Surface
hideIn mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball or bagel. On the other hand, there are surfaces which cannot be embedded in three-dimensional Euclidean space without introducing singularities or intersecting itself — these are the unorientable surfaces.
To say that a surface is "two-dimensional" means that, about each point, there is a coordinate patch on which a two-dimensional coordinate system is defined. For example, the surface of the Earth is (ideally) a two-dimensional sphere, and latitude and longitude provide coordinates on it — except at the International Date Line and the poles, where longitude is undefined. This example illustrates that not all surfaces admits a single coordinate patch. In general, multiple coordinate patches are needed to cover a surface.
Surfaces find application in physics, engineering, computer graphics, and many other disciplines, primarily when they represent the surfaces of physical objects. For example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface.
For more information about Surface, read the full article at
Wikipedia.
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News tagged with surface
Watching Proteins Direct Crystal Growth One Step at a Time (w/ Video)
16 hours ago |
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(PhysOrg.com) -- Scientists at Berkeley Lab's Molecular Foundry imaged the growth of protein-studded mineral surfaces with unprecedented resolution and provided a glimpse into how living systems engineer key ...
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Pre-eruption earthquakes offer clues to volcano forecasters
Space & Earth / Earth Sciences
4 hours ago |
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Like an angry dog, a volcano growls before it bites, shaking the ground and getting "noisy" before erupting. This activity gives scientists an opportunity to study the tumult beneath a volcano and may help ...
Researchers find cells move in mysterious ways (w/ Video)
6 hours ago |
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Our cells are more like us than we may think. They're sensitive to their environment, poking and prodding deliberately at their surroundings with hand-like feelers and chemical signals as they decide whether ...
NASA's Mars Reconnaissance Orbiter Resumes Observations
Space & Earth / Space Exploration
8 hours ago |
4.3 / 5 (3) |
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(PhysOrg.com) -- Researchers are receiving new science data from NASA's Mars Reconnaissance Orbiter after the spacecraft's six science instruments resumed observations today.
Fault weaknesses, the center cannot hold for some geologic faults
Space & Earth / Earth Sciences
8 hours ago |
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Some geologic faults that appear strong and stable, slip and slide like weak faults. Now an international team of researchers has laboratory evidence showing why some faults that "should not" slip are weaker ...
Astronomers Find Super-Earth Using Amateur, Off-the-Shelf Technology (w/ Video)
9 hours ago |
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(PhysOrg.com) -- Astronomers announced today that they have discovered a "super-Earth" orbiting a red dwarf star 40 light-years from Earth. They found the distant planet with a small fleet of ground-based ...
Behavior modification could ease concerns about nanoparticles
Nanotechnology / Bio & Medicine
9 hours ago |
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In an advance that could help ease health and environmental concerns about the emerging nanotechnology industry, scientists are reporting development of technology for changing the behavior of nanoparticles ...
Lost water of the Napa Valley vineyards
Space & Earth / Earth Sciences
11 hours ago |
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Getting the most out of every drop of water is a high priority for grape growers in the southern Napa Valley, where summers are hot and dry and vines have to be irrigated to make it through the growing season. But Stanford ...
Even at sublethal levels, pesticides may slow the recovery of wild salmon populations
12 hours ago |
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Biologists determined that short-term, seasonal exposure to pesticides in rivers and basins may limit the growth and size of wild salmon populations. In addition to the widespread deterioration of salmon habitats, these findings ...
Giant Planet Set for a Cataclysmic Show
12 hours ago |
4.9 / 5 (8) |
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(PhysOrg.com) -- A team of Chinese astronomers have discovered a giant planet close to the exotic binary star system QS Virginis. Although dormant now, in the future the two stars will one day erupt in a violent ...
Black Holes in Star Clusters stir up Time and Space (w/ Video)
14 hours ago |
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(PhysOrg.com) -- Within a decade scientists could be able to detect the merger of tens of pairs of black holes every year, according to a team of astronomers at the University of Bonn’s Argelander-Institut ...
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