dimension

Also known as dimensionality, number of dimensions

thumb|upright=1.2|From left to right: a square (geometry)|square, a [[cube and a tesseract. The square is two-dimensional (2D) and bounded by one-dimensional line segments; the cube is three-dimensional (3D) and bounded by two-dimensional squares; the tesseract is four-dimensional (4D) and bounded by three-dimensional cubes. ]] [[File:Dimension levels.svg|thumb|upright=1.2| The first four spatial dimensions, represented in a two-dimensional picture.

AI overview

A dimension is a measurable direction or axis that describes space—for example, a flat square exists in two dimensions, a cube in three dimensions, and more complex shapes can exist in four or more dimensions. Dimensions matter because they provide a way to understand and describe the structure of objects, from the simple shapes we see around us to more abstract mathematical forms.

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Commons gallery: Dimension
Commons category: Dimensions

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~22 min read

Article

20 sections

Contents

In mathematics
Vector spaces
Manifolds
Complex dimension
Varieties
Krull dimension
Topological spaces
Hausdorff dimension
Hilbert spaces
In physics
Spatial dimensions
Time
Additional dimensions
In computer graphics and spatial data
More dimensions
List of topics by dimension
See also
References
Further reading
External links

thumb|upright=1.2|From left to right: a square (geometry)|square, a [[cube and a tesseract. The square is two-dimensional (2D) and bounded by one-dimensional line segments; the cube is three-dimensional (3D) and bounded by two-dimensional squares; the tesseract is four-dimensional (4D) and bounded by three-dimensional cubes. ]] thumb|upright=1.2| The first four spatial dimensions, represented in a two-dimensional picture.

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. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. 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 coordinates are needed to locate a point within these spaces.