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Bacteria navigate on surfaces using a 'sense of touch'

Many disease-causing bacteria such as Pseudomonas aeruginosa crawl on surfaces through a walk-like motility known as "twitching." Nanometers-wide filaments called type IV pili are known to power twitching, but scientists ...

Meet the Martian meteorite hunters

A team at the Natural History Museum (NHM), London is paving the way for future rovers to search for meteorites on Mars. The scientists are using the NHM's extensive meteorite collection to test the spectral instruments destined ...

Tiny organisms shed big light on ocean nutrients

As the world warms, sweeping changes in marine nutrients seem like an expected consequence of increased ocean temperatures. However, the reality is more complicated. New research suggests that processes below the ocean surface ...

Long-period oscillations of the Sun discovered

A team of solar physicists led by Laurent Gizon of the Max Planck Institute for Solar System Research (MPS) and the University of Göttingen in Germany has reported the discovery of global oscillations of the Sun with very ...

Climate change sees Swiss Alps add over 1,000 lakes: study

Climate change has dramatically altered the Swiss Alp landscape—at a quicker pace than expected—as melting glaciers have created more than 1,000 new lakes across in the mountains, a study published Monday showed.

Scientists get to the bottom of deep Pacific ventilation

Recent findings, with important implications for ocean biogeochemistry and climate science, have been published by Nature Communications in a paper by Associate Professor Mark Holzer from UNSW Science's School of Mathematics ...

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Surface

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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