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Negative curvature – a drawn triangle's angles add up to less than 180°; such 3-dimensional space is locally modeled by a region of a hyperbolic space H 3. Curved geometries are in the domain of non-Euclidean geometry. An example of a positively curved space would be the surface of a sphere such as the Earth.
Roblox (/ ˈ r oʊ b l ɒ k s / ⓘ, ROH-bloks) is an online game platform and game creation system developed by Roblox Corporation that allows users to program and play games created by themselves or other users. It was created by David Baszucki and Erik Cassel in 2004, and released to the public in 2006. As of August 2020, the platform has ...
This map is ineligible for copyright and therefore in the public domain, because it consists entirely of information that is common property and contains no original authorship. For more information, see Commons:Threshold of originality § Maps .
Three-dimensional anti-de Sitter space is like a stack of hyperbolic disks, each one representing the state of the universe at a given time. [a]In mathematics and physics, n-dimensional anti-de Sitter space (AdS n) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature.
Curved spaces play an essential role in general relativity, where gravity is often visualized as curved spacetime. [2] The Friedmann–Lemaître–Robertson–Walker metric is a curved metric which forms the current foundation for the description of the expansion of the universe and the shape of the universe .
It is a singular space (the equator is a singularity), but away from the singularities, it has constant negative Gaussian curvature and therefore is locally isometric to a hyperbolic plane. The name "pseudosphere" comes about because it has a two-dimensional surface of constant negative Gaussian curvature, just as a sphere has a surface with ...
Some physicists, such as Lawrence Krauss, Stephen Hawking or Alexander Vilenkin, call or called this state "a universe from nothingness", although the zero-energy universe model requires both a matter field with positive energy and a gravitational field with negative energy to exist. [2] The hypothesis is broadly discussed in popular sources.
The evolution of the universe and its horizons in proper distances. The x-axis is distance, in billions of light years; the y-axis is time, in billions of years since the Big Bang. This is the same model as in the earlier figure, with dark energy and an event horizon.