Historical evolution of Geometry // Importance in Engineering - Reflection

carlos84 (73)in #sndbox • 8 years ago

Since its inception geometry has been of great significance for the training of the engineer, in this publication I want to highlight the aspect of being able to denote the fundamental elements of geometry within a whole, thus magnifying all the evolutionary processes through which it has passed and the large contributions that have been leaving over time and especially specify the great importance it has for the academic and professional training of the current engineer.

Within the flat metric geometry it can be considered that this is the most abstract part of the geometry, since the intuitive, logical and demonstrative development makes that its compressibility character lacks clear and simple foundations to perceive while we process its study for a later understanding. This has been the fundamental reason that led me to make this publication, in which I will touch on several important points about the "Fundamentals of Flat Metric Geometry".

First conceptions of Geometry.

In the beginning, Geometry was the art of measuring the earth, a technique that consisted of using a series of instruments within a collection of disorganized rules for the calculation of areas, simple volumes and performing some simple constructions. During the first years of training it consisted of a set of empirical knowledge, obtained by induction from the study of many particular cases, without the foundation of a logical demonstration.

The Egyptians had important knowledge of practical geometry, as indicated by the construction of the pyramids, of many temples and channels. Before the Christian era, geometry underwent a remarkable change with the Greeks who took it from the Egyptians and remade it in the form of deductive science, it is this way of perceiving geometry, deductively speaking that is still known today, especially if we talk about flat metric geometry.

The transformation began with Thales of Miletus and Pythagoras, culminating with Euclid, whose famous work "Elements" presented Geometry not as a set of empirical results, but as a well-organized chain of theorems that from certain initial hypotheses are shown following logical procedures.

Euclid deals very little with the geometry of space, scarcely known in his time. It is Archimedes who contributed greatly in this part, especially in relation to the volume of the cylinder, the cone and the sphere. He also discovered many of the properties of these surfaces and the relationships between them.

Foundation and base of the flat metric geometry.

The organization of geometry as a logical deductive structure begins with an axiomatic system that consists of letting oneself be governed by the following postulates:

Consider as a main and fundamental basis a set of propositions of undefined terms that form the basis of the necessary vocabulary.

Be based on a set of initial propositions not demonstrated.

Use laws of logic.

It bases a certain amount of its foundations on a set of theorems that enunciate the properties of the undefined terms.

Based on the aforementioned logical deduction, we can basically structure all the flat metric geometry according to axioms, theorems and corollaries.

An axiom is a proposition which is accepted without demonstration, starting from the laws of logic. An axiomatic system will be more perfect insofar as it has the least number of axioms, since in this way it is easier to investigate the validity of them, while they acquire greater scope in the properties that are deduced from them.

A theorem is a set of propositions whose veracity needs to be demonstrated. A theorem is distinguished from two parts: Hypothesis or supposition and the thesis or conclusion.

Considerations

It is worth mentioning that the importance of the theorems is not only in the flat metric geometry, but also that this structure of deduction was needed as other ideas and concepts were incorporated, to the point where the analytical Geometry was born, in which it was proposed to extend various solutions to topics raised that the flat metric geometry could not solve, since in the flat metric geometry could be treated more about the demonstrations of the diversity of congruence between triangles, angles and circumferences, using the laws of the logic and the axiomatic instruments and theorems of those mentioned above, now the need arises to give a numerical character and calculation to certain geometric figures that resulted in having to calculate slopes of straight lines, calculation of areas of cylinders, triangles , rectangles, circles and other geometric structures, of that need e analytical geometry, which is gaining strength with contributions such as those of René Descartes, which provided a system of X and Y coordinates, where combinatorial essential elements could easily be combined between algebra and geometry, however, with these advances, He left aside the ability to continue demonstrating the origin of each advance through the use of axioms and theorems.

Importance of geometry in Engineering.

It is important to mention that at present, in some universities in my country, the study and understanding of Geometry in the field of Engineering has been reduced, however, training programs such as Engineering: Civil, Mechanical, Geodetic, Electrical, Chemical , of oil among others, continue to maintain this important subject in their curricula, but we can also see how new training programs arise in the area of Engineering that do not possess the chair of geometry in their curricular meshes.

For the aforementioned it is worth reflecting on the issue of the immediate importance that geometry has over future engineers that will be formed over time, geometry is a branch of mathematics that will never lose value, since its ancient knowledge still prevails in the present, great constructions of the ancient world, as the Egyptian pyramids were built based on that foundation of calculations of areas and slopes of geometric shapes such as triangles, rectangles and circles, this means that the constructions of the present need this knowledge, and the advances that are made in the field of engineering in the near future will continue to need geometry to continue innovating in the different systems of engineering.

That is why I urge everyone in a single set and system (universities, teachers and students) to continue to maintain and deepen our knowledge of Geometry, and also contribute our bit in recommending the addition of the curriculum unit Geometry within the curriculum. of the training programs of the different universities that make up our social and academic environment.

Thanks for reading, I hope that my publication is of contribution, and until a next delivery.