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
Newly discovered star one of hottest in Galaxy (w/ Video)
Dec 02, 2009 |
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(PhysOrg.com) -- Astronomers at The University of Manchester's Jodrell Bank Centre for Astrophysics have discovered one of the hottest stars in the Galaxy with a surface temperature of around 200,000 degrees ...
Researchers restore some function to cells from cystic fibrosis patients
Dec 06, 2009 |
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In an encouraging new development, a team led by Scripps Research Institute scientists has restored partial function to lung cells collected from patients with cystic fibrosis. While there is still much work to be done before ...
Loves Me, Loves Me Not: Researchers Discover New Method for Measuring Hydrophobicity at the Nanoscale
Dec 03, 2009 |
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(PhysOrg.com) -- Researchers at Rensselaer Polytechnic Institute have discovered a new, more precise method for measuring how much — or how little - nanoscale interfaces love water.
Nervy research: Researchers take initial look at ion channels in a model system
Dec 02, 2009 |
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Before one of your muscles can twitch, before the thought telling it to flex can race down your nerve, a tiny floodgate of sorts -- called an ion channel -- must open in the surface of each cell in these organs ...
A Tiny Cage of Gold Responds to Light, Opening to Empty Its Contents
Nanotechnology / Bio & Medicine
Nov 19, 2009 |
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(PhysOrg.com) -- Researchers at Washington University in St. Louis have developed a polymer-coated gold nanocage that not only opens in response to light to release a small amount of a drug payload, but then closes when the ...
Engineer Discovers Why Particles Like Flour Disperse on Liquids
Nov 16, 2009 |
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(PhysOrg.com) -- Even if you are not a cook, you might have wondered why a pinch of flour (or any small particles) thrown into a bowl of water will disperse in a dramatic fashion, radiating outward as if it ...
El Nino Picking Up Steam
Space & Earth / Earth Sciences
Nov 13, 2009 |
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(PhysOrg.com) -- The latest image from the U.S./French Jason-2 satellite finds a strong wave of warm water heading toward the Americas, fueling El Nino.
Noise Evidence Could Expand Hurricane Record
Space & Earth / Earth Sciences
Nov 10, 2009 |
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As sea-surface temperatures rise across the globe, some scientists believe that hurricane frequency and intensity may increase. A fresh technique offers promise to generate new data from long-dead storms, ...
Sculptured materials allow multiple channel plasmonic sensors
Nov 10, 2009 |
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(PhysOrg.com) -- Sensors, communications devices and imaging equipment that use a prism and a special form of light -- a surface plasmon-polariton -- may incorporate multiple channels or redundant applications if manufacturers ...
Microsoft Store mirrors popular concept of its rival
Dec 04, 2009 |
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Blink an eye, and the Microsoft Store could be mistaken for an Apple Store.
New method of measuring ocean CO2 uptake could lead to climate change 'early warning system'
Space & Earth / Earth Sciences
Dec 03, 2009 |
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An international team of scientists led by the University of East Anglia (UEA) has developed a new method of measuring the absorption of CO2 by the oceans and mapped for the first time CO2 uptake for the entire North Atlantic.
Will copper keep us safe from the superbugs?
Dec 01, 2009 |
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Three papers scheduled for publication in the January issue of the Journal of Hospital Infection, published by Elsevier, suggest that copper might have a role in the fight against healthcare-associated infections.
NASA's Aqua satellite sees Nida explode into a category 5 Super typhoon
Space & Earth / Earth Sciences
Nov 25, 2009 |
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Typhoon Nida is in a favorable environment that has enabled it to intensify faster and stronger than previously forecast, and has now exploded into a Super typhoon. NASA's Aqua satellite passed over Nida and ...
NASA satellites make a movie and get rainfall, wind info on Ida (w/ Video)
Space & Earth / Earth Sciences
Nov 09, 2009 |
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NASA satellites are amazing examples of technology. The TRMM satellite peers into tropical cyclones and can tell how much rain is falling per hour and where. QuikScat uses microwave technology to measure Ida's ...
'Rational drug design' identifies fragments of FDA-approved drugs relevant to emerging viruses
Dec 06, 2009 |
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A massive, data-crunching computer search program that matches fragments of potential drug molecules to the known shapes of viral surface proteins has identified several FDA-approved drugs that could be the basis for new ...
