Geometry & Graphics最新文献

{"title":"Demonstration of Common Elements of Involution on a Simple Example","authors":"N. Umbetov","doi":"10.12737/2308-4898-2022-10-2-27-34","DOIUrl":"https://doi.org/10.12737/2308-4898-2022-10-2-27-34","url":null,"abstract":"The involution of projective rows with a common support, its geometric interpretation are considered. Taking the special case of the geometric interpretation of involution, the problem of constructing harmonically conjugate points is solved for given initial conditions, when one circle and a radical axis of this circle with a bundle of corresponding circles with a common radical axis are given. A proposal is given on the existence of a single circle in a bundle, the diametrical points of which on the lines of centers make up a harmonic four with diametral points of a given circle. It is shown that using the diametrical points of a given circle and points P, Q of the radical axis in elliptical involution, you can build double points X, Y and the radical axis of the PQ of circles in hyperbolic involution. And the tangent from the vertical diammetral point of the circle w1 to the circle passing through double points of hyperbolic involution - there is a point P(Q) of the radical axis of elliptical involution. The indicated properties make it possible to carry out a mutual transition from one involution to another. It was established that the diagonals of the quadrangles obtained when crossing all the circles of the bundle, orthogonal to the two given in elliptical involution, intersect in the center of the radical axis of the given circles in hyperbolic involution, and the diagonals of the quadrangles of all circles of the beam in hyperbolic involution are intersected in the center of the radical axis of the given circles in elliptical Involution. \u0000The geometric place (GP) of each point of the harmonic four is constructed. In this case, the geometric place a pair of harmonic four in an elliptic involution turns out to be an ellipse that has a common tangent at points P with the circle of double points of the hyperbolic involution. And the GP pairs of the harmonic four for hyperbolic involution are two branches of the hyperbola that pass through the centers of the circles that define the elliptical involution.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129685626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"GEOMETRIC MODEL OF GROUP PURSUIT OF A SINGLE TARGET BY THE CHASE METHOD","authors":"A. Dubanov","doi":"10.12737/2308-4898-2022-10-2-20-26","DOIUrl":"https://doi.org/10.12737/2308-4898-2022-10-2-20-26","url":null,"abstract":"The article describes the model of group pursuit of a single target by the chase method. All objects participating in the pursuit model move with a constant modulo speed. One of the participants in the process moves along a certain trajectory and releases objects at specified intervals, the task of which is to achieve the goal by the chase method. All objects have restrictions on the curvature of the motion path. A single target, in turn, is tasked with achieving the target that releases objects using the parallel approach method. For each pursuing object, a detection area is formed in the form of two beams. The object's velocity vector is directed along the bisector of the angle formed by such rays. If the target enters the detection area, then the object starts pursuit and the velocity vector is directed to the target. If the target leaves the detection area, then the object makes a uniform and rectilinear movement. The task is to implement a dynamic model of multiple group pursuit, where each object has its own tasks, implemented by the chase method. As an example, where the model developed in the article could be in demand, the following example can be given. Consider the movement of a low-maneuverable object that is overtaking a faster target. As a means of protection, instead of releasing passive heat traps, it is proposed to drop a variety of autonomously controlled weapons. An analysis of existing studies has shown that such means of protecting aircraft do not exist. The results of the research can be in demand in the design of unmanned aerial vehicles with elements of autonomous control and artificial intelligence.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132637598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cause and Effect Diagram of the Problems of Geometric and Graphic Training of Students at a Technical University","authors":"E. Verhoturova, G. Ivaschenko","doi":"10.12737/2308-4898-2022-10-2-60-69","DOIUrl":"https://doi.org/10.12737/2308-4898-2022-10-2-60-69","url":null,"abstract":"This article discusses the prospects for applying cause-and-effect analysis - the Ishikawa diagram for visualizing the problems of geometric-graphic training of students of a technical university. The structure of the study using the diagram included the implementation of successive stages. At the first stage, an exhaustive list of problems affecting the level of geometric and graphic training at the university was compiled. At the second stage of the cause-and-effect analysis, problems (factors) were systematized according to semantic sections (logical blocks): employees and the student (person, human factor), material and technical base and educational environment (equipment and other means to ensure the educational process); educational technologies and organization of the educational process, means and technologies for assessing learning outcomes. The next stage included systematization and ranking of problems within logical partitions. This made it possible to identify in a simple and accessible form the most significant factors in the emergence of the problem under study at three levels. The implementation of the last three stages made it possible to complete the study with obtaining the final structure of the factors of the problem of a low level of geometric and graphic training of students. The result of the study was a graphical interpretation of the results of the cause-and-effect analysis. Thus, the possibility of using the diagram to identify the most significant cause-factors that affect the level of mastering the disciplines of the graphic cycle by students, as well as a means of visualizing the cause-and-effect analysis, is shown.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"105 9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124030322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Trends of Training in Engineering Graphics","authors":"Ch. Oyuunzhargal, E. Oyuunzayaa","doi":"10.12737/2308-4898-2022-10-2-53-59","DOIUrl":"https://doi.org/10.12737/2308-4898-2022-10-2-53-59","url":null,"abstract":"In the field of modern education, not only in Mongolia, but also in world renowned technical and technological universities, teaching has moved from a theoretical basis to research universities. Universities are becoming corporate institutions. In this regard, it is necessary to make significant changes in the content of the curriculum. The main trend in modern engineering education is to train specialists with highly developed technical thinking for any field of activity. \u0000With this in mind, an attempt was made to outline the theoretical basis for determining the role of descriptive geometry and engineering graphics in professional education. For this, satisfaction surveys of students, graduates and employers were conducted and the results are analyzed, complex educational competencies are determined, the special role of standards in engineering and graphic education is noted, as well as the importance of feedback between different levels of education (school, basic academic, fundamental and professional). It is concluded that the changes taking place in modern engineering education, in general, lead to a reduction in the gap between the skills of a university graduate and the requirements of employers, that one of the urgent tasks of modern engineering and graphic education is the development of basic textbooks based on new forms and teaching methods in addition to the Internet environment, that the geometric-graphic cycle is key for students to master the most important complex engineering competence, and that the feedback between different levels of geometric-graphic education should be deepened in order to increase the effectiveness of its study.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124797973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"All-Russian Scientific and Methodological Conference «Problems of Engineering Geometry» and the Seminar «Geometry and Graphics» 2021","authors":"Vladimir Vyshnyepolskiy, N. Kadykova, T. Vereschagina","doi":"10.12737/2308-4898-2022-10-2-35-52","DOIUrl":"https://doi.org/10.12737/2308-4898-2022-10-2-35-52","url":null,"abstract":"The article is devoted to the annual All-Russian scientific and methodological conference \"Problems of Engineering Geometry\" and the annual All-Russian scientific and methodological seminar \"Geometry and Graphics\" in 2021. Statistical information about the conference and seminar is provided: the number of participants, universities, the number of cities and countries in which universities are located -participants. Using the expression proposed earlier, the activity of participation of the departments of graphic disciplines in the conference \"Problems of Engineering Geometry\" and the seminar \"Geometry and Graphics\", held in 2021, was determined. The comparison of the number of participants and reports of the conference and seminar in 2021 with the number of participants and reports is given and analyzed International Internet conferences \"Quality of graphic training\" at the Perm National Research Polytechnic University. The results of the All-Russian Seminars \"Geometry and Graphics\" and the All-Russian Conferences \"Problems of Engineering Geometry\" of the last two years are compared with each other. In order to compare conferences and seminars quantitatively, not qualitatively, a relationship has been proposed. The content of the reports of the participants of the conference and the seminar is briefly considered. Conclusions are drawn: 1) in 2021, in terms of the success of the seminar \"Geometry and Graphics\" and the conference \"Problems of Engineering Geometry\", we managed to move forward - the success rate increased; 2) judging by the number of reports, scientific work on the profile of the department is carried out in a small number of departments. This is due to shortcomings in the staffing of departments of graphic disciplines by teachers. One of them is a lack of understanding that the winners or participants of All-Russian and regional Olympiads who have undergone appropriate training should work as teachers.