In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry...

modeling it on a surface of constant curvature, the pseudosphere, and in the interior of an n-dimensional unit sphere, the so-called Beltrami–Klein model...

projective disk model, Klein disk model and Klein model, is named after Eugenio Beltrami and Felix Klein. For the two dimensions this model uses the interior...

ultraparallels p {\displaystyle p} and q {\displaystyle q} . In the Beltrami-Klein model of the hyperbolic geometry: two ultraparallel lines correspond to...

{I, −I}. Along with the Klein model and the Poincaré half-space model, it was proposed by Eugenio Beltrami who used these models to show that hyperbolic...

half-plane model, an ideal triangle is modeled by an arbelos, the figure between three mutually tangent semicircles. In the Beltrami–Klein model of the hyperbolic...

the hyperboloid of two sheets, treated as a model for the hyperbolic plane, is called the Beltrami–Klein model. The gnomonic projection is said to be the...

(n+1)-dimensional Euclidean space. Other models of hyperbolic space can be thought of as map projections of S+: the Beltrami–Klein model is the projection of S+ through...

geometry Klein configuration, in geometry Klein cubic (disambiguation) Klein graphs, in graph theory Klein model, or Beltrami–Klein model, a model of hyperbolic...

mechanics and potential theory. The research facility Klein established at Göttingen served as model for the best such facilities throughout the world. He...

q(x)=0} inside projective space for the half-space. Beltrami–Klein model: This is another model realised on the unit ball of R n {\displaystyle \mathbb...

considered as points in the Beltrami–Klein model of hyperbolic geometry and so vector addition in the Beltrami–Klein model can be given by the velocity...

coordinates. The Beltrami coordinates of a point are the Cartesian coordinates of the point when the point is mapped in the Beltrami–Klein model of the hyperbolic...

Spinors in three dimensions SO(4) 3D rotation group Beltrami–Klein model (Cayley–Klein model) Cayley–Klein metric Goldstein (1980) considers a passive (contravariant...

Klein's icosahedral cubic surface Klein's j-invariant Beltrami–Klein model Cayley–Klein metric Clifford–Klein form Schottky–Klein prime form Klein's Encyclopedia...

curvature case of hyperbolic geometry, this is justified by the Beltrami–Klein model. In the positive curvature case of spherical geometry, it is justified...

Poincaré disk model and the Beltrami–Klein model in hyperbolic geometry. Similarly, the real line is the absolute of the Poincaré half-plane model. The extent...

their isometry groups. Another model of hyperbolic space is also built on the open unit disk: the Beltrami–Klein model. It is not conformal, but has the...

Poincaré's other models of hyperbolic geometry (Poincaré disk model, Poincaré half-plane model) as well as the Beltrami–Klein model can be related to...

construction. ↔ . A view of the order-4 dodecahedral honeycomb under the Beltrami-Klein model There are four regular compact honeycombs in 3D hyperbolic space:...

that Beltrami, followed by Klein in 1871 and Poincaré in 1882, gave concrete analytic models for what Klein dubbed hyperbolic geometry. The four models of...

the models of a non-Euclidean plane were presented by Beltrami, Klein, and Poincaré, Euclidean geometry stood unchallenged as the mathematical model of...

automorphism group as Riemann surfaces. The smallest Hurwitz surface is the Klein quartic (genus 3, automorphism group of order 168), and the induced tiling...

several models of non-Euclidean geometry that are now known as the Beltrami–Klein model, the Poincaré disk model, and the Poincaré half-plane model, together...

Gudermann/Escherich in terms of the Beltrami–Klein model and the Weierstrass coordinates of the hyperboloid model - this relation was pointed out by Homersham...

honeycomb order-4 dodecahedral honeycomb (Beltrami–Klein model) order-4 hexagonal tiling honeycomb (Poincaré disk model) Vertex figure (Octahedron) (Octahedron)...

hyperbolic tree commonly utilizes the Poincaré disk model of hyperbolic geometry, though the Klein-Beltrami model can also be used. Both display the entire hyperbolic...

half-plane model is named after Henri Poincaré, but it originated with Eugenio Beltrami who used it, along with the Klein model and the Poincaré disk model, to...

helps propel the dimensional reduction of Kaluza–Klein theories. In its most basic form, the sigma model can be taken as being purely the kinetic energy...

independence of Euclid's fifth postulate. (Note: Eugenio Beltrami had previously given such a model in 1868.) W. Stanley Jevons publishes the popular textbook...