the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space. More general three-dimensional spaces...

Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible...

plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space R 3 {\displaystyle...

A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because...

Three-dimensional chess (or 3‑D chess) is any chess variant that replaces the two-dimensional board with a three-dimensional array of cells between which...

five-dimensional space is a space with five dimensions. In mathematics, a sequence of N numbers can represent a location in an N-dimensional space. If...

finite-dimensional if the dimension of V {\displaystyle V} is finite, and infinite-dimensional if its dimension is infinite. The dimension of the vector space V {\displaystyle...

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

Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions...

dimensions. Although the space we live in is considered three-dimensional, there are practical applications for four-dimensional space. Quaternions, one of...

A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described...

In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several...

dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is...

plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space R 3 {\displaystyle...

3-sphere, or glome is a 4-dimensional analogue of a sphere, and is the 3-dimensional n-sphere. In 4-dimensional Euclidean space, it is the set of points...

This system maps the space of lines in three-dimensional space to projective space RP5, but with the additional requirement the space of lines corresponds...

also refer to a seven-dimensional manifold such as a 7-sphere, or a variety of other geometric constructions. Seven-dimensional spaces have a number of special...

dimension is an infinite cardinal. Finite-dimensional vector spaces occur naturally in geometry and related areas. Infinite-dimensional vector spaces...

are one-dimensional spaces but are usually referred to by more specific terms. Any field K {\displaystyle K} is a one-dimensional vector space over itself...

Euclidean space of dimension n, En (Euclidean line, E; Euclidean plane, E2; Euclidean three-dimensional space, E3) form a real coordinate space of dimension n...

the geometry of three-dimensional Euclidean space (3D space). A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for...

{\displaystyle \mathbb {R} ^{4}} to some three-dimensional subspace. The nullity of a matrix is the dimension of the null space, and is equal to the number of columns...

The Klein bottle can be constructed (in a four dimensional space, because in three dimensional space it cannot be done without allowing the surface to...

1-dimensional object that may be straight (like a line) or not; curves in 2-dimensional space are called plane curves and those in 3-dimensional space are...

mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible...

be used for indicating sides (e.g., interior or exterior). In three-dimensional space, a surface normal, or simply normal, to a surface at point P is...

space of a manifold is a generalization of tangent lines to curves in two-dimensional space and tangent planes to surfaces in three-dimensional space...

intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each...

mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quaternions is often denoted by H (for Hamilton)...

in n-dimensional space. When n = 8, the set of all such locations is called 8-dimensional space. Often such spaces are studied as vector spaces, without...