Software

Artificial intelligence shines light on the dark web

Beneath the surface web, the public form of the internet you use daily to check email or read news articles, exists a concealed "dark web." Host to anonymous, password-protected sites, the dark web is where criminal marketplaces ...

Robotics

A friction reduction system for deformable robotic fingertips

Researchers at Kanazawa University have recently developed a friction reduction system based on a lubricating effect, which could have interesting soft robotics applications. Their system, presented in a paper published in ...

Robotics

Robots with sticky feet can climb up, down, and all around

Jet engines can have up to 25,000 individual parts, making regular maintenance a tedious task that can take over a month per engine. Many components are located deep inside the engine and cannot be inspected without taking ...

Engineering

Geckos filmed to find out how they walk on water

Anyone who's seen a gecko will likely know they can climb walls. But these common lizards can also run across water nearly as fast as they can move on solid ground. Yet while we know how geckos scale smooth vertical surfaces ...

Energy & Green Tech

A paper battery powered by bacteria

In remote areas of the world or in regions with limited resources, everyday items like electrical outlets and batteries are luxuries. Health care workers in these areas often lack electricity to power diagnostic devices, ...

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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