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ultraparallel lines

См. также в других словарях:

  • Ultraparallel theorem — In hyperbolic geometry, the ultraparallel theorem states that every pair of ultraparallel lines in the hyperbolic plane has a unique common perpendicular hyperbolic line.Proof in the Poincaré half plane modelLet :a < b < c < d be four distinct… …   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

  • Hypercycle (geometry) — In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight line.Given a straight line L and a point P not on L, we can construct a hypercycle by taking… …   Wikipedia

  • Hjelmslev transformation — In mathematics, the Hjelmslev transformation is an effective method for mapping an entire hyperbolic plane into a circle with a finite radius. The transformation was invented by Danish mathematician Johannes Hjelmslev. It utilizes Nikolai… …   Wikipedia

  • Differential geometry — A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparallel lines. Differential geometry is a mathematical discipline that uses the techniques of differential and integral calculus, as well as… …   Wikipedia

  • Parallel (geometry) — Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of Euclid s… …   Wikipedia

  • Klein model — In geometry, the Klein model, also called the projective model, the Beltrami–Klein model, the Klein–Beltrami model and the Cayley–Klein model, is a model of n dimensional hyperbolic geometry in which the points of the geometry are in an n… …   Wikipedia

  • Poincaré half-plane model — Stellated regular heptagonal tiling of the model.In non Euclidean geometry, the Poincaré half plane model is the upper half plane, together with a metric, the Poincaré metric, that makes it a model of two dimensional hyperbolic geometry.It is… …   Wikipedia

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