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Singapore's first 3D-printed artefact to be launched to the moon

The Moon Gallery Foundation is developing an art gallery to be sent to the Moon, contributing to the establishment of the first lunar outpost and permanent museum on Earth's only natural satellite. The international initiative ...

Microfountain pen draws minute patterns for live cells, circuits

Advances in intuitive microwriting devices that can print microstructures could pattern electric circuits and more. The setup, featuring a robot arm to hold the micropen, deposits ink onto the surface, much like writing by ...

Image: Tiny crystal of power as basis for solar cell

This crystal of iron pyrite, just four hundredths of a millimeter in size, could function as the light absorbing layer of a tiny solar cell—potentially a promising future source of power on the moon.

Lunar radar data uncovers new clues about moon's ancient past

The dusty surface of the moon—immortalized in images of Apollo astronauts' lunar footprints—formed as the result of asteroid impacts and the harsh environment of space breaking down rock over millions of years. An ancient ...

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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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