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
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 ...
Voyage to the centre of the 'Plastic Vortex'
Space & Earth / Earth Sciences
May 25, 2009 |
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A group of conservationists and scientists is due to set sail for an obscure corner of the Pacific Ocean in the coming months to explore a vast swirl of waste known as the "Plastic Vortex."
Global warming: Our best guess is likely wrong
Space & Earth / Earth Sciences
Jul 14, 2009 |
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No one knows exactly how much Earth's climate will warm due to carbon emissions, but a new study this week suggests scientists' best predictions about global warming might be incorrect.
Regular Light Bulbs Made Super-Efficient with Ultra-Fast Laser
May 29, 2009 |
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(PhysOrg.com) -- An ultra-powerful laser can turn regular incandescent light bulbs into power-sippers, say optics researchers at the University of Rochester. The process could make a light as bright as a 100-watt ...
Our Sun: A Little Slow On the Uptake for Cycle 24
Apr 27, 2009 |
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A very recent article carried by the BBC called, 'Quiet Sun Baffling Astronomers' sent me in a twitter of research activity. The BBC article's head notes include "The Sun is the Dimmest It Has Been for Nearly ...
World's smallest semiconductor laser heralds new era in optical science
Aug 30, 2009 |
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(PhysOrg.com) -- Researchers at the University of California, Berkeley, have reached a new milestone in laser physics by creating the world's smallest semiconductor laser, capable of generating visible light ...
Scientists create metal that pumps liquid uphill
Jun 02, 2009 |
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(PhysOrg.com) -- In nature, trees pull vast amounts of water from their roots up to their leaves hundreds of feet above the ground through capillary action, but now scientists at the University of Rochester ...
Scientists solve decade-long mystery of nanopillar formations
Oct 22, 2009 |
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Scientists at the California Institute of Technology have uncovered the physical mechanism by which arrays of nanoscale pillars can be grown on polymer films with very high precision, in potentially limitless ...
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 ...
Researchers reveal the internal dance of water
Aug 12, 2009 |
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(PhysOrg.com) -- Water is familiar to everyone - it shapes our bodies and our planet. But despite this abundance, the molecular structure of water has remained a mystery, with the substance exhibiting many ...
'Invisibility cloak' could protect against earthquakes
Jul 20, 2009 |
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(PhysOrg.com) -- Research at the University of Liverpool has shown it is possible to develop an 'invisibility cloak' to protect buildings from earthquakes.
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 ...
Going platinum: New catalyst could boost cleaner fuel use
Nanotechnology / Nanomaterials
May 14, 2009 |
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(PhysOrg.com) -- Material scientists at Washington University in St. Louis have developed a technique for a bimetallic fuel cell catalyst that is efficient, robust and two to five times more effective than ...
Long-standing sunspot puzzle solved
Space & Earth / Space Exploration
Aug 19, 2009 |
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(PhysOrg.com) -- Scientists at the Universities of Glasgow, Strathclyde and Central Lancashire have used 21st Century solar observations and image processing to finally solve a sunspot puzzle first noticed ...
2008 Was Earth's Coolest Year Since 2000
Feb 23, 2009 |
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(PhysOrg.com) -- Climatologists at the NASA Goddard Institute for Space Studies (GISS) in New York City have found that 2008 was the coolest year since 2000. The GISS analysis also showed that 2008 is the ...
