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Fractured ice sheets on Mars

Where the two hemispheres of Mars meet, the planet is covered in broken-up terrain: a sign that slow-but-steady flows of icy material once forged their way through the landscape, carving out a fractured web of valleys, cliffs ...

How to expand and contract curved surfaces of all shapes

Researchers at TU Delft's department of Precision and Microsystems Engineering (PME) have designed a dilation method that can be applied to any curved surface. This universal method may have a range of applications, including ...

Australia bushfires renew anger over climate change

Unprecedented bushfires in eastern Australia have turbocharged demands the country's conservative government do more to tackle climate change, and have rekindled an ideological fight over the science behind the blazes.

ESA's Mars orbiters did not see latest Curiosity methane burst

In June, NASA's Curiosity rover reported the highest burst of methane recorded yet, but neither ESA's Mars Express nor the ExoMars Trace Gas Orbiter recorded any signs of the illusive gas, despite flying over the same location ...

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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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