Energy & Green Tech

A cooling system that works without electricity

It looks like a regular roof, but the top of the Packard Electrical Engineering Building at Stanford University has been the setting of many milestones in the development of an innovative cooling technology that could someday ...

Computer Sciences

'Surfing attack' hacks Siri, Google with ultrasonic waves

Ultrasonic waves don't make a sound, but they can still activate Siri on your cellphone and have it make calls, take images or read the contents of a text to a stranger. All without the phone owner's knowledge.

Engineering

3-D printing hair structures opens up fascinating design space

(Tech Xplore)—Scientific research into stuff—what things are made of, what they could be made of, what everyday applications could expand into groundbreaking applications with everyday materials—is very much alive and ...

Energy & Green Tech

Could a seawater battery help end our dependence on lithium?

With the ubiquity of lithium-ion batteries in smartphones and other rechargeable devices, it's hard to imagine replacing them. But the rising price of lithium has spurred a search for alternatives. One up-and-coming battery ...

page 1 from 8

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.

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