Hyperbolic geometry (redirect from Hemisphere model) 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... 56 KB (6,945 words) - 18:48, 26 January 2024 |
Horocycle (section Hyperboloid model) cases of Apollonius' problem. In the hyperboloid model they are represented by intersections of the hyperboloid with planes whose normal lies on the asymptotic... 10 KB (1,291 words) - 06:28, 8 November 2023 |
Hyperbolic space (section Formal definition and models) hyperboloid model is immediate through the action of the connected component of S O ( n , 1 ) {\displaystyle \mathrm {SO} (n,1)} on the hyperboloid.... 11 KB (1,538 words) - 00:57, 19 April 2024 |
Horosphere (section Models) 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... 3 KB (381 words) - 17:01, 28 June 2022 |
Pseudosphere (section Hyperboloid) 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... 11 KB (1,125 words) - 18:09, 24 April 2024 |
Non-Euclidean geometry (redirect from Models of non-Euclidean geometry) as Minkowski did in 1908. The relevant structure is now called the hyperboloid model of hyperbolic geometry. The non-Euclidean planar algebras support... 44 KB (6,013 words) - 04:15, 7 April 2024 |
This page is a list of hyperboloid structures. These were first applied in architecture by Russian engineer Vladimir Shukhov (1853–1939). Shukhov built... 33 KB (1,041 words) - 06:05, 10 May 2024 |
Ideal point (section Hyperboloid model) 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... 7 KB (878 words) - 07:29, 8 May 2024 |
Lorentz group, point stabilizer orthogonal group, corresponding to hyperboloid model): Hn ≅ O+(1, n) / O(n) Oriented hyperbolic space: SO+(1, n) / SO(n)... 14 KB (1,727 words) - 11:09, 22 March 2024 |
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... 80 KB (10,536 words) - 17:19, 14 May 2024 |
Spacetime (category Conceptual models) 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... 198 KB (27,819 words) - 08:35, 10 May 2024 |
excess hyperbolic geometry hyperbolic space hyperboloid model Poincaré disc model Poincaré half-plane model Poincaré metric Angle of parallelism Prime... 8 KB (679 words) - 11:05, 12 February 2024 |
Four-gradient Algebra of physical space Congruence (general relativity) Hyperboloid model Rapidity Technically, the four-vector should be thought of as residing... 10 KB (1,711 words) - 20:41, 20 November 2023 |
frame. In 1881 Poincaré described hyperbolic geometry in terms of the hyperboloid model, formulating transformations leaving invariant the Lorentz interval... 90 KB (9,879 words) - 07:53, 13 May 2024 |
the complex plane. Hyperbolic motions can also be described on the hyperboloid model of hyperbolic geometry. This article exhibits these examples of the... 9 KB (1,233 words) - 18:42, 22 January 2024 |
Shukhov Tower (category Hyperboloid structures) 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... 11 KB (1,145 words) - 11:17, 1 September 2023 |
relativity it was used in topics such as the Cayley–Klein metric, hyperboloid model and other models of hyperbolic geometry, computations of elliptic functions... 95 KB (15,374 words) - 14:06, 12 May 2024 |
hyperbolic rotations. Pseudo-Riemannian manifold Hyperbolic equation Hyperboloid model Paravector Élie Cartan (1981), The Theory of Spinors, Dover Publications... 19 KB (2,365 words) - 14:14, 30 January 2024 |
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... 35 KB (5,034 words) - 06:29, 10 May 2024 |
been considerable work associating this "velocity space" with the hyperboloid model of hyperbolic geometry. In special relativity, the hyperbolic angle... 23 KB (3,234 words) - 01:51, 9 May 2024 |
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... 15 KB (2,291 words) - 14:57, 18 August 2023 |