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Limitation exposed in promising quantum computing material

Quantum computers promise to perform operations of great importance believed to be impossible for our technology today. Current computers process information via transistors carrying one of two units of information, either ...

Partial lunar eclipse to grace U.K. evening sky

Tuesday, 16 July, will see a partial eclipse of the moon, visible in the U.K. after sunset. The eclipse, 50 years to the day after the launch of Apollo 11, will also be seen across a large part of Asia, the whole of Africa, ...

Model development is crucial in understanding climate change

Numerical models are a key tool for climate scientists in understanding the past, present and future climate change arising from natural, unforced variability or in response to changes, according to Dr. Qing Bao, Research ...

Moon dust is not to be sneezed at

When the astronauts of the Apollo 11 mission returned to Earth, they had almost 22 kilograms of rock from the surface of the moon in their baggage. Josef Zähringer from the Max Planck Institute for Nuclear Physics in Heidelberg ...

The habitability of Titan and its ocean

Saturn's largest moon, Titan, is a hotbed of organic molecules, harboring a soup of complex hydrocarbons similar to that thought to have existed over four billion years ago on the primordial Earth. Titan's surface, however, ...

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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.

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