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
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 Assessing New Roles for Ailing QuikScat Satellite
Space & Earth / Space Exploration
Nov 24, 2009 |
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(PhysOrg.com) -- NASA mission managers are assessing options for future operations of the venerable QuikScat satellite following the age-related failure of a mechanism that spins the scatterometer antenna. ...
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 ...
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 ...
Computer predicts reactions between molecules and surfaces, with 'chemical precision'
Chemistry / Analytical Chemistry
Nov 06, 2009 |
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Good news for heterogeneous catalysis and the hydrogen economy: computers can now be used to make accurate predictions of the reactions of (hydrogen) molecules with surfaces. An international team of researchers, headed by ...
Caribbean, Gulf spared widespread coral damage
Nov 06, 2009 |
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(AP) -- Lower-than-feared sea temperatures this summer gave a break to fragile coral reefs across the Caribbean and the central Gulf of Mexico that were damaged in recent years, scientists said Thursday.
How Size Matters For Catalysts: Study Links Size, Activity, Electronic Properties
Nanotechnology / Nanomaterials
Nov 05, 2009 |
3.7 / 5 (3) |
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(PhysOrg.com) -- University of Utah chemists demonstrated the first conclusive link between the size of catalyst particles on a solid surface, their electronic properties and their ability to speed chemical ...
New Digital 'Electronics' Concept May Continue Moore's Law
Nov 05, 2009 |
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(PhysOrg.com) -- Computers of the future could be operating not on electrons, but on tiny waves traveling through an electron "fluid," if a new proposal is successful. The new circuit design, recently introduced ...
Lasers put a shine on metals
Nov 03, 2009 |
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(PhysOrg.com) -- Polishing metal surfaces is a demanding but monotonous task, and it is difficult to find qualified young specialists. Polishing machines do not represent an adequate alternative because they ...
Snows Of Kilimanjaro shrinking rapidly, and likely to be lost
Space & Earth / Earth Sciences
Nov 02, 2009 |
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The remaining ice fields atop famed Mount Kilimanjaro in Tanzania could be gone within two decades and perhaps even sooner, based on the latest survey of the ice fields remaining on the mountain .
Scientists Propose New Explanation for Flu Virus Antigenic Drift
Oct 29, 2009 |
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(PhysOrg.com) -- Influenza viruses evade infection-fighting antibodies by constantly changing the shape of their major surface protein. This shape-shifting, called antigenic drift, is why influenza vaccines ...
