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The concept of semi-plane It is used in the field of geometry to name the portions of a plane that are delimited by any of its lines. It should be noted that each line divides the plane into two parts (that is, two semi-planes).

To understand what a semi-plane is, it is essential to understand the notion of flat . It can be said that a plane is an ideal geometric object that houses an infinite amount of lines and points and has only two dimensions. He flat , the straight and the point These are the essential concepts of the specialty of mathematics that we know as geometry.

The planes, therefore, are divided into semiplanes by straight that go through it. Each of the lines, in this way, generates two half-planes in the plane . These semiplanes, of course, do not necessarily have the same dimensions.

The laws of geometry indicate that in each pair of semiplanes created by a line x there is an infinite amount of points . Every point belonging to the plane in question, on the other hand, belongs to one of the two semiplanes determined by the line or the line itself.

Two points contained in the same semiplane, in addition, form a segment that does not intersect with the straight x , while two points contained in different semiplanes create a segment that does cut the line x .

In the same way, we cannot forget that there are two fundamental types of semiplanes:
-Sepiplano open, which is one in which the intersection is the straight common edge. That is, it does not contain the line that limits it.
-Sepiplano closed. Under this denomination is the semiplane that, unlike the previous one, does contain the aforementioned line in charge of limiting it.

So:

If the semiplane 1 house the point P and the semiplane 2 contains the point S , the segment $ will cut the straight X . On the other hand, if the semiplane 1 count the points P and W , the segment PW will not cut the line.

There are also other interesting data that are worth knowing about this element that concerns us, such as the following:
-Every point of a plane belongs to the line of the division or to one of the two mentioned semiplanes.
-Any segment that is determined by what are two points of the same semiplane does not cut what is called the division line. On the contrary, any segment that is determined by what are two points of the different semiplanes does proceed to cut the mentioned division line.

In addition to all of the above, we cannot ignore the existence of different types of semiplanes that have become fundamental elements of Geometry. This would be the case, for example, of the so-called half-plane of Poincaré or upper half-plane of Poincaré, which was discovered by the mathematician who gives it its name.

Basically under that denomination is a semiplane model that is the fundamental axis of hyperbolic geometry and is known as the upper semiplane. It has the peculiarity that it takes the top of what is the Cartesian plane but without "taking" what is the x-axis.

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