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Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point). This is the informal meaning of the term dimension.

In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called three-dimensional Euclidean space (or simply Euclidean space when the context is clear). It is commonly represented by the symbol 3.[1][2] This serves as a three-parameter model of the physical universe (that is, the spatial part, without considering time), in which all known matter exists. While this space remains the most compelling and useful way to model the world as it is experienced,[3] it is only one example of a large variety of spaces in three dimensions called 3-manifolds. In this classical example, when the three values refer to measurements in different directions (coordinates), any three directions can be chosen, provided that vectors in these directions do not all lie in the same 2-space (plane). Furthermore, in this case, these three values can be labeled by any combination of three chosen from the terms width, height, depth, and length.

Wikipedia's globe logo in 3-D

Three-dimensional space has a number of topological properties that distinguish it from spaces of other dimension numbers. For example, at least three dimensions are required to tie a knot in a piece of string.[12]

In differential geometry the generic three-dimensional spaces are 3-manifolds, which locally resemble .

In finite geometry

Many ideas of dimension can be tested with finite geometry. The simplest instance is PG(3,2), which has Fano planes as its 2-dimensional subspaces. It is an instance of Galois geometry, a study of projective geometry using finite fields. Thus, for any Galois field GF(q), there is a projective space PG(3,q) of three dimensions. For example, any three knot in a piece of string.[12]

In differential geometry the generic three-dimensional spaces are 3-manifolds, which locally resemble differential geometry the generic three-dimensional spaces are 3-manifolds, which locally resemble .

Many ideas of dimension can be tested with finite geometry. The simplest instance is PG(3,2), which has Fano planes as its 2-dimensional subspaces. It is an instance of Galois geometry, a study of projective geometry using finite fields. Thus, for any Galois field GF(q), there is a projective space PG(3,q) of three dimensions. For example, any three skew lines in PG(3,q) are contained in exactly one regulus.[13]

See also