In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space. If the space is two-dimensional...

Half-space may refer to: Half-space (geometry), either of the two parts into which a plane divides Euclidean space (Poincaré) Half-space model, a model...

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

Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel...

mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of...

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an...

which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be equivalent...

In non-Euclidean geometry, the Poincaré half-plane model is a way of representing the hyperbolic plane using points in the familiar Euclidean plane. Specifically...

non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the...

Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional...

the intersection of half-spaces. In non-Euclidean geometry, the ambient space might be the n-dimensional sphere or hyperbolic space, or more generally...

Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space). A solid figure is the region of 3D space bounded by a two-dimensional...

parallelism of lines. Affine geometry can be developed in two ways that are essentially equivalent. In synthetic geometry, an affine space is a set of points to...

In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical...

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It...

In mathematics, the Siegel upper half-space of degree g (or genus g) (also called the Siegel upper half-plane) is the set of g × g symmetric matrices over...

A five-dimensional (5D) space is a space with five dimensions. 5D Euclidean geometry designated by the mathematical sign: E {\displaystyle \mathbb {E}...

to any surrounding space. In plane (Euclidean) geometry, the basic concepts are points and (straight) lines. In spherical geometry, the basic concepts...

minimal model program and the construction of moduli spaces sets the field apart from differential geometry, where the classification of possible smooth manifolds...

Geometry, New York: McGraw-Hill, p. 68, ISBN 0-07-072191-2 {{citation}}: ISBN / Date incompatibility (help) Senechal, Marjorie (2013), Shaping Space:...

Sacred geometry ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions. It is associated with the belief of...

plane it is not. Affine plane Half-plane Hyperbolic geometry Janich, P.; Zook, D. (1992). Euclid's Heritage. Is Space Three-Dimensional?. The Western...

space or Bolyai–Lobachevsky space after the names of the author who first published on the topic of hyperbolic geometry. Sometimes the qualificative...

geometry Spherical geometry Sphere-world Angle excess hyperbolic geometry hyperbolic space hyperboloid model Poincaré disc model Poincaré half-plane model Poincaré...

and computational geometry, the notion of centerpoint is a generalization of the median to data in higher-dimensional Euclidean space. Given a set of points...

the geometry of Euclidean space of two dimensions (plane geometry) or of three dimensions (solid geometry). In the first half of the nineteenth century...

points in three-dimensional Euclidean space determine a solid figure called tetrahedron. In non-Euclidean geometries, three "straight" segments (having zero...

upper half-plane becomes a metric space. The generic name of this metric space is the hyperbolic plane. In terms of the models of hyperbolic geometry, this...

solve this problem by building a set of half-spaces that describe the interior of the geometry. These half-spaces are used to describe primitives that can...

In geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a plane...