The Origins of Formation of Descriptive Geometry

The translation "Descriptive geometry" is not entirely accurate. In fact, the phrase should be translated as "Narrative geometry". Based on this translation, it can be confidently stated that the science under consideration serves not only as a theoretical basis for orthogonal projections, a special case of which are ordinary drawings, but also for any images – in this the author of the article fully agrees with such authorities as N.A. Rynin, N.F. Chetverukhin, V.O. Gordon, S.A. Frolov, N.A. Sobolev and many others. The paper considers the origins of one of the directions of geometry – descriptive geometry. The hypothesis is put forward that in reality descriptive geometry, or rather, its elements, was originally involved in ancient times, during the primitive communal system when making drawings on the walls of caves and rocks. Orthogonal projections were used in the ancient world and in the Middle Ages, and Gaspard Monge at the end of the XVIII century systematized all the existing disconnected developments on descriptive geometry, adding his own research. Most likely, geometry in general was the very first science that originated when our ancestors who lived in caves faced the problem of increasing the living area due to population growth. And descriptive geometry began to develop from the moment when the first artist depicted scenes from life on the cave wall: hunting, fishing, tribal wars, events that shocked people, etc. Ancient artists existed on all continents of the globe, except perhaps Antarctica, since rock carvings were found on all other continents. And the earliest was performed somewhere 25-30 thousand years ago. Thus, the hypothesis that the elements of descriptive geometry originated in the primitive communal system can be considered proven.

Features of Distance Learning in Geometric and Graphic Disciplines Using Methods of Constructive Geometric Modeling

The article is devoted to the peculiarities of teaching the discipline "Descriptive geometry" in the conditions of distance learning, it examines the application of information technologies in the educational process in geometric and graphic disciplines. Increasing the speed of information processes, reducing the number of hours for mastering the discipline. the conditions of distance learning set new tasks for teachers and dictate their requirements for teaching graphic disciplines and the use of teaching experience in a new reality; there is a need to introduce and develop new forms of education without losing the quality of education. Geometric-graphic disciplines occupy one of the important places in technical education, the complexity of the study of which lies in the development of a graphical representation of phenomena, objects and processes by methods of constructive geometric modeling. The knowledge and skills acquired by students contribute to the development of spatial, imaginative and rational thinking, which is necessary for future professional activities. Descriptive geometry is a discipline that is not easy to master on your own without a conscious understanding of the logic and sequence of geometric constructions, without deep knowledge of theoretical foundations and constant, repeated implementation of practical tasks. The acquisition of practical skills in mastering the methods of discipline has become more difficult in the current epidemiological situation. In modern conditions of distance learning, the use of the Simplex geometric modeling system made it possible to develop and propose a new concept of geometric-graphic interaction, which significantly reduced the time for completing and checking educational tasks in real time. The proposed technology reveals the deep informational essence of the studied discipline "Descriptive Geometry" and becomes a powerful research tool for students. The integration of traditional teaching methods in the graphic preparation of students with computer and communication facilities increases the possibilities of communication and improves the quality of teaching.

Descriptive geometry: Designing surfaces

In the textbook, in addition to the geometric design of surfaces, the elements of analytical and parametric geometries are proposed that contribute to the design and bring the result to a higher level of knowledge, as well as a frame method for designing surfaces. Meets the requirements of the federal state educational standards of higher education of the latest generation. For students of the specialties "Architect" and " Designer of the architectural environment "(qualifications "bachelor", "specialist", "master"). It may be useful for students of other fields of study.

End-to-end design training: from descriptive geometry to computer modeling of cutting tools

Modern trends in the development of technology are based mainly on successful engineering activities. The combination of the most modern computer technologies and the traditions of using a pencil, drawing, drafts, and, of course, a living fruitful thought is a guarantee of the education of a genuine Engineer. On the one hand, educational technologies in engineering universities at the initial stage should be based, in our deep conviction, on school geometry. On the other hand, descriptive geometry and engineering graphics should contain examples for immersion in the chosen specialty. By order of the Ministry of Education and Science of the Russian Federation, engineering classes, in which lecturers of technical universities were involved, were organized 10 years ago in Moscow schools. The creation of engineering classes is caused by the need to instill in students an interest in the engineering profession. To successfully solve this problem, it is necessary to increase the level of students» knowledge in geometry and drawing. On the basis of these subjects, one should develop design skills and skills of using computer modeling tools. The result of this cooperation should be the involvement of schoolchildren to participate in competitions and olympiads. The Department of Engineering Graphics, Bauman Moscow State Technical University, has accumulated 30 years of experience in cooperation with specialized schools in order to develop students» interest in the engineering profession. The article provides an example of the introduction of a common cutting tool, i. e. a drill, which demonstrates the depth of engineering thought formed over a thousand-year history, into the educational process when studying geometry at school and descriptive geometry at a technical university. The drill as an object comprehensible to first-year students is used to provide the basic knowledge of descriptive geometry. In addition, the problem related to the improvement of the technology of end-to-end training throughout the course of obtaining an engineering education is touched upon.

