Diseases, Conditions, Syndromes

Researchers develop long-lasting disinfecting spray for surfaces

Researchers at the University of Arkansas and the University of Arkansas for Medical Sciences have developed a long-lasting spray that disinfects surfaces for extended periods, even in heavy use, and is less likely to transmit ...


A new optical system shows how decisions light up the brain

When we make even simple decisions about how to interact with the world, we rely on computations performed by networks of neurons that span our brains. But what exactly are these neural networks computing?

Medical research

New molecule stops drug cravings in mice, with fewer side effects

Duke University researchers have developed a synthetic molecule that selectively dampen the physiological rewards of cocaine in mice. It also may represent a new class of drugs that could be more specific with fewer side ...

Oncology & Cancer

Cancer cells deactivate their 'Velcro' to go on the attack

Cancer cells remain clumped together via a sort of 'Velcro' which allows them to adhere to each other wherever they appear. In order for cancer cells to leave a tumour and spread throughout the body during metastatic processes, ...

Diseases, Conditions, Syndromes

Why don't antibodies guarantee immunity?

With millions of COVID-19 cases reported across the globe, people are turning to antibody tests to find out whether they have been exposed to the coronavirus that causes the disease. But what are antibodies? Why are they ...

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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.

This text uses material from Wikipedia, licensed under CC BY-SA