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In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space.
A right-handed three-dimensional Cartesian coordinate system used to indicate positions in space. Space is a three-dimensional continuum containing positions and directions. [1] In classical physics, physical space is often conceived in three linear dimensions.
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events ...
For example, brane gas cosmology [10] [11] attempts to explain why there are three dimensions of space using topological and thermodynamic considerations. According to this idea it would be since three is the largest number of spatial dimensions in which strings can generically intersect.
A point in three-dimensional Euclidean space can be located by three coordinates. Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer ...
Zero curvature (flat) – a drawn triangle's angles add up to 180° and the Pythagorean theorem holds; such 3-dimensional space is locally modeled by Euclidean space E 3. Positive curvature – a drawn triangle's angles add up to more than 180°; such 3-dimensional space is locally modeled by a region of a 3-sphere S 3.
A three-dimensional Euclidean space is a special case of a Euclidean space. In Bourbaki's terms, [2] the species of three-dimensional Euclidean space is richer than the species of Euclidean space. Likewise, the species of compact topological space is richer than the species of topological space. Fig. 3: Example relations between species of spaces
The 3-sphere is homeomorphic to the one-point compactification of R 3. In general, any topological space that is homeomorphic to the 3-sphere is called a topological 3-sphere. The homology groups of the 3-sphere are as follows: H 0 (S 3, Z) and H 3 (S 3, Z) are both infinite cyclic, while H i (S 3, Z) = {} for all other indices i.