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Electrons take new shape inside unconventional metal

One of the biggest achievements of quantum physics was recasting our vision of the atom. Out was the early 1900s model of a solar system in miniature, in which electrons looped around a solid nucleus. Instead, quantum physics ...

Best of Last Year: The top articles of 2022

It was a good year for research of all kinds as three men shared the Nobel Prize in physics for their work that showed that tiny particles separated from one another at great distances can be entangled. Alain Aspect, John ...

The secret to the skillful skydiving of wingless springtails

Early in the pandemic, Víctor Ortega-Jiménez was exploring creeks near his home and observing springtails. The organisms are the most abundant non-insect hexapods on earth, and Ortega-Jiménez suspected their avoidance ...

Magma on Mars likely, study finds

Since 2018, when the NASA InSight Mission deployed the SEIS seismometer on the surface of Mars, seismologists and geophysicists at ETH Zurich have been listening to the seismic pings of more than 1,300 marsquakes. Again and ...

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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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