hyperbolic perpendicular

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• 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

• Hyperbolic space — In mathematics, hyperbolic n space, denoted H n , is the maximally symmetric, simply connected, n dimensional Riemannian manifold with constant sectional curvature −1. Hyperbolic space is the principal example of a space exhibiting 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-orthogonal — In mathematics, two points in the Cartesian plane are hyperbolically orthogonal if the slopes of their rays from the origin are reciprocal to one another.If the points are ( x , y ) and ( u , v ), then they are hyperbolically orthogonal if : y /… …   Wikipedia

• Hyperbola — This article is about a geometrical curve, a conic section. For the term used in rhetoric, see Hyperbole …   Wikipedia

• 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

• Apollonian circles — Some Apollonian circles. Every blue circle intersects every red circle at a right angle. Every red circle passes through the two points, C and D, and every blue circle separates the two points. This article discusses a family of circles sharing a …   Wikipedia

• Non-Euclidean geometry — Behavior of lines with a common perpendicular in each of the three types of geometry Non Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate,… …   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

• Coxeter–Dynkin diagram — See also: Dynkin diagram Coxeter Dynkin diagrams for the fundamental finite Coxeter groups …   Wikipedia

• Law of cosines — This article is about the law of cosines in Euclidean geometry. For the cosine law of optics, see Lambert s cosine law. Figure 1 – A triangle. The angles α, β, and γ are respectively opposite the sides a, b, and c …   Wikipedia