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
Will copper keep us safe from the superbugs?
12 hours ago |
5 / 5 (2) |
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Three papers scheduled for publication in the January issue of the Journal of Hospital Infection, published by Elsevier, suggest that copper might have a role in the fight against healthcare-associated infections.
Climate change in Kuwait Bay
Space & Earth / Earth Sciences
Nov 30, 2009 |
3.7 / 5 (13) |
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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 ...
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Special ultrasound accurately identifies skin cancer
17 hours ago |
4 / 5 (1) |
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High-frequency ultrasound with elastography can help differentiate between cancerous and benign skin conditions, according to a study presented today at the annual meeting of the Radiological Society of North America (RSNA).
NASA captures Typhoon Nida's clouds from 2 angles
Space & Earth / Earth Sciences
Nov 30, 2009 |
not rated yet |
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NASA satellites capture amazing views of tropical cyclones, and the Aqua and CloudSat satellites captured a top-down look at temperatures in Typhoon Nida's clouds, and an image of what they look like from ...
Nanoimaging in 3-D
14 hours ago |
4.9 / 5 (10) |
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(PhysOrg.com) -- As technology shrinks ever smaller, interest in objects and devices on the nanoscale becomes more apparent. However, visualizing these objects in three dimensions comes with special challenges. ...
It takes two to infect: Structural biologists shed light on mechanism of invasion protein
Nov 30, 2009 |
5 / 5 (1) |
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Bacteria are quite creative when infecting the human organism. They invade cells, migrate through the body, avoid an immune response and misuse processes of the host cell for their own purposes. To this end every bacterium ...
Chang'E-1 has blazed a new trail in China's deep space exploration
Space & Earth / Space Exploration
17 hours ago |
5 / 5 (1) |
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A huge amount of scientific data have been accumulated by the CE-1 lunar orbiter. Using laser altimeter data, Jinsong Ping and Qian Huang et al obtained improved 3D lunar topography, and based on this, they ...
Peat fires drive temperatures up
Nov 30, 2009 |
3.4 / 5 (5) |
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Peatlands, especially those in tropical regions, sequester gigantic amounts of organic carbon. Human activities are now having a considerable impact on these wetlands. For example, drainage projects, in combination with the ...
Security ID cards with built-in holograms (w/ Video)
14 hours ago |
4.7 / 5 (3) |
0
(PhysOrg.com) -- Plastic cards with security features are ubiquitous these days, having a wide variety of uses such as credit cards, employee cards, licenses, and so on. Many have holographic images, but they ...
New cancer study takes major step toward improved treatment
7 hours ago |
5 / 5 (1) |
1
Cancer researchers at the University of Oklahoma Health Sciences Center have found a way to turn ineffective new cancer drugs into cancer-fighters. By using their patented chemical compound, SHetA2, researchers tricked cancer ...
Superior Super Earths
Space & Earth / Space Exploration
Nov 30, 2009 |
4.8 / 5 (42) |
13
Super Earths are named for their size, but these planets - which range from about 2 to 10 Earth masses - could be superior to the Earth when it comes to sustaining life. They could also provide an answer to ...
Shape shifters: Researchers create new breed of antennas
9 hours ago |
4.6 / 5 (8) |
3
Antennas aren't just for listening to the radio anymore. They're used in everything from cell phones to GPS devices. Research from North Carolina State University is revolutionizing the field of antenna design ...
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