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New property of light discovered

A team of researchers affiliated with several institutions in Spain and the U.S. has announced that they have discovered a new property of light—self-torque. In their paper published in the journal Science, the group describes ...

Filming how our immune system kill bacteria

To kill bacteria in the blood, our immune system relies on nanomachines that can open deadly holes in their targets. UCL scientists have now filmed these nanomachines in action, discovering a key bottleneck in the process ...

Study shows that the Moon is older than previously believed

A new study spearheaded by Earth scientists at the University of Cologne's Institute of Geology and Mineralogy has constrained the age of the Moon to approximately 50 million years after the formation of the solar system. ...

The space rock that hit the moon at 61,000 kilometers an hour

Observers watching January's total eclipse of the Moon saw a rare event, a short-lived flash as a meteorite hit the lunar surface. Spanish astronomers now think the space rock collided with the Moon at 61,000 kilometres an ...

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Surface

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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