The point in geometry can be described as a fundamental entity.
We are likely to encounter the idea of point in various contexts. The term can refer to a circle -shaped mark ( "There is a red dot on the wall" ), to an orthographic sign ( "Don't forget to close sentences with a period" ), to a unit that allows punctuation to be kept in a game ( “Manu Ginobili scored 34 points in a new victory for the Argentine national team” ) or even a place ( “The church is the only safe spot in the city” ).
On this occasion, we are going to focus on the notion of a point in geometry . It should be explained, first of all, that geometry is the branch of mathematics oriented to the analysis of measurements and properties of figures in a space or on a plane.
The notion of point in geometry
The point in geometry is a fundamental entity : this means that it can only be defined by making a comparison with other elements. In this way, the point is not defined by itself, but rather acquires its meaning from its relationship with other concepts .
Geometry has two other fundamental entities in addition to the point: the plane and the line . Thus we can say that a line is an infinite succession of points and that a plane is the ideal object that houses an infinite number of points and lines.
The point, in this way, is a figure that lacks dimensions (it does not have volume, length, etc.) and that, therefore, does not belong to the physical world. What a point does in geometry is to point out a certain spatial position that is established from a coordinate system.
The point in geometry can be considered in a plane or in three-dimensional space.
Depending on the needs, we can talk about a point on a two -dimensional plane, which will have a value on the x axis and another on the y axis, or in a three-dimensional plane, in which its position in the z axis. Although the notion of axis is theoretical and as arbitrary as many other mathematical concepts, by convention it is usually understood that: the x axis represents the horizontal position; the and, the vertical; the z is perpendicular to the point of view. In some cases, the z and y are vertical and perpendicular, respectively.
Utility of the concept
The concept of a point in geometry is useful in many areas, many of them outside mathematics . Two clear examples are the computer animation industry and the video game industry, which use geometry for the graphic representation of objects and characters in two or three dimensions. Leaving aside the very advanced techniques, which only a few graphics engines use, both a four-legged table and a human being or a vase are positioned in the virtual universe by means of a single point.
When a point is used to represent the location of a complex object in space, it must have an invariant position with respect to the last one. It is important to note that this point is called the " center ", although it is rarely the geometric center itself. For example, if it is a humanoid character, we could decide that its center is located right at the base of the body, aligned to the center on the x and z axes, to be in the middle of the feet and below them.
This point is used not only to calculate the position of an object in space, but also to use it as a reference for its rotations, although in this case it is also necessary to have a vector that indicates the orientation at all times, so that we always know where it is looking and how to distinguish each of its sides or faces. In more complex cases, more than one point is used, to detect the position of individual parts and achieve more precise results.