New computer program predicts crack initiation in 3-D

Most structures and materials have defects, and if the conditions are right, these defects can lead to the initiation and propagation of cracks. Finding out where and with what orientation a surface crack is most likely to ...

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.


Snakes help engineers design search and rescue robots

Snakes live in diverse environments ranging from unbearably hot deserts to lush tropical forests, where they slither up trees, rocks and shrubbery every day. By studying how these serpents move, Johns Hopkins engineers have ...

Energy & Green Tech

How a surface treatment improves the inside of a solar cell

Physicists from the University of Luxembourg with European experts have succeeded in explaining the recent efficiency improvements in thin film solar cells. The work of the whole consortium has been published in the prestigious ...

Computer Sciences

Patent talk: Mobile device with solar panels

Are we to expect to see a future Surface Pro with solar panels? Microsoft has thought about a solar power idea as apparent in a patent that the tech giant filed with the USPTO, namely, "Mobile device cover with integrated ...

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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.

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