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NASA space station research helps power moon science

The International Space Station supports a wide range of scientific activities, from looking out at our universe to breakthroughs in medical research, and is an active proving ground for technology for future moon exploration ...

SwRI-led sounder instrument deploys across lunar surface

Just hours after touching down on the surface of the moon on March 2nd aboard Firefly Aerospace's Blue Ghost 1 lander, the Southwest Research Institute-led Lunar Magnetotelluric Sounder (LMS) was activated and deployed its ...

Asteroid probe snaps rare pics of Martian moon

On the way to investigate the scene of a historic asteroid collision, a European spacecraft swung by Mars and captured rare images of the red planet's mysterious small moon Deimos, the European Space Agency (ESA) said Thursday.

Opening a new chapter in 3D microprinting with MXene

The Smart 3D Printing Research Team at KERI, led by Dr. Seol Seung-kwon has developed the world's first technology for printing high-resolution 3D microstructures using MXene, a material known as the dream material.

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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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