In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called sides or edges and three...

positive). For an ideal triangle, a generalization of hyperbolic triangles, this sum is equal to zero. For a spherical triangle, the sum of the angles...

In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...

straight segments also determine a triangle, for instance a spherical triangle or hyperbolic triangle. A geodesic triangle is a region of a general two-dimensional...

cosh is the hyperbolic cosine. This formula is a special form of the hyperbolic law of cosines that applies to all hyperbolic triangles: cosh ⁡ c R =...

triangle can be an ordinary Euclidean triangle, a triangle on the sphere, or a hyperbolic triangle. Each triangle group is the symmetry group of a tiling...

sector. The hyperbolic functions may be defined in terms of the legs of a right triangle covering this sector. In complex analysis, the hyperbolic functions...

the former. When in standard position, a hyperbolic sector determines a hyperbolic triangle, the right triangle with one vertex at the origin, base on the...

A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular...

In hyperbolic geometry, a uniform hyperbolic tiling (or regular, quasiregular or semiregular hyperbolic tiling) is an edge-to-edge filling of the hyperbolic...

In hyperbolic geometry an ideal triangle is a hyperbolic triangle whose three vertices all are ideal points. Ideal triangles are also sometimes called...

premised on hyperbolic analogies to the corresponding circular trigonometric functions by regarding a hyperbolic angle as defining a hyperbolic triangle. The...

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...

triangles Hyperbolic triangle, a triangle that has straight sides in hyperbolic geometry, but is drawn as circular in some models of hyperbolic geometry Lune...

as Euclidean polygons. In particular, the sum of the angles of a hyperbolic triangle is less than 180 degrees. Coxeter decompositions are named after...

the hyperbolic plane by congruent hyperbolic triangles known as the V6.6.∞ Infinite-order triangular tiling is created. Note that each such triangle has...

In geometry, a triangle center or triangle centre is a point in the triangle's plane that is in some sense in the middle of the triangle. For example,...

Euclidean plane, or the hyperbolic plane. Each Schwarz triangle on a sphere defines a finite group, while on the Euclidean or hyperbolic plane they define an...

mathematics, hyperbolic trigonometry can mean: The study of hyperbolic triangles in hyperbolic geometry (traditional trigonometry is the study of triangles in plane...

cases of Gauss–Bonnet. In spherical trigonometry and hyperbolic trigonometry, the area of a triangle is proportional to the amount by which its interior...

In the hyperbolic plane, as in the Euclidean plane, each point can be uniquely identified by two real numbers. Several qualitatively different ways of...

In the theory of Riemann surfaces and hyperbolic geometry, the triangle group (2,3,7) is particularly important for its connection to Hurwitz surfaces...

hypercubic honeycomb Triangle Automedian triangle Delaunay triangulation Equilateral triangle Golden triangle Hyperbolic triangle (non-Euclidean geometry)...

As the triangle gets larger or smaller, the angles change in a way that forbids the existence of similar hyperbolic triangles, as only triangles that have...

hyperbolic spaces as they are 0-hyperbolic (i.e. all triangles are tripods). The 1-skeleton of the triangulation by Euclidean equilateral triangles is...

precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group...

may refer to: Angle of parallelism, in hyperbolic geometry, the angle at one vertex of a right hyperbolic triangle that has two hyperparallel sides Axial...

defect of a hyperbolic triangle; and the excess also arises in two ways: the excess of a toroidal polyhedron. the excess of a spherical triangle; In the Euclidean...

definition of curvature, the theorem also applies in spherical geometry and hyperbolic geometry. In higher dimensions, an analogous quadratic equation applies...

parallel to the base. An analogous theorem can also be proven for hyperbolic triangles, for which the apex lies on a hypercycle. Given a fixed base A B...