Robots collect underwater litter

Removing litter from oceans and seas is a costly and time-consuming process. As part of a European cooperative project, a team at the Technical University of Munich (TUM) is developing a robotic system that uses machine learning ...

Energy & Green Tech

Prospects for more efficient solar energy conversion

Energy is an essential commodity of our existence, as such, having a sustainable, renewable and affordable energy source is vital. Of all the renewable energy sources, the sun is the most promising due to the vast amount ...

Energy & Green Tech

Is it sensible to use rainwater to flush the toilet?

As a world first, a new residential district in Aarhus is using secondary water from the local water utility for toilets and washing machines. The solution is supported by a life cycle assessment.

Energy & Green Tech

An ironclad future for solar arrays

Solar energy plays an important role in the fight against climate change as a substitute for fossil fuels. Dye-sensitized solar cells promise to be a low-cost supplement to the photovoltaic systems we know today. Their key ...


Marangoni surfer robots look and move like water bugs

From birds in the sky to fish in the sea, nature's creatures possess characteristics naturally perfected over millennia. Studying them leads engineers to create new technologies that are essential to our way of life today. ...


National shortage of Australian groundwater experts

Australia's future growth is closely aligned to good resources management, and water is top of the list. This is underpinning a growing shortage of groundwater scientists and engineers.

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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.

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