## What is: "surface" ‒Definiciones and concepts -

### 1. Concept of surface in the Wikipedia Encyclopedia

A surface is in fact a set of points in a Euclidean space which is a two-dimensional topological space which locally, i.e., seen closely resembles the two-dimensional Euclidean space. Thus around every point on a surface this is approximated well by the plane tangent to the surface at that point.
A traditional definition of surface which refers to intuitive terms but that it is easy to work from a mathematical point of view was the one given by Euclid:
A surface is what only has length and width. Euclid, elements, book I, definition 5.

#### Formal definitions

A surface is a two-dimensional variety, i.e. a topological object which locally "looks" to the flat Euclidean $\mathbb{R}^2$ (technically locally homeomorfo to the plane). That means that if we take a lot very little of the surface is similar to the Euclidean plane, like in the middle of a plain local land surface seems flat.
More formally the local homeomorphism between a surface and the flat Euclidean implies that for each point on a surface there is a neighbourhood of P (a small region that surrounds it) that is homeomorphic to an open disk of $\mathbb{R}^2$. This property of being homeomorphic to the plane allows you to build a two-dimensional local coordinate system around any point on the surface. You can call the local homeomorphism that will surface to $\mathbb{R}^2$ and letter to the inverse (of this homeomorphism) parameterization. It is not always possible to parameterize a surface with a unique local homeomorphism.
A surface (topological) with border is a topological space of Hausdorff type in which each point has a neighborhood open V for which there exists a homeomorphism φ with an open Assembly of the upper semiplano of the flat Euclidean $\mathbf{E}^2$. The ordered pair (V, φ) is called letter (local) coordinate of the point [this letter is not unique because there are indeed many possible choices of coordinates for each point].

### 2. Definition of surface

The word surface has a common use in our language, and we have several references since it is used in different way according to the field in question.
In geographical terms, a surface will be the extension that presents a certain territory and therefore will be the area that occupies the same. Water, flood has covered the entire surface of the province of Chaco, in the Argentina.
Also, in physics, we find a reference to the word given that here also indicates the extension that presents something considering two-dimensional: its width and length.
Noteworthy is that the unit par excellence and from which is measured a surface is square meter, which is equivalent to the surface that has a square that measures one meter from side. Another unit that is also widely used in this sense is the square kilometre.
The surface of the countries that make up our planet are precisely expressed in square kilometers. Thus for example Italy has an area of 301.338 square kilometers.
Meanwhile, the surfaces of houses, apartments, land, are expressed in square meters. My uncle sells a Department of 200 square meters in the center of the city.
To determine the values of the properties is what multiply value that presents the square meter in the area or district corresponding by the number of meters that presents the House or apartment in question.
On the other hand, we call surface on the outside of any body, object that well serves as a boundary with the outside or something in particular.
For mathematics, the surface will be that extension of which only takes into account the length and the width. In this way we have a two-dimensional space.
In the colloquial language, it is also usual that this word is used to indicate the aspect that presents an issue, a person, or their appearance. Only I know Laura on surface, I could not tell you how to react to this situation.
And on the other hand the concept of large surface is used to refer to an establishment of commercial type which has a significant size and is characterized by offering outstanding offers to the public.

### 3. Definition of surface

The surface word derives from the latin superficĭes. In its most common use, refers to a portion of land or to the extent of something (i.e. a difference between what is a body or entity and what is not).
For example: "Argentina has an area of 2.780.400 km2, it is one of the eight largest countries in the world", "much of the surface of the province has been affected by the floods", "the ball bounced off the surface of the playing field".
Starting with the first example we can establish that Russia is the country with largest area of all over the world because it has more than 17 million square kilometers. They would continue to the others such as Canada, United States, China, Brazil, Australia, India and Argentina.
Also as opposed all these Nations that are placed in the top ten of the most extensive that exist in the world, we have to stress that the Vatican is the lower surface of the same country as your extension does not exceed what is the square kilometre.
Very important also is the different measures of surface there and employ on a daily basis to determine the same. In this sense, we can establish that unquestionably the fundamental unit to measure those areas is square meter that would amount to the surface that has a square with side 1 meter.
However, can also be use of other measures as it would be the case of the square kilometre which is equivalent to one million square meters, the square hectometre which is equal to ten thousand square meters or the square decametre which is equivalent to one hundred square meters.
Among the measures that are used below the fundamental unit are the square decimeter (0.01 square meter), (0.0001 square meter) square centimeter and the square millimeter (0,000001 square meter).
Based on all this, we see that for some units to other option is multiplied or divided by the unit followed by so many pairs of zeros as places there are between.
The surface, on the other hand, is the outward appearance of something: "table has a surface too rough and uncomfortable at lunchtime", "I like dresses for smooth surface", "the surface of this fruit is rough".
Geometry and mathematics, the surface is an extension that only two dimensions are taken into account. Surface, in these cases, is described as a two-dimensional variety.
For physics, the surface is also a magnitude that indicates the extent of an object in two dimensions: the length and the width. Your unit in the international system is the square meter (m²).
A surface of revolution, finally, is that which occurs when a planar curve rotated about an axis that is in the same plane. If what rota is a straight line that is parallel to its axis, it speaks of surface of cylindrical revolution. Other surfaces of revolution are the conical revolved surface, the surface of spherical revolution and revolution toroidal surface.

### 4. Definition of surface

Surface is a word of Latin origin which may indicate the limit and extent of bodies, as when it is said that a House has a surface area of 100 square meters. In geography refers to the area which occupies a territory. On the surface, the longitude and latitude only are taken into account. In the international system of measurements, measurements of surface unit is square meter.
The Earth's surface is all that occupies the planet Earth in terms of its land. The surface of the water is the outer-most of them, contrary to its depth. The surface of things in general is its outside. Thus we say for example, that the trunk of the tree has a rough surface and Brown.
In geometry is called cylindrical surface which is formed by a straight line, when it moves in the same direction and that three consecutive positions are located in the same plane. When a straight, turn, happens to always equal point, unless consecutively three positions are at same point, is called a conical surface. A surface is flat, when straight lines in any direction; be plotted on it otherwise it is a curved surface.
To rotate a semicircle around its diameter, as the axis of revolution, it forms a spherical surface, where all points are equidistant from the Center, which is an interior point. For the spherical surface area the area of the maximum circle of the sphere must multiply by four.