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Most commonly, it is the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space. More general three-dimensional spaces are called 3-manifolds. The term may also refer colloquially to a subset of space, a three-dimensional region (or 3D domain), [1] a solid figure.
The dimension of a vector space is the number of vectors in any basis for the space, i.e. the number of coordinates necessary to specify any vector. This notion of dimension (the cardinality of a basis) is often referred to as the Hamel dimension or algebraic dimension to distinguish it from other notions of dimension.
Direct projection of 3-sphere into 3D space and covered with surface grid, showing structure as stack of 3D spheres (2-spheres) In mathematics, a 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
3D display, a type of information display that conveys depth to the viewer; 3D film, a motion picture that gives the illusion of three-dimensional perception; 3D modeling, developing a representation of any three-dimensional surface or object; 3D printing, making a three-dimensional solid object of a shape from a digital model
A view from inside a 3-torus. All of the cubes in the image are the same cube, since light in the manifold wraps around into closed loops. The three-dimensional torus , or 3-torus , is defined as any topological space that is homeomorphic to the Cartesian product of three circles, T 3 = S 1 × S 1 × S 1 . {\displaystyle \mathbb {T} ^{3}=S^{1 ...
In 3D computer graphics, 3D modeling is the process of developing a mathematical coordinate-based representation of a surface of an object (inanimate or living) in three dimensions via specialized software by manipulating edges, vertices, and polygons in a simulated 3D space. [1] [2] [3] Three-dimensional (3D) models represent a physical body ...
It is a compact, smooth manifold of dimension 3, and is a special case Gr(1, R 4) of a Grassmannian space. RP 3 is (diffeomorphic to) SO(3), hence admits a group structure; the covering map S 3 → RP 3 is a map of groups Spin(3) → SO(3), where Spin(3) is a Lie group that is the universal cover of SO(3).
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