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Planning for a smooth landing on Mars

A U.S. mission to land astronauts on the surface of Mars will be unlike any other extraterrestrial landing ever undertaken by NASA.

Researchers discover way to bind nanotubes to metals

Carbon nanotubes have shown promise for everything from microelectronics to aviation to energy storage. Researchers think this material might one day fulfill the science fiction dream of creating an elevator to space.

Magnetizing water drops to make them hop

A small combined team of material scientists from Sun Yat-sen University and Dalian University of Technology, both in China, has found that it is possible to make a single drop of water hop in desired ways by putting a magnetic ...

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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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