List of publications on a keyword: «geometry»

Periodicity of wide class of functions as a result of reflection of even and arbitrary regular functions is proved. By consideration of new scalar work in space of linear shell of initial n vectors the equivalence of values of two different scalar productions is proved. The example of linear transformation is considered on plane for the symmetric case, resulting in possibility to make to use the orthogonal sides of rhombus at projection on the plane of its parties.

In the article we consider a new scalar production in the linear subspace of n vectors (by analogy with the geometry of Lobachevsky, all two vectors are orthogonal as projections of the third vector). With help of the production we obtain a new form of linear projection of the additional vector to the subspace. The rapid algorithm of finding of optimum linear estimation of additional vector on the known vectors ensues from the projection.

This article can be considered the final proof of Euclid’s 5th postulate. Nevertheless, its main purpose is to show that the difference between Lobachevskian and Euclidean geometry is much more significant than is commonly believed to date.

If we replace the V Postulate of Euclid with the Postulate of Lobachevsky, then we can get rectangles with more than 4 angles. The article describes the methodology for constructing such rectangles.

This article is about teaching methods by means of IT. The given examples are all about different teaching methods of incorporating IT in the process of studying geometry in 10th grade. In the final part the authors came to the conclusion made on the basis of showcased material.

In the process of solving geometric problems secondary school students often make mistakes. These mistakes are connected with poor-quality construction of an explanatory figure or scheme. This is due to the low level of formation of a student's common culture of geometric sheme constructions. This article discusses some of the problems associated with the formation of a culture of sheme construction in the process of geometric problems solving.

This work fits into a framework of a program, elucidated in [1–3], of the geometrization of physics, as set in motion by the mathematical works of William Kingdon Clifford and continued into Einstein’s theory of General Relativity as well as the theories of John Archibald Wheeler. It discusses the physical and mathematical foundations of vacuum light-geometry and the Algebra of Signatures. The vacuum is investigated by probing it with mutually perpendicular monochromatic rays of light with different wavelengths. The result is a hierarchy of nested 3-D light landscapes («λmn-vacua»). We consider a locally uncurved and curved state of a vacuum region on the basis of the mathematical theory known as the Algebra of Signatures. A «vacuum condition» is formulated, based on the definition of the «vacuum balance». Inert properties of the λmn-vacuum are considered. A kinematic basis for the possibility of discontinuities in a local neighborhood of a λmn-vacuum is introduced. On the basis of the foundations of the Algebra of Signatures described in [2; 3], metric-dynamic models of all elementary particles included in the Standard Model are obtained. In this paper new concepts are introduced, some of them with correspondingly new terminology. Therefore, at the end of the article a glossary of new terms is provided.

The author shares his experience in project disciplines teaching using computer systems of middle level, starting from primary classes with subsequent transition to a higher level. The results of experimental methodics of project teaching input is shown in the article. The author also offers to place his experimental method of project education into the course "basis of automized and robot-technical systems"

One of professional activities of the future bachelors studying at the direction "Pedagogical education" is a research activity. This article describes the course work as a form of teaching and research activities of students. As a subject of study dynamic geometry system (DGS) is chosen, the application of which in the educational process defines professional standards and the concept of mathematical education in Russia. Investigation of possibilities of DGS in the educational process contributes to the formation of professional competencies in the research activity of bachelors of the direction "Pedagogical Education".

The article considers the dynamic geometry systems (DHS) as an object of research activity of students of the direction "Pedagogical education" when doing the course work. The necessity of studying and using DHS as a new innovative learning technology that is also reflected in Professional Standard and the Concept of mathematical education development in Russia. Study of DHS and their possible application in the educational process within the framework of the course work contributes to the formation of cognitive independence and ICT competencies among bachelors of the direction "Pedagogical Education".

This article deals with the application of information and communication technologies (ICT) tools while teaching the bachelors of economy in the study of mathematics in high school. For example, a dynamic geometry system (DGS) GeoGebra illustrates the feasibility of computer tools in solving the problems of the section "Analytic geometry in the plane." The author shows the classification of the software used in mathematics education.

This article notes the fundamental importance of geometric training in engineering education. The author shows that co-operation of schools and universities should pay attention at geometric-graphic preparation as soon as possible. The study examines the experience BSTU "Military-mechanics" regarding cooperation with LEIED and the use of innovative educational technologies.

The article considers the various aspects of the application of information technology in the preparation of program-methodical mate-rials in the teaching environment in reading lectures on descriptive geometry and computer graphics.

The article presents an overview of correction and developing work methods for the cultivation of spatial functions at preschool and early school age children. Basic types of geometric puzzles are investigated. The paper also describes the options for their use in the work on the formation and development of spatial functions.