Surface

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In 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

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NASA's Aqua satellite sees Nida explode into a category 5 Super typhoon

Space & Earth / Earth Sciences

Nov 25, 2009 | 4 / 5 (3) | 0

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 ...

Climate change in Kuwait Bay

Space & Earth / Earth Sciences

5 hours ago | 4 / 5 (8) | 0

Since 1985, seawater temperature in Kuwait Bay, northern Arabian Gulf, has increased on average 0.6°C per decade. This is about three times faster than the global average rate reported by the Intergovernmental ...

Living buildings could mop up carbon dioxide

Other Sciences / Other

Nov 27, 2009 | 1 / 5 (2) | 0

(PhysOrg.com) -- Architecture could help us tackle climate change, if we start to design our buildings with 'living' materials, according to Dr Rachel Armstrong, UCL Bartlett School of Architecture.

NASA Assessing New Roles for Ailing QuikScat Satellite

Space & Earth / Space Exploration

Nov 24, 2009 | 4 / 5 (1) | 1

(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. ...

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Gullies and Flow Features on Crater Wall

Space & Earth / Space Exploration

Nov 26, 2009 | 4.5 / 5 (2) | 0

(PhysOrg.com) -- This image from the High Resolution Imaging Science Experiment (HiRISE) camera on NASA's Mars Reconnaissance Orbiter shows a sample of the variety and complexity of processes that may occur ...

Peptides control crystal growth with 'switches, throttles and brakes'

Nanotechnology / Bio & Medicine

Nov 23, 2009 | 4.8 / 5 (5) | 0

(PhysOrg.com) -- By producing some of the highest resolution images of peptides attaching to mineral surfaces, scientists have a deeper understanding how biomolecules manipulate the growth crystals. This research ...

Control of blood clotting by platelets described; provides medical promise

Medicine & Health / Research

Nov 24, 2009 | not rated yet | 0

Cell fragments called platelets are essential to promote blood clotting. Virginia Tech faculty members and students have discovered novel molecular interactions at the surface of platelets that control blood clotting.

Cassini Sends Back Images of Enceladus as Winter Nears

Space & Earth / Space Exploration

Nov 23, 2009 | 4.4 / 5 (7) | 0

(PhysOrg.com) -- NASA's Cassini spacecraft has sailed seamlessly through the Nov. 21 flyby of Saturn's moon Enceladus and started transmitting uncalibrated temperature data and images of the rippling terrain. ...

Oceanic crust formation is dynamic after all

Space & Earth / Earth Sciences

Nov 25, 2009 | 4.8 / 5 (8) | 0

Imagine the Earth's crust as the planet's skin: Some areas are old and wrinkled while others have a fresher, more youthful sheen, as if they had been regularly lathered with lotion.

Chemists get custom-designed microscopic particles to self-assemble in liquid crystal

Chemistry / Materials Science

Nov 25, 2009 | 5 / 5 (5) | 0

(PhysOrg.com) -- The scientists anticipate their "LithoParticles" will have significant applications in photonics, optical communications and other areas.

Nanotech in Space: Experiment To Weather the Trials of Orbit

Nanotechnology / Nanomaterials

Nov 24, 2009 | 4 / 5 (2) | 0

Novel nanomaterials developed at Rensselaer were sent into orbit on Nov. 16 aboard Space Shuttle Atlantis.

China is set to launch its second moon orbiter next October, state media have reported

China to launch second lunar probe: state media

Space & Earth / Space Exploration

Nov 27, 2009 | 5 / 5 (6) | 0

China will launch its second moon orbiter next October, state media reported Friday, as it powers ahead with a space programme that has sparked concerns abroad.

Monster Waves on the Sun are Real (w/ Video)

Space & Earth / Astronomy

Nov 25, 2009 | 4.9 / 5 (20) | 2

Sometimes you really can believe your eyes. That's what NASA's STEREO (Solar Terrestrial Relations Observatory) spacecraft are telling researchers about a controversial phenomenon on the sun known as the "solar ...