- hyperbolic triangle
- мат.гиперболический треугольник
English-Russian scientific dictionary. 2008.
hyperbolic triangle
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Hyperbolic triangle — In mathematics, the term hyperbolic triangle has more than one meaning.In the foundations of the hyperbolic functions sinh, cosh and tanh, a hyperbolic triangle is a right triangle in the first quadrant of the Cartesian plane :{(x,y):x,y in… … Wikipedia
Hyperbolic geometry — Lines through a given point P and asymptotic to line R. A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparall … Wikipedia
Triangle group — In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle. The triangle can be an ordinary Euclidean triangle, a triangle on the sphere, or a hyperbolic triangle.… … Wikipedia
Triangle — This article is about the basic geometric shape. For other uses, see Triangle (disambiguation). Isosceles and Acute Triangle redirect here. For the trapezoid, see Isosceles trapezoid. For The Welcome to Paradox episode, see List of Welcome to… … Wikipedia
Hyperbolic angle — A hyperbolic angle in standard position is the angle at (0, 0) between the ray to (1, 1) and the ray to ( x , 1/ x ) where x > 1.The magnitude of the hyperbolic angle is the area of the corresponding hyperbolic sector which is loge x .Note that… … Wikipedia
Hyperbolic group — In group theory, a hyperbolic group, also known as a word hyperbolic group, Gromov hyperbolic group, negatively curved group is a finitely generated group equipped with a word metric satisfying certain properties characteristic of hyperbolic… … Wikipedia
Hyperbolic motion — In geometry, a hyperbolic motion is a mapping of a model of hyperbolic geometry that preserves the distance measure in the model. Such a mapping is analogous to congruences of Euclidean geometry which are compositions of rotations and… … Wikipedia
hyperbolic geometry — Geom. the branch of non Euclidean geometry that replaces the parallel postulate of Euclidean geometry with the postulate that two distinct lines may be drawn parallel to a given line through a point not on the given line. Cf. Riemannian geometry … Universalium
Hyperbolic sector — A hyperbolic sector is a region of the Cartesian plane {( x , y )} bounded by rays from the origin to two points ( a , 1/ a ) and ( b , 1/ b ) and by the hyperbola xy = 1.A hyperbolic sector in standard position has a = 1 and b > 1 .The area of a … Wikipedia
(2,3,7) triangle group — In the theory of Riemann surfaces and hyperbolic geometry, the triangle group (2, 3, 7) is particularly important. This importance stems from its connection to Hurwitz surfaces, namely Riemann surfaces of genus g with the largest possible order,… … Wikipedia
Ideal triangle — In hyperbolic geometry an ideal triangle is a hyperbolic triangle whose three vertices all lie on the circle at infinity. In the Poincaré disk model an ideal triangle is bounded by three circles which intersect the boundary circle at right angles … Wikipedia
