THE HISTORICAL EVOLUTION OF THE GEOMETRY
Geometry is one of the oldest science and it arose as the field of knowledge dealing with spatial relationships.
Geometry as word has two Greek roots: γῆ gē (earth) and μετρία (measure); That means "measure of the Earth." Its origin, some three thousand years before Christ, goes back to the Middle East, in particular to ancient Egypt, in which it was needed to measure agrarian land. The main causes were to remark the boundaries of the riparian lands and to build parallel dikes to channel their waters. This is due to the overflows caused by periodic flooding of the Nile river.
Moreover, the geometry was present in Egypt in the construction of pyramids and monuments and here is the figure of Thales of Miletus. Indeed, Thales remained in Egypt a long season of his life, learning from the Egyptian priests and scribes all about their knowledge in general, and these were astonished when he was able to measure the height of the pyramid of Keops through the shadow of this and his cane and also, he was able to predict a Solar eclipse.
The Greek geometry was the first to be formal. Part of the concrete and practical knowledge of the Egyptian and Mesopotamian civilizations, and takes a step of abstraction when considering objects as ideal entities (an any single square, instead of a concrete square wall, a circle instead of the eye of a well and so on) which can be manipulated mentally, with the sole help of the ruler and the compass. It appears for the first time the demonstration as justification of the veracity of a knowledge, although at first they were more intuitive justifications than true formal demonstrations. This attitude allowed the measurement of the Earth by Eratosthenes, as well as the measurement of the distance to the moon, and the invention of the lever by Archimedes, several centuries later.
Euclid proposed a system of study in which it assumes the veracity of certain propositions to be intuitively clear, and to deduce from them all the other results. The Greek geometry had all these mathematical successes, but there were three famous problems that were unable to solve:
During the following centuries, the Middle Age, the mathematics begins new paths (algebra and trigonometry) of the hand of Indians and Arabs, and the geometry hardly has new contributions, except some theorems of character rather anecdotal.
It is in the Renaissance, the Modern Age, when the new needs of representation of art and technique push certain humanists to study geometrical properties to obtain new instruments that allow them to represent reality. Here it is framed the figure of the mathematician and architect such as Lucca Pacioli, Leonardo da Vinci or Albrecht Dürer.
Geometry as word has two Greek roots: γῆ gē (earth) and μετρία (measure); That means "measure of the Earth." Its origin, some three thousand years before Christ, goes back to the Middle East, in particular to ancient Egypt, in which it was needed to measure agrarian land. The main causes were to remark the boundaries of the riparian lands and to build parallel dikes to channel their waters. This is due to the overflows caused by periodic flooding of the Nile river.
Moreover, the geometry was present in Egypt in the construction of pyramids and monuments and here is the figure of Thales of Miletus. Indeed, Thales remained in Egypt a long season of his life, learning from the Egyptian priests and scribes all about their knowledge in general, and these were astonished when he was able to measure the height of the pyramid of Keops through the shadow of this and his cane and also, he was able to predict a Solar eclipse.
The Greek geometry was the first to be formal. Part of the concrete and practical knowledge of the Egyptian and Mesopotamian civilizations, and takes a step of abstraction when considering objects as ideal entities (an any single square, instead of a concrete square wall, a circle instead of the eye of a well and so on) which can be manipulated mentally, with the sole help of the ruler and the compass. It appears for the first time the demonstration as justification of the veracity of a knowledge, although at first they were more intuitive justifications than true formal demonstrations. This attitude allowed the measurement of the Earth by Eratosthenes, as well as the measurement of the distance to the moon, and the invention of the lever by Archimedes, several centuries later.
Euclid proposed a system of study in which it assumes the veracity of certain propositions to be intuitively clear, and to deduce from them all the other results. The Greek geometry had all these mathematical successes, but there were three famous problems that were unable to solve:
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During the following centuries, the Middle Age, the mathematics begins new paths (algebra and trigonometry) of the hand of Indians and Arabs, and the geometry hardly has new contributions, except some theorems of character rather anecdotal.
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| Vitruvian Man and its proportions |
De Divina Proportione
In the Contemporary Age, Gauss returned the geometric character that pervades part of the mathematical analysis, mainly with two contributions: the birth of the complex Variable and the differential geometry. Gauss was the first to create a non-Euclidea geometry and he was the first to consider a new property in geometry: the orientation. Moreover, it is the age where most of the big mathematical problems of the antiquity has been solves such as the three mentioned before and the controversy over the postulated V.
Geometry, like another science, has had a period of evolution and it has been throughout the generations where it has been provided with formulas, data, methods, theories and experiences for future generations. As the Egyptians and Greeks, we have to use it in order to solve problems that could arise in our day to day and as mathematicians and future thinkers, who preceded them, we have to resort to it to be able to advance as a society.
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