Super-strong surgical tape detaches on demand

Last year, MIT engineers developed a double-sided adhesive that could quickly and firmly stick to wet surfaces such as biological tissues. They showed that the tape could be used to seal up rips and tears in lungs and intestines ...


Microlandscaped abrasive tools deliver perfect grinding results

Tiny pyramids and cubes precisely aligned in rows and columns or radial lines of minute raised dots—these microscopic structures whose size is similar to the width of a human hair, are enabling engineers to design novel ...

Energy & Green Tech

Stiffer roadways could improve truck fuel efficiency

Every time you hear a deep rumble and feel your house shake when a big truck roars by, that's partly because the weight of heavy vehicles causes a slight deflection in the road surface under them. It's enough of a dip to ...

Energy & Green Tech

Water vapor in the atmosphere may be prime renewable energy source

The search for renewable energy sources, which include wind, solar, hydroelectric dams, geothermal, and biomass, has preoccupied scientists and policymakers alike, due to their enormous potential in the fight against climate ...


Image fusion method for underground pipeline leakage detection

The water supply network is closely connected to all aspects of society. Acoustic methods could be applied to underground pipe network monitoring and leakage detection through measurements using acoustic/vibration sensors ...

page 1 from 8


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.

This text uses material from Wikipedia, licensed under CC BY-SA