Engineering

Researchers flip how electrical signals move liquid droplets

When medical laboratories analyze blood samples for signs of disease, they sometimes use instruments that rely on a technology called digital microfluidics. The technique uses electric signals to pull tiny droplets of the ...

Robotics

Enhancing the locomotion of small robots with microwheels

Microbots could have several useful applications, particularly within biomedical and healthcare settings. For instance, due to their small size, these small machines could be inserted within the human body, allowing doctors ...

Robotics

How can robots land like birds?

Under the watchful eyes of five high-speed cameras, a small, pale-blue bird named Gary waits for the signal to fly. Diana Chin, a graduate student at Stanford University and Gary's trainer, points her finger to a perch about ...

Machine Learning & AI

Machine learning predicts blackouts caused by storms

Thunderstorms are common all over the world in summer. As well as spoiling afternoons in the park, lightning, rain and strong winds can damage power grids and cause electricity blackouts. It's easy to tell when a storm is ...

Robotics

Researchers develop new flying / driving robot

The first experimental robot drone that flies like a typical quadcopter, drives on tough terrain and squeezes into tight spaces using the same motors, has been developed by Ben-Gurion University of the Negev (BGU) researchers.

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 ...

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, ...

page 1 from 4

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