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...

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

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...

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

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...

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

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...

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

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...

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

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...

is the maximum possible kissing number for n-dimensional spheres in (n + 1)-dimensional Euclidean space? More unsolved problems in mathematics In geometry...

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...

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...

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...

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...

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

a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter of the...

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...

hypersphere or 3-sphere 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...

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...

definitive source regarding 3-dimensional space groups is the International Tables for Crystallography Hahn (2002). Space groups in 2 dimensions are the...

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...

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...

physics textbooks restrict the Helmholtz decomposition to the three-dimensional space and limit its application to vector fields that decay sufficiently...

perspective, which may be considered as a central projection of the three dimensional space onto a plane (see Pinhole camera model). More precisely, the entrance...

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)...