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ESA and Auroch Digital launch Mars Horizon game

You're controlling your very own space agency at the dawn of the space age, with the ultimate goal of setting foot on the surface of Mars. Which technologies should you research? Which rockets should you build? Should you ...

Stable catalysts for new energy

On the way to a CO2-neutral economy, we need to perfect a whole range of technologies—including the electrochemical extraction of hydrogen from water, fuel cells, or carbon capture. All these technologies have one thing ...

Understanding the utility of plasmas for medical applications

Plasma medicine is an emerging field, as plasmas show promise for use in a wide range of therapies from wound healing to cancer treatment. Plasma jets are the main plasma sources typically used in plasma-surface applications. ...

COVID-19 virus survives on surfaces within thin film

How does the COVID-19 virus manage to survive on surfaces? To find out, researchers in India are exploring the drying times of thin liquid films that persist on surfaces after most respiratory droplets evaporate.

Nature's toolkit for killing viruses and bacteria

They burst out of toilet bubbles, swim across drinking water, spread through coughs. Tiny infectious microbes—from the virus that causes COVID-19 to waterborne bacteria—kill millions of people around the world each year. ...

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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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