Ads
related to: hyperbolic geometry theorems examples list of figureskutasoftware.com has been visited by 10K+ users in the past month
Search results
Results from the WOW.Com Content Network
Hyperbolic geometry is a non-Euclidean geometry where the first four axioms of Euclidean geometry are kept but the fifth axiom, the parallel postulate, is changed.The fifth axiom of hyperbolic geometry says that given a line L and a point P not on that line, there are at least two lines passing through P that are parallel to L. [1]
The theorems of Alhacen, Khayyam and al-Tūsī on quadrilaterals, including the Ibn al-Haytham–Lambert quadrilateral and Khayyam–Saccheri quadrilateral, were the first theorems on hyperbolic geometry. Their works on hyperbolic geometry had a considerable influence on its development among later European geometers, including Witelo ...
This is a consequence of the uniformization theorem for surfaces and the geometrization theorem for 3-manifolds proved by Perelman. A perspective projection of a dodecahedral tessellation in H 3. This is an example of what an observer might see inside a hyperbolic 3-manifold. The Pseudosphere. Each half of this shape is a hyperbolic 2-manifold ...
Hyperbolic geometry is the most rich and least understood of the eight geometries in dimension 3 (for example, for all other geometries it is not hard to give an explicit enumeration of the finite-volume manifolds with this geometry, while this is far from being the case for hyperbolic manifolds). After the proof of the Geometrisation ...
Hyperbolic 3-manifold; Hyperbolic coordinates; Hyperbolic Dehn surgery; Hyperbolic functions; Hyperbolic group; Hyperbolic law of cosines; Hyperbolic manifold; Hyperbolic metric space; Hyperbolic motion; Hyperbolic space; Hyperbolic tree; Hyperbolic volume; Hyperbolization theorem; Hyperboloid model; Hypercycle (geometry) HyperRogue
This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures; List of data structures; List of derivatives and integrals in alternative calculi; List of equations; List of fundamental theorems; List of hypotheses; List of inequalities; Lists of ...
In hyperbolic geometry, a uniform hyperbolic tiling (or regular, quasiregular or semiregular hyperbolic tiling) is an edge-to-edge filling of the hyperbolic plane which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).
In hyperbolic geometry, the "law of cosines" is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar law of cosines from plane trigonometry, or the spherical law of cosines in spherical trigonometry. [1] It can also be related to the relativistic velocity addition formula. [2] [3]
Ads
related to: hyperbolic geometry theorems examples list of figureskutasoftware.com has been visited by 10K+ users in the past month