Wolfram Mathematica Functional Possibilities for Curved Lines and Surfaces Visualization

The paper states that the current conditions in which the education system is located, and the rapid development of IT require constant improvement of methodological materials, taking into account the full capacity of the current software. Examples of programs necessary for preparation of methodological materials for high-quality classes are given. The purpose of the paper was to identify the Wolfram Mathematica didactic potential when conducting classes in the disciplines of the geometric and graphic profile at a technical high educational institution. In this paper has been performed analysis of literature sources both domestic and foreign ones on the Wolfram Mathematica system application in science and teaching of various disciplines. It has been shown that the program use scope is very wide, in fact, it is comprehensive and requires additional and in-depth study. Examples of Wolfram Mathematica using in mathematics, physics, chemistry, geometry, robotics, virology, and the humanities are given. In the paper have been provided examples for pedagogical design of simulation models for an electronic course on descriptive geometry in the Moodle system. An example of code written in the Wolfram Mathematica is provided. Interactive models developed during the design are presented, which allow the user to change the constructed curves and surfaces’ parameters. Have been defined some functional capabilities of the system, and has been revealed the Wolfram Mathematica didactic potential for teaching geometric and graphic disciplines. Have been considered other authors’ similar models, which can be used in the educational process to increase the clarity of the material presented in the classroom. In conclusion it is pointed out that interactive visualization in the "Descriptive Geometry" discipline, together with classical working practices, significantly enriches the content of geometric education.

FORMATION OF GRAPHIC COMPETENCE OF THE HIGHER EDUCATION SEEKERS BY MEANS OF COMPUTER-ORIENTED TECHNOLOGIES

The role of graphic competence in the training process of future teachers of labor education and technology has been substantiated in this article. Examples of students' use of the acquired knowledge in Descriptive Geometry and Engineering Graphics in further educational and practical activities have been established. There are reading drawings of products (parts) for their manufacture; design and execution of graphic images of products (parts); development of a logical sequence of the technological process for the manufacture of the product; designing a garment pattern, etc. The growing role of machines with digital program control (DPC) is taken into account and the role of graphic representation of the part (product) in digital format for their manufacture on such machines is also investigated. It is proposed to provide the emphasized training of students to perform drawings of parts (products) by means of graphic editors with the prospect of their manufacture on machines with DPC. The purpose of the article is to reveal the features of preparation of future teachers of labor education and technology to perform drawings of product details in graphic editors with the subsequent manufacture of these objects on machines with digital program control. The peculiarities of training students in Computer Graphics at Volodymyr Hnatiuk Ternopil National Pedagogical University during studying of disciplines «Descriptive Geometry, Drawings and Computer Graphics», «Computer Graphics and Multimedia» have been analyzed. It is determined that students are not able to fully master Computer Graphics due to the lack of hours and the large number of commands and functions that are provided by such computer programs. It is proposed to enhance the preparation of students for mastering computer graphics through the independent implementation of students' drawings of product details using a graphic program in extracurricular time in the form of an individual educational research tasks (IERT). The expediency of making drawings of product parts by means of a graphic program with their subsequent manufacture by a machine with digital program control (DPC) has been substantiated. Plywood is proposed as a construction material for the design of the products by means of graphic editors with the subsequent manufacturing by machines with DPC. The structure of IERT is proposed: to make drawings of details of a product according to the instruction; provide a “photo report” of the sequence of drawings according to the instructions with a short description; to change the design of the product based on the knowledge and skills formed by making drawings according to the instructions. An example of IERT instructions for students is given. It involves the use of KOMPAS-3D. The phone stand is considered as a sample of performance by students for IERT.

