History of the development of geometry

History of the development of geometry

The very first concepts in geometry people have acquiredback in antiquity. There was a need to determine the areas of land, the volume of various vessels and premises and other practical needs. The history of development of geometry, as a science, takes its origin in ancient Egypt about 4 thousand years ago. Then the knowledge of the Egyptians was borrowed by the ancient Greeks, who used them primarily to measure the area of ​​land. It is from ancient Greece that the origin of geometry, as a science, originates. Ancient Greek word "geometry" is translated as "land surveying".

Greek scientists based on the discovery of the setgeometric properties were able to create a coherent system of knowledge of geometry. The basis of geometric science was laid down the simplest geometric properties, taken from experience. The remaining positions of science were derived from the simplest geometric properties by reasoning. The entire system was published in its final form in the "Elements" of Euclid about 300 BC, where he laid out not only theoretical geometry, but also the foundations of theoretical arithmetic. From this source also begins the history of the development of mathematics.

However, in the work of Euclid nothing is said either aboutmeasuring the volume, nor about the surface of the ball, nor about the ratio of the length of the circle to its diameter (although there is a theorem on the area of ​​the circle). The history of the development of geometry was continued in the middle of the 3rd century BC thanks to the great Archimedes, who was able to compute the Pi number, and also was able to determine the ways of calculating the surface of the sphere. Archimedes applied methods to solve the above problems, which later became the basis for higher mathematics. With their help, he was already able to solve difficult practical problems of geometry and mechanics, which were important for navigation and for construction. In particular, he found ways to determine the centers of gravity and volumes of many physical bodies and was able to study the equilibrium of bodies of various shapes when immersed in liquid.

Ancient Greek scientists conducted researchproperties of various geometric lines, important for the theory of science and practical applications. Apollonius in the II century BC made many important discoveries on the theory of conic sections, which remained unsurpassed for the next eighteen centuries. Apollonius applied the method of coordinates to study conic sections. This method was further developed only in the XVII century, scientists Fermat and Descartes. But they used this method only to study flat lines. And only in 1748 the Russian academician Euler was able to apply this method to study curved surfaces.

The system developed by Euclid was consideredimmutable more than two thousand years. However, in the future the history of the development of geometry received an unexpected turn, when in 1826 the brilliant Russian mathematician N.I. Lobachevsky was able to create a completely new geometric system. In fact, the main provisions of his system differ from the positions of Euclidean geometry in only one point, but it is from this point that the basic features of the Lobachevsky system follow. This is the statement that the sum of the angles of a triangle in Lobachevsky geometry is always less than 180 degrees. At first glance, it may seem that this statement is incorrect, however, for small sizes of triangles, modern measuring tools do not give a correct measurement of the sum of its angles.

Further history of the development of geometry has provedthe correctness of Lobachevsky's brilliant ideas and showed that the Euclidean system is simply incapable of solving many questions of astronomy and physics, where mathematicians deal with figures of practically infinite dimensions. It is with the works of Lobachevsky that the further development of geometry, and with it of higher mathematics and astronomy, is already connected.

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