The boundary between solid metal and liquid metal can be much less "solid" than we ever suspected. RMIT researchers have discovered that the liquid-solid boundary can fluctuate back and forth, with metallic atoms near the ...
Analytical Chemistry
12 hours ago
0
94
This image may resemble the surface of Mars, but it was actually captured by the Copernicus Sentinel-2 mission, revealing the stunning terrain of northwest Namibia.
Planetary Sciences
May 3, 2024
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80
The interest in antimicrobial solutions for personal and multi-user touch screens, such as tablets and mobile devices, has grown in recent years. Traditional methods like sprayable alcohols or wipes are not ideal for these ...
Nanomaterials
May 3, 2024
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36
China on Friday launched a lunar probe to land on the far side of the moon and return with samples that could provide insights into differences between the less-explored region and the better-known near side.
Space Exploration
May 3, 2024
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155
A bemused fishmonger at a seafood market in Portsmouth, N.H., weighed and packaged a dozen filets of fish and three lobster tails for his unusually exacting customers, Dartmouth researchers Celia Chen, Guarini, a research ...
Environment
May 2, 2024
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5
Researchers have discovered the missing piece of the puzzle behind a rare opening in the sea ice around Antarctica, which was nearly twice the size of Wales and occurred during the winters of 2016 and 2017.
Earth Sciences
May 1, 2024
1
244
We all have our own preferred drinking temperatures for different alcoholic beverages, with people commonly enjoying beer or white wine chilled, red wine near room temperature, or baijiu (Chinese whisky) or sake warmed.
Analytical Chemistry
May 1, 2024
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27
A research team using the ChemCam instrument onboard NASA's Curiosity rover discovered higher-than-usual amounts of manganese in lakebed rocks within Gale Crater on Mars, which indicates that the sediments were formed in ...
Astrobiology
May 1, 2024
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4636
A Chinese spacecraft returned to Earth on Tuesday with three astronauts who completed a six-month mission aboard the country's orbiting space station.
Space Exploration
Apr 30, 2024
0
8
The past 10 years have seen a series of "warm blobs" in the northeast Pacific Ocean. These marine heat waves do widespread damage to ecosystems and marine life in the area, but the mechanisms by which they develop and are ...
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.
This text uses material from Wikipedia, licensed under CC BY-SA
