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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.
In mathematics, a solid Klein bottle is a three-dimensional topological space (a 3-manifold) whose boundary is the Klein bottle. [ 1 ] It is homeomorphic to the quotient space obtained by gluing the top disk of a cylinder D 2 × I {\displaystyle \scriptstyle D^{2}\times I} to the bottom disk by a reflection across a diameter of the disk.
A two-dimensional representation of the Klein bottle immersed in three-dimensional space. In mathematics, the Klein bottle (/ ˈ k l aɪ n /) is an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down.
The Shape of Space: How to Visualize Surfaces and Three-dimensional Manifolds. A Warning on terminology: Our two-sphere is defined in three-dimensional space, where it is the boundary of a three-dimensional ball. This terminology is standard among mathematicians, but not among physicists.
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.
The Klein bottle immersed in three-dimensional space The surface of the Earth requires ... For example, a sheet of paper is a 2-manifold with a 1-dimensional boundary.
In mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3- manifold can be thought of as a possible shape of the universe . Just as a sphere looks like a plane (a tangent plane ) to a small and close enough observer, all 3-manifolds look like our universe does to a small enough observer.
The holographic principle is a property of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region – such as a light-like boundary like a gravitational horizon.