Wolfram Mathematica Functional Possibilities for Curved Lines and Surfaces Visualization

The paper states that the current conditions in which the education system is located, and the rapid development of IT require constant improvement of methodological materials, taking into account the full capacity of the current software. Examples of programs necessary for preparation of methodological materials for high-quality classes are given. The purpose of the paper was to identify the Wolfram Mathematica didactic potential when conducting classes in the disciplines of the geometric and graphic profile at a technical high educational institution. In this paper has been performed analysis of literature sources both domestic and foreign ones on the Wolfram Mathematica system application in science and teaching of various disciplines. It has been shown that the program use scope is very wide, in fact, it is comprehensive and requires additional and in-depth study. Examples of Wolfram Mathematica using in mathematics, physics, chemistry, geometry, robotics, virology, and the humanities are given. In the paper have been provided examples for pedagogical design of simulation models for an electronic course on descriptive geometry in the Moodle system. An example of code written in the Wolfram Mathematica is provided. Interactive models developed during the design are presented, which allow the user to change the constructed curves and surfaces’ parameters. Have been defined some functional capabilities of the system, and has been revealed the Wolfram Mathematica didactic potential for teaching geometric and graphic disciplines. Have been considered other authors’ similar models, which can be used in the educational process to increase the clarity of the material presented in the classroom. In conclusion it is pointed out that interactive visualization in the "Descriptive Geometry" discipline, together with classical working practices, significantly enriches the content of geometric education.

THREE TIME PERIODS OF THE FORMATION OF THE SCIENTIFIC SCHOOL OF APPLIED GEOMETRY OF THE KIEV NATIONAL UNIVERSITY OF CONSTRUCTION AND ARCHITECTURE

The main historical periods of the scientific school of applied geometry of the Kiev National University of Construction and Architecture are presented. The main three stages of the formation of the school are considered - from the beginning of the creation of the Department of Descriptive Geometry and Engineering Graphics to the present. Today, the scientific school of applied geometry of the KNUSA has many unresolved tasks and current problems. In recent years, the number of people wishing to defend candidate and doctoral dissertations has decreased significantly. In accordance with this, the work of the department in training young scientists has decreased, the number of graduate students and doctoral students has decreased. In addition, despite the fact that applied geometry is applied science, it is quite difficult today to establish ties with production, to introduce into production the latest results of scientific work of graduate students and applicants. Therefore, the main task of the department today is to preserve the traditions of the scientific school of applied geometry of KNUBA. The further work of the Department of Descriptive Geometry and Engineering Graphics of KNUBA will be aimed at ensuring that the scientific school does not cease to exist, but continues to develop and expand.

CURRENT STATE AND DEVELOPMENT PROSPECTS OF APPLIED GEOMETRY SCIENTIFIC SCHOOL OF IGOR SIKORSKY KPI

The emergence of the applied geometry school of the Igor Sikorsky Kyiv Polytechnic Institute is associated with the formation of an educational institution at the end of the 19th century. For more than 120 years of history, significant results have been achieved, which have been implemented into production and the educational process. The available significant theoretical and practical achievements allowed to identify promising directions for further development. During this period, the Department of Descriptive Geometry, Engineering and Computer Graphics has published thousands of scientific works, hundreds of educational and methodological publications, 15 doctoral and more than 60 candidate dissertations have been defended. The scientific topics are connected with the shaping of complex curves and surfaces by methods of algebraic, differential, projective geometry, taking into account the needs of production; construction of agricultural machinery; multidimensional geometry; involute-evolutionary models; design and manufacture of aircrafts; optimization of industrial products; computer geometry, etc. The obtained results have been implemented at the leading machine-building enterprises of Ukraine, such as SE “Antonov”, Kharkiv State Aviation Production Enterprise, OJSC “Meridian” named after S.P. Korolyov, Research and Production Association "Kyiv Automatiсs Plant", etc. Over the past decade, more than 30 patents for utility models have been obtained, which are successfully applied in practice. Thus, the school of applied geometry of the Igor Sikorsky Kyiv Polytechnic Institute has more than a century of history. Over the years, a significant contribution has been made to the development of domestic science, industry, and higher education. Today the existing achievements contribute to improving the efficiency of computer-aided design of various technical products, processes of its manufacture, and operation. Nowadays, the staff of the Department of Descriptive Geometry, Engineering and Computer Graphics faces a number of important scientific, educational and production problems, which are successfully solved thanks to the accumulated theoretical and practical experience. This is also facilitated by the wide involvement of young people in these activities.