Electronics & Semiconductors

A better pen-and-ink system for drawing flexible circuits

Conductive ink is a great tool for printing flexible electronic circuits on surfaces. But these inks can be costly, they do not work on some materials, and devices to apply them can plug up. Now, scientists report in ACS ...


Researchers invent flexible and highly reliable sensor

Real-time health monitoring and sensing abilities of robots require soft electronics, but a challenge of using such materials lie in their reliability. Unlike rigid devices, being elastic and pliable makes their performance ...


Robotics enter the COVID-19 fight

A decontamination robot funded by the Office of Naval Research (ONR) and designed by several local universities was recently tested in Richmond Va. The robot—initially designed for shipboard firefighting and maintenance ...

Energy & Green Tech

Offshore wind research buoys float into California's waters

Two offshore wind research buoys managed by the U.S. Department of Energy's (DOE's) Pacific Northwest National Laboratory (PNNL) were deployed recently off the coast of California. This marks the first time the buoys have ...


Engineers print wearable sensors directly on skin without heat

Wearable sensors are evolving from watches and electrodes to bendable devices that provide far more precise biometric measurements and comfort for users. Now, an international team of researchers has taken the evolution one ...

Electronics & Semiconductors

Printing high-speed low-power organic transistors

For around 10 years, smartphones and computer screens have been based on a display technology composed of so-called thin film transistors. These are inorganic transistors that require very little power, and they have proven ...

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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