Electronics & Semiconductors

Smart films facilitate human-machine interaction

Imagine this: A smooth touchscreen display placed on top of a thin silicone polymer film suddenly generates the feeling of a tiny raised button under the user's finger. Or how about the idea of wearing that same polymer film ...


4D composite printing could improve the wings of drones

The aviation industry faces multiple pressures from higher fuel costs and increased scrutiny over the environmental and quality-of-life impacts from its aircraft. Researchers are looking for new methods of keeping expenses ...

Energy & Green Tech

Perovskite solar modules: High efficiency on a large surface area

From cell to module without loss of efficiency: This is one of the main challenges of perovskite photovoltaics. Researchers at Karlsruhe Institute of Technology (KIT) have now managed to produce perovskite solar modules with ...


A fluid-magnetic solution for sorting plastic waste

With the ever-increasing worldwide mass production of plastic, the inefficiency of current plastic recycling strategies has raised several environmental, societal, and economic concerns. Magnetic density separation (MDS) ...

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 ...

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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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