ( n , 1 ) {\displaystyle \mathrm {SO} (n,1)} on the hyperboloid....

horizon plane, or as a plane parallel to the horizon plane. In the hyperboloid model, a horosphere is represented by a plane whose normal lies in the asymptotic...

from the chord length in the Minkowski metric between points in the hyperboloid model, chord ⁡ ( p 1 , p 2 ) = 2 sinh ⁡ 1 2 dist ⁡ ( p 1 , p 2 ) , {\textstyle...

the hyperboloid model of the hyperbolic plane, the hyperboloid is referred to as a pseudosphere. This usage of the word is because the hyperboloid can...

as Minkowski did in 1908. The relevant structure is now called the hyperboloid model of hyperbolic geometry. The non-Euclidean planar algebras support...

model (but rays parallel to the positive y-axis approach it). In the hyperboloid model there are no ideal points. Ideal triangle Ideal polyhedron Points...

This page is a list of hyperboloid structures. These were first applied in architecture by Russian engineer Vladimir Shukhov (1853–1939). Shukhov built...

Lorentz group, point stabilizer orthogonal group, corresponding to hyperboloid model): Hn ≅ O+(1, n) / O(n) Oriented hyperbolic space: SO+(1, n) / SO(n)...

R is a Riemannian manifold. It is one of the model spaces of Riemannian geometry, the hyperboloid model of hyperbolic space. It is a space of constant...

The mathematical basis of Minkowski space can also be found in the hyperboloid model of hyperbolic space already known in the 19th century, because isometries...

isometries in hyperbolic space which is often expressed in terms of the hyperboloid model.: 3.2.3  In a Cartesian plane, ordinary rotation leaves a circle unchanged...

{\displaystyle ~p\neq \pm i~} . The Poincaré sphere model used since 1892 has been compared to a 2-sheet hyperboloid model, and the practice of SU(1, 1) interferometry...

Four-gradient Algebra of physical space Congruence (general relativity) Hyperboloid model Rapidity Technically, the four-vector should be thought of as residing...

Minkowski space restricts to the isometric action of PSL(2, R) on the hyperboloid model of the hyperbolic plane. The eigenvalues of an element A ∈ SL(2, R)...

excess hyperbolic geometry hyperbolic space hyperboloid model Poincaré disc model Poincaré half-plane model Poincaré metric Angle of parallelism Prime...

frame. In 1881 Poincaré described hyperbolic geometry in terms of the hyperboloid model, formulating transformations leaving invariant the Lorentz interval...

during the Russian Civil War. Vladimir Shukhov invented the world's first hyperboloid structure in the year 1890. Later he wrote a book, Rafters, in which...

been described by other models such as the Klein model or the hyperboloid model, obtained by considering the two-sheeted hyperboloid q(x, y, z) = −1 in three-dimensional...

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...

hyperbolic rotations. Pseudo-Riemannian manifold Hyperbolic equation Hyperboloid model Paravector Élie Cartan (1981), The Theory of Spinors, Dover Publications...

the scalar curvature is S = n(n − 1)/r2. Hyperbolic space By the hyperboloid model, an n-dimensional hyperbolic space can be identified with the subset...

the complex plane. Hyperbolic motions can also be described on the hyperboloid model of hyperbolic geometry. This article exhibits these examples of the...

relativity it was used in topics such as the Cayley–Klein metric, hyperboloid model and other models of hyperbolic geometry, computations of elliptic functions...

been considerable work associating this "velocity space" with the hyperboloid model of hyperbolic geometry. In special relativity, the hyperbolic angle...