## What Does half plane Mean

The concept of semi - plane 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 portions (that is, into two half-planes).

To understand what a half plane is, it is essential to understand the notion of plane . It can be said that a plane is an ideal geometric object that contains an infinite number of lines and points and that it has only two dimensions. The plane , the line and the point are the essential concepts of the specialty of mathematics that we know as geometry.

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

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

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

In the same way, we cannot forget that there are two fundamental types of semi-

planes : -Open semi-plane , which is one in which the intersection is the straight common edge. That is, it does not contain the line that limits it.

-Closed half-plane. Under this name is the semi-plane that, unlike the previous one, does contain the aforementioned line in charge of delimiting it.

Then:

If the half plane 1 contains the point P and the half - plane two containing the point S , the segment PS cut the line X . On the other hand, if the half plane 1 has points P and W , the segment PW will not cut the line.

Likewise, there are other data of interest that are worth knowing about this element in question, such as the following: -

Every point in a plane belongs to the division line or to one of the two aforementioned semi-planes.

-Any segment that is determined by what two points of the same half-plane are does not intersect 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 the above, we cannot ignore the existence of different types of semi-planes that have become fundamental elements of Geometry. This would be the case, for example, of the so-called Poincaré half-plane or Poincaré upper half-plane, which was discovered by the mathematician who gives it its name.

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