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122309814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Velaroidal Shells and Shells of the Velaroidal Type","authors":"Stanislav Strashnov","doi":"10.12737/2308-4898-2022-10-2-11-19","DOIUrl":"https://doi.org/10.12737/2308-4898-2022-10-2-11-19","url":null,"abstract":"A group of velaroidal surfaces and surfaces of the velaroidal type belong to the class of \"Translation Surfaces\". In contrast to the direct translation surfaces, velaroidal surfaces are formed by curves of variable curvature so that the formed surface rests on straight lines of a flat rectangular contour. Only about a dozen velaroidal surfaces have been described and studied in the scientific and technical literature. Velaroidal surfaces are also formed by curves of variable curvature but supported by a flat oval or circular contour. A super ellipse can be taken as a flat contour. The contour may consist of fragments of two identical curves located symmetrically about the axis of symmetry. In Russia velaroidal surfaces are studied so far only in the Peoples' Friendship University of Russia (RUDN University), Moscow. They are popular with both research geometrists and students - architects and builders, who believe that these shapes can be used within parametric, nonlinear, evolutionary and generative architecture. The article provides information with reference to the extensive used bibliographic material on the geometry of known velaroidal surfaces and surfaces of the velaroidal type. Information on the construction and visualization of new velaroidal surfaces with an oval flat contour as a super ellipse, as well as with a frame and a guide super ellipse. The data on determination of the stress-strain state of thin shells with median surfaces in the form of the surfaces under consideration is given. The fields of practical application of velaroidal shells and velaroidal shells are indicated. As shown in the sources used, geometers and calculation engineers have solved almost all the issues related to the design of these shells. Architects use velaroidal shells rarely, mostly to cover industrial buildings. Enclosures of velaroidal type have been used only in draft designs and in diplom works of architecture students.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123958064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ABOUT IMAGES","authors":"N. Sal'kov","doi":"10.12737/2308-4898-2022-10-2-3-10","DOIUrl":"https://doi.org/10.12737/2308-4898-2022-10-2-3-10","url":null,"abstract":"In this paper, a completely different statement about the ownership of images is proposed from the generally accepted opinion. First there are definitions of well-known concepts, such as the purpose of descriptive geometry, its method, its subject. Then, gradually approaching the opinion that descriptive geometry is the theory of images, it is said about those areas of knowledge and human activity that are impossible without descriptive geometry. It is shown that images are characteristic of absolutely all areas of human activity. Mention is made of painters, graphic artists and sculptors who study descriptive geometry during training. The first drawings made on the walls of caves are mentioned, which indicates the use of descriptive geometry even before the conscious division of science into different branches of research. It is shown that any image is a mental activity of the brain, which includes the works of abstractionists to any works of painters, as well as to the halo of belonging to descriptive geometry. And since descriptive geometry deals with abstract points, lines and compartments of surfaces, then all directions of images consisting of points, lines and compartments of surfaces simply have to be attached to the field of activity of descriptive geometry.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"30 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133785166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"To the Question of the Classification for Analytical Surfaces","authors":"Stanislav Strashnov, M. Rynkovskaya","doi":"10.12737/2308-4898-2022-10-1-36-43","DOIUrl":"https://doi.org/10.12737/2308-4898-2022-10-1-36-43","url":null,"abstract":"Until this day, in scientific and technical literature there are descriptions of around 600 analytical surfaces, divided into 38 classes. In turn, it is possible to divide almost each class of surfaces into sub-classes, groups, or types, that is, to compose a classification for surfaces. It will make it easier their further study. For some classes of surfaces there is no sense to set up classification schemes, since these classes consist of a small number of surfaces, or the classification will contain a bare listing of surfaces. These surfaces can include minimal and one-sided surfaces, spiral and helical ones, surfaces of Ciceika and Edlinger, as well as undulating, wavy and corrugated surfaces, and several others. The \"others\" category includes surfaces which, although highlighted in separate classes, are few, or they are in the process of studying. The study of scientific literature has shown that a classification for revolution surfaces, as well as for transfer and Peterson ones has not yet been set up. This paper is devoted to these classes of analytical surfaces. As the study has showed, it is possible to draw interesting conclusions based on presented classifications. In this paper it has been shown how the appearance of scientific publications devoted to classification for surfaces promote the emergence of numerous works on application of relevant surfaces in architecture, construction, engineering, shipbuilding, light industry products, topography and cartography. But devotion to analytic surfaces’ geometric forms should not be an end in itself in actual practice. So, today architects are passionate about parametric architecture, which is based on knowledge of analytical surfaces’ geometry. However, some leading architects believe that the parametric architecture oversaturated the human life’s space, resulting in a style crisis. Despite architects and engineers’ conflicting opinions, geometers must go ahead of society's immediate demands, creating new forms, classifications, and proposals.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134263565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"To the Question of Teaching Staff Readiness to Digital Training","authors":"I. Stolbova, K. Nosov, Lyubov Tarasova","doi":"10.12737/2308-4898-2022-10-1-24-35","DOIUrl":"https://doi.org/10.12737/2308-4898-2022-10-1-24-35","url":null,"abstract":"The question of teaching staff readiness to digitalize the educational process is considered in this paper. Digital education is a prerequisite for training of specialists meeting the requirements for the XXI century digital economy. There are a number of challenges in introducing digital learning, including those in engineering education. Digitalization of the technical subject area is very costly process that has its own specifics and requires developers to possess not only professional competencies related to a particular discipline, but also to be advanced in the arear of information and communication technologies. Besides modern teaching and laboratory facilities, and computer systems for various purposes, an important condition for promoting of digitization in subject teaching is teaching staff willingness to improve their teaching skills along with fluency in modern digital technologies. \u0000 As an example of subject teaching, in this paper are considered informatization and digitalization of basic geometric and graphic training for students at technical higher education institutes. The analysis is carried out from the point of view related to preparation of the academic teaching staff for creation and implementation of the educational environment that meets the requirements for dynamically developing design as a type of engineering activity. The scheme for realization of mixed learning has been presented, which introduction is determined by students' individual work implementation, and the process of students' online geometric-graphic training during self-isolation for COVID-19 prevention has been described. An analysis of teacher's activity content increase in the full online training mode has been carried out. Has been presented a set of practical measures acting to raise the chair’s teaching staff qualification and providing readiness to solving urgent problems of students’ learning through the digital educational environment. \u0000As a conclusion of the study, it is stated that in digitalization conditions the most successful form for implementing of basic geometric and graphic training is the form of blended learning.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125738300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"About Geometry, One More Time","authors":"M. Leparov","doi":"10.12737/2308-4898-2022-10-1-3-13","DOIUrl":"https://doi.org/10.12737/2308-4898-2022-10-1-3-13","url":null,"abstract":"This paper has been devoted to an analysis of geometry from an engineering point of view. Has been based 23 statements about geometry contribution to physics, mathematics, engineering, as well as to other sciences. Geometry propagation in all types of objects and processes (such as material, energetic and information/signal ones), as well as in everything and everywhere (all-encompassing geometry) has been shown. Special attention is paid to geometry importance, emphasizing its crucial role at each stage of any technical object design (which predetermines geometry as the basis of design), as well as in other cases. It is proposed to establish a strict line of demarcation between the science \"General Geometry\" as \"Geometry of Everything\" with a construct (any object considered as a geometric structure) on the one hand, and with a subject (a study of spatial structures and construct relations with an assigned aim) – on the other hand, and to develop them separately.","PeriodicalId":426623,"journal":{"name":"Geometry & Graphics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123714037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}