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Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.
The space P n (K) is often called the projective space of dimension n over K, or the projective n-space, since all projective spaces of dimension n are isomorphic to it (because every K vector space of dimension n + 1 is isomorphic to K n+1). The elements of a projective space P(V) are commonly called points.
The regular complex polytope 4 {4} 2, , in has a real representation as a tesseract or 4-4 duoprism in 4-dimensional space. 4 {4} 2 has 16 vertices, and 8 4-edges. Its symmetry is 4 [4] 2, order 32. It also has a lower symmetry construction, , or 4 {}× 4 {}, with symmetry 4 [2] 4, order 16. This is the symmetry if the red and blue 4-edges are ...
[4] The two-dimensional analogue of a 4-polytope is a polygon, and the three-dimensional analogue is a polyhedron. Topologically 4-polytopes are closely related to the uniform honeycombs, such as the cubic honeycomb, which tessellate 3-space; similarly the 3D cube is related to the infinite 2D square tiling.
[4] [5] Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography. All projections of a sphere on a plane necessarily distort the surface in some way. [6]
Hermann Minkowski (1864–1909) found that the theory of special relativity could be best understood as a four-dimensional space, since known as the Minkowski spacetime.. In physics, Minkowski space (or Minkowski spacetime) (/ m ɪ ŋ ˈ k ɔː f s k i,-ˈ k ɒ f-/ [1]) is the main mathematical description of spacetime in the absence of gravitation.
For the lowest dimensions, the relevant conditions may be stated in equivalent form as follows. A projective space is of: (L1) at least dimension 0 if it has at least 1 point, (L2) at least dimension 1 if it has at least 2 distinct points (and therefore a line), (L3) at least dimension 2 if it has at least 3 non-collinear points (or two lines ...
Four-dimensional space, the concept of a fourth spatial dimension Spacetime , the unification of time and space as a four-dimensional continuum Minkowski space , the mathematical setting for special relativity