dimension
Sign in to savethumb|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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Article
20 sectionsContents
- In mathematics
- Vector spaces
- Manifolds
- Complex dimension
- Varieties
- Krull dimension
- Topological spaces
- Hausdorff dimension
- Hilbert spaces
- In physics
- Spatial dimensions
- Time<!--'Temporal dimension' and 'Temporal dimensions' redirect here-->
- 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.