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Toward the scaling up of nanocages to trap noble gases

Over the past few years, scientists have demonstrated how cage-like, porous structures made of silicon and oxygen and measuring only billionths of a meter in size can trap noble gasses like argon, krypton, and xenon. However, ...

Why boiling droplets can race across hot oily surfaces

When you're frying something in a skillet and some droplets of water fall into the pan, you may have noticed those droplets skittering around on top of the film of hot oil. Now, that seemingly trivial phenomenon has been ...

Dragonfly mission to Titan announces big science goals

Among our solar system's many moons, Saturn's Titan stands out—it's the only moon with a substantial atmosphere and liquid on the surface. It even has a weather system like Earth's, though it rains methane instead of water. ...

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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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