The history of the development of geometry - from Euclid to Lobachevsky
Geometry is a rather ancient science whose East is considered to be its birthplace. In her development, she went through several stages, which includes the history of the development of mathematics, since the first geometric concepts were associated with land surveying. And only much later the separation of geometry into an independent science took place.
Initial stage of development
The initial period can be called the birth of science in Babylon and Egypt. It was about the fifth century BC, but then all sorts of calculations were associated not so much with the study of concepts, as with using them for practical purposes. Altars were built, land areas were measured, which led to the establishment of scientific foundations. It was there, in the East, that the history of the origin of geometry originates.
The second stage in the formation of geometry
Significant for the development of this science becomes the seventh century BC, when the land-measuring Eastern wisdom finds its distribution in Greece.The history of the development of geometry makes a rather sharp jump, as the Greek philosophers begin to engage in a systematic presentation of the basics, proving any proposal. This period is known for Thales' theorem on the sum of the angles of a triangle, the discovery of the irrational numbers by Pythagoras, famous for the "Principles" of Euclid. It is the latter in his 13-tomnik systematized geometry as a science, where the axioms were the main points.
The history of the development of geometry - the third stage
Many Greek, Indian, Arabic scientists continued to develop the "Beginning" and enrich their discoveries, but the development of geometry experienced a new qualitative leap in the 17th century. This time is considered the beginning of the third period, which is strongly associated with the names of Descartes and Fermat. They are called creators of analytic geometry. The essence of this applied science lies in the fact that the properties of figures begin to be studied according to their algebraic equations, where the method of coordinates is taken as the basis. But the qualitative development of geometry does not end there. Two more versions of it appear: differential, associated with the names of Monge and Euler, and projective, to which Pascal and Desargues contributed.
The fourth stage in the development of the science of figures
In the 19th century, the history of the development of geometry was marked by the emergence of so-called "non-Euclidean" geometry. Its founder is considered to be Lobachevsky. It was he who was the ancestor, that is, considered the position of the figures, namely parallel lines, in space. A little later, another scientist, Riemann, formulated the concept of space as the totality of any homogeneous phenomena and objects. It is worth clarifying here that neither Lobachevsky’s geometry nor Riemann’s geometry does not deny Euclid’s teachings, they consider their positions from the point of view of the theory of spatial relations, but do not detract from the merits of Euclid, whose works are the basis of the school program.
Thus, in the development of science its main milestones are clearly visible. But I must say that the history of the development of geometry is not frozen and dead. Geometrical science is constantly in action: the circle of figures expands, their studied properties, the very notions of objects change.