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Electrons take new shape inside unconventional metal

One of the biggest achievements of quantum physics was recasting our vision of the atom. Out was the early 1900s model of a solar system in miniature, in which electrons looped around a solid nucleus. Instead, quantum physics ...

'Superdeep' diamond deepens our understanding of plate tectonics

A unique combination of minerals trapped inside a "superdeep" diamond that originated hundreds of kilometers beneath Earth's surface sheds new light on plate tectonics, the geological processes that give rise to mountains, ...

Rapid production of antibubbles with a jet

University of Twente researchers succeeded in the rapid fabrication of microscopic "antibubbles." Previous methods to produce these liquid droplets surrounded by an air layer were either lacked controllability or were prone ...

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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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