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 ...
'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. ...
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 ...
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 ...
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 ...
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 ...
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 ...
How the Moon produces its own water
Space & Earth / Space Exploration
Oct 15, 2009 |
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(PhysOrg.com) -- The Moon is a big sponge that absorbs electrically charged particles given out by the Sun. These particles interact with the oxygen present in some dust grains on the lunar surface, producing ...
Giving cockroaches the slip (w/ Video)
Oct 13, 2009 |
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(PhysOrg.com) -- A breakthrough by scientists at Cambridge University may terminate the threat of termites, cockroaches and other pests such as ants and locusts - responsible for billions of pounds worth of ...
Researchers: Champagne's aroma comes from bubbles
Chemistry / Analytical Chemistry
Sep 28, 2009 |
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(AP) -- Don Ho was right. It is the tiny bubbles. A team of researchers - in Europe not surprisingly - found that Champagne's bursting bubbles not only tickle the nose, they create a mist that wafts the aroma to the drinker.
Harnessing nanopatterns: Tiny textures can produce big differences
Nanotechnology / Nanomaterials
Sep 24, 2009 |
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(PhysOrg.com) -- Research at MIT has uncovered new information about how nanoscale patterns on the surface of a material can produce significant changes in the way it interacts with liquids. The discovery ...
Ego City: Cities organized like human brains
Sep 03, 2009 |
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(PhysOrg.com) -- Cities are organized like brains, and the evolution of cities mirrors the evolution of human and animal brains, according to a new study by researchers at Rensselaer Polytechnic Institute.
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 ...
Study: Small fluctuations in solar activity, large influence on the climate
Space & Earth / Earth Sciences
Aug 27, 2009 |
4.7 / 5 (15) |
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(PhysOrg.com) -- Subtle connections between the 11-year solar cycle, the stratosphere, and the tropical Pacific Ocean work in sync to generate periodic weather patterns that affect much of the globe, according ...
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 ...
