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.
This text uses material from Wikipedia and is available under the GNU Free Documentation License.
News tagged with surface
Added sugar in raisin cereals increases acidity of dental plaque
Dec 18, 2009 |
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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
Dec 18, 2009 |
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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, ...
Scientists discover fog on Titan
Space & Earth / Space Exploration
Dec 18, 2009 |
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Saturn's largest moon, Titan, looks to be the only place in the solar system—aside from our home planet, Earth—with copious quantities of liquid (largely, liquid methane and ethane) sitting on its surface. ...
Tiny whispering gallery: Sensor can detect a single nanoparticle and take its measurement
Dec 18, 2009 |
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Nanotechnology has already made it to the shelves of your local pharmacy and grocery: nanoparticles are found in anti-odor socks, makeup, makeup remover, sunscreen, anti-graffiti paint, home pregnancy tests, ...
Physicists see through the opaque with 'T-rays'
Dec 18, 2009 |
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"T-rays" may make X-rays obsolete as a means of detecting bombs on terrorists or illegal drugs on traffickers, among other uses, contends a Texas A&M physicist who is helping lay the theoretical groundwork to make the concept ...
Computer-simulated Thunderstorms with Ice Clouds Reveal Insights for Next-generation Computer Models
Space & Earth / Earth Sciences
Dec 18, 2009 |
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(PhysOrg.com) -- Computer simulations of thunderstorms using data from a field campaign in Australia confirm that the "ice-phase" cloud processes in climate models contribute most to the wide discrepancy between ...
How the daisy got its spots... and why
Dec 18, 2009 |
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Dark spots on flower petals are common across many angiosperm plant families and occur on flowers such as some lilies, orchids, and daisies. Much research has been done on the physiological and behavioral ...
Acid oceans: the 'evil twin' of climate change
Dec 18, 2009 |
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(AP) -- Far from Copenhagen's turbulent climate talks, the sea lions, harbor seals and sea otters reposing along the shoreline and kelp forests of this protected marine area stand to gain from any global ...
Research project yields better understanding of the defective protein that causes cystic fibrosis
Dec 18, 2009 |
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A team of researchers studying the protein that, when defective or absent, causes cystic fibrosis (CF) has made an important discovery about how that protein is normally controlled and under what circumstances ...
From terrorism to HIV, it's all about the network
Other Sciences / Social Sciences
Dec 18, 2009 |
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(PhysOrg.com) -- Similarities between webs of terrorists and networks of rescue personnel may seem unlikely. To an eclectic collaboration of engineers and social scientists, the connections are not only possible, but a potential ...
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