Euclidean geometry studies the properties of the so-called Euclidean spaces.
Geometry is 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 Ancient Greece . And not only that, but also that this illustrious figure became a teacher to important disciples such as Apollonius of Perga or Archimedes, among many others.
In the 3rd century BC , Euclid proposed five postulates that allow us to study the properties of regular shapes (lines, triangles, circles, etc.). Thus gave birth to Euclidean geometry .
Currently, Euclidean geometry is considered to be that focused on the analysis of the properties of Euclidean spaces : geometric spaces that comply with the axioms of the Greek thinker. It should be noted that Euclid compiled his postulates in his work "Elements" .
The pillars of Euclidean geometry
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, a circle can be drawn with any distance and center; that all right angles are identical to each other; and that, if one line cuts two others and the sum of the interior angles on the same side is less than two right angles, the other two lines when extended will be cut by the side on which the angles less than the right angles are located.
When working with Euclidean spaces, Euclidean geometry deals with complete vector spaces that have an inner product and are therefore normed metric and vector spaces. The spaces of non-Euclidean geometries, on the other hand, are curved spaces or spaces with different characteristics than those mentioned in Euclid 's propositions.
Euclid is the father of Euclidean geometry.
Euclid's work
From this work titled "Elements" we must establish other data of interest, among which we can highlight that it is made up of thirteen books, that it was the masterpiece of its author and that it focuses on dealing with both two-dimensional and three-dimensional geometry. dimensions.
Likewise, it must be taken into account 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 proposals or postulates are presented axiomatically.
-It did not begin to spread and stand out in Europe until the Late Middle Ages.
-For the scientific community it became an essential work and remained 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 three dimensions, the geometries in bodies that are solid.