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New research sheds light on the possibility of past life on Venus

While today Venus is a very inhospitable place with surface temperatures hot enough to melt lead, geological evidence, supported by computer model simulations, indicate it may have been much cooler billions of years ago and ...

Satellites yield insight into not so permanent permafrost

Ice is without doubt one of the first casualties of climate change, but the effects of our warming world are not only limited to ice melting on Earth's surface. Ground that has been frozen for thousands of years is also thawing, ...

Israeli spacecraft Beresheet crash site spotted on moon

SpaceIL, an Israeli nonprofit organization, is dedicated to landing the first Israeli spacecraft on the Moon. Beresheet was their first attempt at meeting this goal. While the spacecraft did land, it first touched the surface ...

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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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