18 relations: Affine space, Convex set, Dimension, Euclidean space, Geometry, Hyperplane, Inequality (mathematics), Line (geometry), Linear equation, Nef polygon, Open set, Partition of a set, Plane (geometry), Poincaré half-plane model, Polyhedron, Siegel upper half-space, Two-dimensional space, Upper half-plane.
In mathematics, an affine space is a geometric structure that generalizes the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.
In mathematics, an inequality is a relation that holds between two values when they are different (see also: equality).
The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.
In mathematics, a linear equation is an equation that may be put in the form where x_1, \ldots, x_n are the variables or unknowns, and c, a_1, \ldots, a_n are coefficients, which are often real numbers, but may be parameters, or even any expression that does not contain the unknowns.
Nef polygons and Nef polyhedra are the sets of polygons (resp. polyhedra) which can be obtained from a finite set of halfplanes (halfspaces) by Boolean operations of set intersection and set complement.
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
In non-Euclidean geometry, the Poincaré half-plane model is the upper half-plane, denoted below as H \, together with a metric, the Poincaré metric, that makes it a model of two-dimensional hyperbolic geometry.
In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.
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 the complex numbers whose imaginary part is positive definite.
Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).
In mathematics, the upper half-plane H is the set of complex numbers with positive imaginary part: The term arises from a common visualization of the complex number x + iy as the point (x,y) in the plane endowed with Cartesian coordinates.