LOBACHEWSKY GEOMETRY AND ITS ELEMENTS

Abstract

This scientific article describes the research and features of non-Euclidean geometry in world practice. We can also see that Lobachevsky's geometry, which became known to the world with the beginning of Lobachevsky, who is considered one of the founders, has become one of the largest branches of mathematical science. It is known that the elements of Lobachevsky geometry and their features have contributed to the development of modern geometry. It is known that Lobachevsky geometry is currently being studied at a new pace by world researchers. It is true that it, in turn, plays its role as an assistant tool in the scientific formation of a professional geometer. On the basis of the scientific tradition established in the world experience, it has been taken up by large international mathematical research institutes since the last century and is being fully considered from the point of view of empirical research. It is known that the Queen's Institute of Mathematical Research in London conducted in-depth research on the basis of Lobachevsky geometry and began to consider geometry as a separate science from mathematics. In order to develop the field of domestic geometry as much as possible, first of all, there is a need for high-level world experience in which research institutes in the geometric direction are formed. It is known that Lobachevsky geometry can be used as a scientific springboard during the teaching of other fields of geometry. On the basis of Lobachevsky's geometry, it is possible to introduce the fields of differential and integral geometry, which are little studied, into the field of domestic geometry, and raise domestic geometry to a higher level. In the scientific article, theoretical and practical aspects of Lobachevsky geometry are considered, and scientific analysis of its main elements is carried out.