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)
Dec 16, 2009 |
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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 ...
'Environmental Atlas of Europe' unveiled at COP15
Dec 14, 2009 |
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In support of the United Nations Framework Convention on Climate Change taking place in Copenhagen, the European Environment Agency hosted the 'Bend the Trend' event on Sunday evening to provide a global climate ...
Added sugar in raisin cereals increases acidity of dental plaque
20 hours ago |
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Elevated dental plaque acid is a risk factor that contributes to cavities in children. But eating bran flakes with raisins containing no added sugar does not promote more acid in dental plaque than bran flakes alone, according ...
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Light-Driven Nanorod Could Roll on Water
23 hours ago |
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(PhysOrg.com) -- In a recent study, researchers have examined the possibility of rolling a nanorod on the surface of water. On the macroscale, perhaps the closest analogy might be the sport of logrolling, ...
Sucker-footed bats don't use suction after all (w/ Video)
Dec 14, 2009 |
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There are approximately 1,200 species of bats worldwide. Of that total, only six are known to roost with their heads pointed upward. Investigators did not know why, because they knew next to nothing about ...
Magnetic Dance of Titan and Saturn To Be Main Attraction during Flyby
Space & Earth / Space Exploration
Dec 14, 2009 |
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(PhysOrg.com) -- When it flies by Saturn's largest moon, Titan, this weekend, NASA's Cassini spacecraft will study the interactions between the magnetic field of Saturn and Titan. The flyby will take place ...
Journal highlights forest service early warning system
Dec 13, 2009 |
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A national early warning system designed to assist land managers in rapidly detecting threats to forest health is featured in the cover article of the October 2009 issue of Photogrammetric Engineering and Remote Sensing (PE&RS), ...
A Search for Stability for Platinum Catalysts
Nanotechnology / Nanomaterials
Dec 17, 2009 |
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(PhysOrg.com) -- A new carbon support that greatly increases the durability of proton-exchange membrane fuel cells has been developed by scientists at Pacific Northwest National Laboratory and Princeton University. ...
Icy moons of Saturn and Jupiter may have conditions needed for life
Dec 15, 2009 |
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(PhysOrg.com) -- Scientists once thought that life could originate only within a solar system's "habitable zone," where a planet would be neither too hot nor too cold for liquid water to exist on its surface. ...
Heart cells on lab chip display 'nanosense' that guides behavior
Nanotechnology / Bio & Medicine
Dec 15, 2009 |
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Johns Hopkins biomedical engineers, working with colleagues in Korea, have produced a laboratory chip with nanoscopic grooves and ridges capable of growing cardiac tissue that more closely resembles natural ...
NASA unveils latest results from lunar mission
Space & Earth / Space Exploration
Dec 15, 2009 |
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NASA's current mission in orbit around the moon, the Lunar Reconnaissance Orbiter, or LRO, has been providing crucial insights about our nearest celestial neighbor since its launch in June. At a scientific ...
From greenhouse to icehouse -- reconstructing the environment of the Voring Plateau
Space & Earth / Earth Sciences
Dec 15, 2009 |
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The analysis of microfossils found in ocean sediment cores is illuminating the environmental conditions that prevailed at high latitudes during a critical period of Earth history.
Glint of Sunlight Confirms Liquid in Northern Lake District of Titan
Space & Earth / Space Exploration
Dec 17, 2009 |
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(PhysOrg.com) -- NASA's Cassini Spacecraft has captured the first flash of sunlight reflected off a lake on Saturn's moon Titan, confirming the presence of liquid on the part of the moon dotted with many large, ...
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