Geometry Throughout The History Of Humanity

Geometry throughout the history of humanity

Geometry has been present since primitive times even when man did not have a clear knowledge or stable settlement, but lived on day -to -day needs. From that moment on, the human being began to use this branch of mathematics to function in his daily life, and in much of life is used to solve situations of measures and in architecture, buildings and drawings. That said, it is very important to have knowledge of geometry, inclusive, terms such as points, straight, curves are commonly addressed in society. Therefore, this work focuses on recognizing, explaining and describing the relevant aspects to this area, clearly and easily. Taking into account the analyzed in the sources consulted.

Geometry is one of the areas of mathematics that is responsible for studying the properties of figures in the plane or space, such as: lines, curves, points, plans, among others. In practice, geometry serves to solve concrete problems in the world of visible. Among its profits are the justification of some instruments such as: compass, theodolite, pantograph, and global positioning system. The origin of the geometry begins with the first pictograms, which traced the primitive man, classified in an unconscious way it surrounded him, according to his form, such as: the graphics in ceramic vessels. Geometry consists of several fields, such as: analytical geometry, descriptive geometry, geometry of spaces with four or more dimensions, fractal geometry, and non -Euclidian geometry.

In sum, in ancient Egypt an empirical geometry was born that comes from the observation of objects. This geometry later was improved and made by the Greeks and this is the geometry we know today. In the fourth century Pythagoras, he settled that the different arbitrary and unconnected laws of primitive geometry can be understood, establishing a number of axioms or postulates. Pythagoras created the Pythagoras theorem that alleges that the square of the hypotenuse is equal to the sum of the squares of the catetos.

Greek geometry was the first to be formal, and part of the concrete and practical knowledge of the thesis. The truth of the thesis will depend on the validity of the reasoning with which it has been extracted and the veracity of the hypothesis. But we must start from true hypotheses to precisely affirm the thesis. On the other hand, the Greeks called demonstrative geometry to the study that implies these postulates, which analyzed and studied polygons and circles of the three -dimensional figures. This geometry was detailed by the Greek mathematician Euclid, in his book "The Elements". Euclid’s book has served as a basic geometry textbook.

At the beginning of the 17th century in Europe, Pierre Fermat and René Descartes discovered the analytical geometry that links algebra and mathematics through points within a plane and numbers. Fermat and Descartes also observed that algebraic equations belong to geometric figures. This means that geometric lines and figures can be expressed as equations and equations can be graphic as geometric lines or figures. The Greeks and especially Apollonius of Perga, studied the curves known as conical and discovered many of their fundamental properties. The conics is of the utmost importance for many fields of physical sciences, for example;The orbits of the planets around the sun are fundamentally conical. Archimedes, who is a scientist also made numerous contributions to geometry. He invented several ways to measure the area of certain curved figures, as well as the surface and volume of solids limited by curved surfaces, such as paraboloids and cylinders.

In addition, he built a method to calculate an approximation of the value of the PI, the proportion between the diameter and circumference of a circle. Geometry advanced little from the end of the Greek era to the Middle Ages. An important step in this science was given by the French mathematician René Descartes, whose treaty "The speech of the method", published in 1637, made time. This work created a relationship between geometry and algebra by demonstrating how to apply the methods of one discipline to another. This is a support of analytical geometry, in which the figures represent through algebraic expressions, subject to most of modern geometry.

Another important development of the 18th century was the study of the properties of the geometric figures that do not vary when the figures are projected from one plane to another. However, in the nineteenth century geometry suffered a great radical change. The Nikolai Lobachevski, János Bolyai and Carl Friedrich Gauss mathematicians worked separately and developed non -Euclidian geometry coherent systems. These systems appeared from the work on the so -called “parallel postulate” of Euclid, by raising alternatives that generate strange and non -intuitive models of spaces, although coherent.

Later, the mathematician Arthur Cayley develops geometry for spaces with more than three dimensions. These have an important number of applications in physical sciences, specifically in the development of relativity theories. Also, analytical methods have been used to examine geometric figures in four or more dimensions and compare them with similar figures in three or less dimensions. This geometry is known as structural geometry. An easy example of this is the definition of the simplest geometric figure that can be drawn in spaces with zero, one, two, three or more dimensions.

In the first cases, the figures are the well -known point, line, triangle and tetrahedron. In the four -dimensional space, it can be expressed that the simplest figure is formed by five points as vertices, ten segments such as edges, ten triangles such as face and five tetrahedra. Another dimensional concept is that of fractional dimensions, appeared in the 19th century. In 1970, the concept developed as fractal geometry.

In conclusion, it is necessary to point out that geometry has a significant value for humanity, from the moment man needed to measure lands in prehistory until becoming a more formal branch of mathematics. In addition, this is related to other fields of knowledge how: the natural sciences and social sciences specifically. Another important aspect that stood out in this essay is the usefulness of this area in everyday life, as well as the civilizations that contributed to this field. For example, the Babylonians who invented the wheel, and from there the properties of the circumference were discovered. Also, another group that contributed were the Egyptians, because they were the first to name the part of the mathematics in charge of the earth. Although, it is in Greece that, it applies as a deductive science, and this culture perfected and applied it as a branch of knowledge.

On the other hand, mention was made of the most prominent characters or that significantly supported geometry such as Archimedes, René Descartes, Euclid, Pythagoras. Also, as this area has evolved over time, acquiring a formal property. Finally, the teaching of geometry must be oriented to problem solving and that these are related to daily life, in this way effective learning will be built in the educational environment.

Bibliography

• Arteaga, j. (2012). A relationship between geometry and algebra (Erlangen program). Tecné, Episteme and Didaxis: Ted, Vol. 32, pp. 143-148.
• Ávila, or. History of descriptive geometry. UPAP Scientific Magazine. 2017.
• Fernández, e. (2018). Geometry for life and its teaching. AIBI Research, Administration and Engineering Magazine. Volume 6, number 1 of 2018 Page 33-61. Libertador Experimental Pedagogical University