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
Watching Proteins Direct Crystal Growth One Step at a Time (w/ Video)
11 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 ...
The Meandering Channels of Mars
Space & Earth / Space Exploration
Dec 10, 2009 |
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Sinuous channels on the Martian surface may be evidence of relatively recent rainfall. Researchers plan to test this hypothesis by studying sinuous streams on Earth.
'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 ...
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 ...
Successful stem cell therapy for treatment of eye disease
Dec 10, 2009 |
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Newly published research, by investigators, at the North East England Stem Cell Institute (NESCI) in the journal Stem Cells reported the first successful treatment of eight patients with "Limbal Stem Cell Deficiency" (LSCD) ...
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 ...
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 ...
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 ...
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.
Single-Molecule Magnets Open New Door for Information Technology
Mar 09, 2009 |
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(PhysOrg.com) -- Recent research by scientists in Italy and France shows that that single molecules have the ability to store information via their magnetic state. Their work is a first step toward a new generation ...
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.
Scientists See Smallest-Ever Square Nanotube
Feb 20, 2009 |
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(PhysOrg.com) -- Scientists have observed the smallest reported nanotube that has a square cross-section. The structure formed spontaneously and unexpectedly when silver nanowires were stretched and is a reminder ...
How Size Matters For Catalysts: Study Links Size, Activity, Electronic Properties
Nanotechnology / Nanomaterials
Nov 05, 2009 |
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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 ...
'Writing' Patterns on Carbon Nanotubes With Polymer Chains
Nanotechnology / Nanomaterials
May 19, 2009 |
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(PhysOrg.com) -- Carbon nanotubes are at the center of the nanoelectronics research movement, with scientists making great progress toward getting nanotube-based electronic devices into the hands of consumers. ...
