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Belgium creates garbage highway for flood victims' waste

In eastern Belgium, an abandoned highway is almost completely buried under kilometres of piled-up rubbish: crushed refrigerators, splintered furniture, torn curtains, twisted metal, stuffed toys, defunct electronics and shards ...

Ultrafast electron microscopy leads to pivotal discovery

Everyone who has ever been to the Grand Canyon can relate to having strong feelings from being close to one of nature's edges. Similarly, scientists at the U.S. Department of Energy's (DOE) Argonne National Laboratory have ...

Ocean surface climates may disappear by 2100: study

Up to 95 percent of Earth's ocean surface will have changed by the end of the century unless humanity reins in its carbon emissions, according to research published Thursday.

The boiling crisis and how to avoid it

It's rare for a pre-teen to become enamored with thermodynamics, but those consumed by such a passion may consider themselves lucky to end up at a place like MIT. Madhumitha Ravichandran certainly does. A Ph.D. student in ...

Adding foreign atoms to graphene boosts its properties

Monolayer graphene finds practical applications in many fields, thanks to its desirable intrinsic properties. However, these properties can also limit its potentials. The addition of foreign atoms can help, but requires precise ...

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 ...

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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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