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Metal scar found on cannibal star

When a star like our sun reaches the end of its life, it can ingest the surrounding planets and asteroids that were born with it. Now, using the European Southern Observatory's Very Large Telescope (ESO's VLT) in Chile, researchers ...

Projection mapping leaves the darkness behind

Images projected onto objects in the real world create impressive displays that educate and entertain. However, current projection mapping systems all have one common limitation: they only work well in the dark. In a study ...

Advancing tissue engineering with shape memory hydrogels

One of the primary goals in the field of tissue engineering and regenerative medicine is the development of artificial scaffolds that can serve as substitutes for damaged tissue. These materials must ideally resemble natural ...

Soft support can make unexpectedly stable glass

Glasses are ubiquitous materials found in building materials, beverage containers, soft electronics, and mobile phone screens. The creation of naturally dense and rigid glass occurs through a process known as aging. It involves ...

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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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