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 ...

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, ...

Energy & Green Tech

Inside view could make organic solar cells more efficient

Organic solar cells have the potential to become a source of renewable energy which is inexpensive and fast to roll out and scale up. Physicists at the University of Oxford have explored some of the scientific fundamentals ...

Energy & Green Tech

Could a seawater battery help end our dependence on lithium?

With the ubiquity of lithium-ion batteries in smartphones and other rechargeable devices, it's hard to imagine replacing them. But the rising price of lithium has spurred a search for alternatives. One up-and-coming battery ...

Surface area

Surface area is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved then the definition of arc length of a curve. For polyhedra (objects with flat polygonal faces) the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of the surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.

General definition of surface area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century. Their work led to the development of geometric measure theory which studies various notions of surface area for irregular objects of any dimension. An important example is the Minkowski content of a surface.

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