What is analytic geometry?

What Does analytic geometry Mean

The branch of Mathematics that has as its object of study the proportions and singularities of different figures located on a plane or in space is defined as geometry . This discipline , according to experts, in order to represent reality appeals to axiomatic systems ; in this way, it employs symbol-based mathematical structures that allow it to develop strings which, in turn, are linked via certain rules and generate new strings.

When it comes to establishing the origin of analytical geometry, there are still many discussions among mathematicians and historians as some attribute its paternity to one scientist and others to a different one. However, what is true and indisputable is that there are three historical figures who were the first to use and develop it in one way or another.
One of them was the Persian mathematician and astronomer Omar Jayam (1048-1131). This carried out a series of works that would become fundamental in this scientific area and that would act as pillars for the development of later theories. Among those are, for example, Dissertation on a possible proof of the parallel postulate or Thesis on proofs of algebra .

From these texts made by said Persian author it seems that the French scientist René Descartes (1596 - 1650) could have “drunk”, who is another of the key figures in the origin of analytic geometry and is that many authors rule that he is the father of it. Thus, among his main contributions would be found the so-called Cartesian axes and among his most influential works is, for example, Geometry .
Along with these two important figures, the French mathematician Pierre de Fermat (1601-1665), also known as Eric Temple Bell, should not be overlooked. This is considered as the discoverer of the fundamental principle of analytical geometry and has gone down in history not only for this but also for his theory of numbers.
It should be noted that there are different classes of geometries that mark a specialization from their name, as happens when talking about descriptive, projective, plane geometry or the geometry of space. In the case of analytical geometry , it is a discipline that proposes to analyze the figures from a coordinate system and using the methods of mathematical analysis and the field of algebra.
Analytical geometry tries to obtain the equation of the coordinate systems as a function of their locus. On the other hand, this discipline allows to determine the geometric place of the points that are part of the equation of the coordinate system.
A point in the plane that is part of a coordinate system is determined by two figures, which are called the abscissa and the ordinate of the point. In this way, it is achieved that all the points of the plane are represented by two ordered real numbers and vice versa (that is, every ordered pair of digits is related to a certain point of that plane).

These characteristics allow the coordinate system to establish a correspondence between the geometric concept of the points in the plane and the algebraic concept of the ordering pairs of numbers, laying the foundations of analytical geometry.
Thanks to this relationship, it is possible to determine plane geometric figures through equations formulated with two unknowns.