Thin-film technologies for the energy transition

Glass facades characterize modern architecture. While solar radiation serves to support heating in winter, the building interior heats up in summer and requires active cooling. Smart windows can regulate the solar radiation ...


Artificial soft surface autonomously mimics shapes of nature

Engineers at Duke University have developed a scalable soft surface that can continuously reshape itself to mimic objects in nature. Relying on electromagnetic actuation, mechanical modeling and machine learning to form new ...

Energy & Green Tech

Research team undertakes study of perovskite photovoltaic modules

A research team has conducted a review of recent advances in perovskite photovoltaic modules. Perovskite solar cells hold great promise for the next generation of photovoltaic technology. With this promising technology comes ...


Laser polishes 3D-printed metal parts better than ever before

Researchers from Skoltech and MEPhI have devised a laser polishing technique that effectively removes both surface roughness and subsurface pores in intricately shaped metal parts manufactured with a 3D printer. Described ...

Energy & Green Tech

Wireless tech measures soil moisture at multiple depths in real time

Researchers from North Carolina State University have developed a wireless system that uses radio transmitters and receivers to estimate soil moisture in agricultural fields at multiple depths in real time, improving on existing ...

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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