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

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...

A hyperbolic sector is a region of the Cartesian plane bounded by a hyperbola and two rays from the origin to it. For example, the two points (a, 1/a)...

ones: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse...

In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between...

In mathematics, a hyperbolic metric space is a metric space satisfying certain metric relations (depending quantitatively on a nonnegative real number...

ᗉ IAI'. Case 2b: IB' is parallel to I'B Construct the line segment BB' and using a hyperbolic ruler, construct the line OI" such that OI" is perpendicular...

for the logarithm while attempting to calculate the area under a hyperbolic segment. 1671 – James Gregory develops a series expansion for the inverse-tangent...

cone Hyperbolic cylinder Hyperbolic paraboloid Hyperboloid of one sheet Hyperboloid of two sheets Elliptic cone Hyperbolic cylinder Hyperbolic paraboloid...

This article lists the regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank....

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

In geometry, hyperbolic motions are isometric automorphisms of a hyperbolic space. Under composition of mappings, the hyperbolic motions form a continuous...

In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It...

points, but connects them by hyperbolic line segments instead of horocyclic segments, so that each tile becomes a hyperbolic convex pentagon. This makes...

for the logarithm while attempting to calculate the area under a hyperbolic segment. François Mauriceau publishes Traité des Maladies des Femmes Grosses...

geometries, three "straight" segments (having zero curvature) also determine a triangle, for instance a spherical triangle or hyperbolic triangle. A geodesic...

model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside the unit disk, and straight lines...

metric, the Poincaré metric, that makes it a model of two-dimensional hyperbolic geometry. Equivalently the Poincaré half-plane model is sometimes described...

hyperbola) then the solid cylinder is said to be parabolic, elliptic and hyperbolic, respectively. For a right circular cylinder, there are several ways in...

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