What is euclidean geometry?

What Does euclidean geometry Mean

Geometry is called the study of the magnitudes and characteristics of figures that are in space or on a plane. Euclidean , for his part, is that linked to Euclid , a mathematician who lived in Ancient Greece . And not only that but also that this illustrious figure became the teacher of 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 he gave birth to Euclidean geometry .

At present, Euclidean geometry is considered to be that centered 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 Euclides compiled 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 be extended 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 a line cuts two others 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 complete vector spaces that have an inner product and are therefore normed vector and metric spaces. The spaces of non-Euclidean geometries, on the other hand, are curved spaces or with different characteristics from those mentioned in Euclid's propositions .
From that work entitled 'Elements', other data of interest must be established, among which we can highlight that it is composed of thirteen books, that it was the author's masterpiece and that it focuses on treating geometry in both two and three dimensions. dimensions.
Likewise, it must be taken into account that it is considered one of the most edited works of all 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.

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