Is called geometry to the study of the magnitudes and characteristics of figures found in space or on a plane. Euclidean, for its part, is that linked to Euclid, a mathematician who lived in the Ancient Greece. And not only that but also that this illustrious figure became a teacher for important disciples such as Apollonius of Perga or Archimedes, among many others.
In the 3rd century BC, Euclid proposed five postulates that allow to study the properties of the regular shapes (lines, triangles, circles, etc.). Thus gave birth to euclidean geometry.
Euclidean geometry is currently considered to be that centered on the analysis of the properties of Euclidean spaces: geometric spaces that meet the axioms of the Greek thinker. Notably Euclid collected his postulates in his work “Elements”.
In this treatise, Euclid points out that a straight line can be created from the union of any two points; that a segment of a line can extend indefinitely in a straight line; that, given a line segment, we can draw a circumference with any distance and center; that all right angles are identical to each other; and that, if a line cuts two other lines and the sum of the interior angles of the same side is less than two right angles, the other two lines when extended will cut on the side where the angles smaller than the right ones are located.
When working with Euclidean spaces, Euclidean geometry takes care of full vector spaces that have a product internal and, therefore, they are metric and normed vector spaces. The spaces of non-Euclidean geometries, on the other hand, are curved spaces or with different characteristics from those mentioned in the propositions of Euclid.
Regarding this work entitled ‘Elements’, other data of interest must be established, among which we can highlight that it consists of thirteen books, that it was the author’s masterpiece and that it focuses on treating both two-dimensional and three-dimensional geometry. dimensions.
Likewise, it must be borne in mind that it is considered one of the most edited works in all of history, as it has more than a thousand editions. However, one of the most interesting editions, without a doubt, is the one carried out by Archimedes of Syracuse.
In addition to all these data, there are others that must also be taken into consideration:
-All the proposals or postulates are presented in an axiomatic way.
-It did not begin to spread and become prominent in Europe until the late Middle Ages.
-For the scientific community, it became an essential work and was so for many centuries. Specifically, until the appearance of Albert Einstein’s theory of relativity.
-The structure of this work is as follows: books 1 to 4 focus on plane geometry, books 5 to 10 revolve around what proportions and ratios are, while the last three books address what is the geometry of the three dimensions, the geometries in the bodies that are solid.