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How chlorine stabilizes next-gen solar cells at an atomic scale

A team of researchers led by Professor Yabing Qi in the Energy Materials and Surface Sciences Unit at the Okinawa Institute of Science and Technology Graduate University (OIST) in Japan have imaged the atoms at the surface ...

Novel functional biochar composites help to treat wastewater

A team led by Prof. Wu Zhengyan from the Hefei Institutes of Physical Science of the Chinese Academy of Sciences (CAS) recently fabricated novel functional biochar composites (FBCs) using two solid waste-red mud and corn ...

Ancient sea ice core sheds light on modern climate change

A 170 m record of marine sediment cores extracted from Adélie Land in Antarctica by the Integrated Ocean Drilling Programme is yielding new insights into the complicated relationship between sea ice and climate change.

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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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