Test Tasks on Bases of 3D-Modelling

The “Geometry and Graphics” journal is celebrating its eight-year birthday in 2020. It was set up in 2012. From the moment of its set up until 2016, it was the first period of the journal's life, when pedagogical papers were published three times more than the geometrical ones. In 2016 the journal was put in the list of the State Commission for Academic Degrees and Titles in specialties 05.01.01 and 13.08.00. It was the second period in the journal's life. The number of scientific and pedagogical papers have become approximately equal, which indicates a more careful selection of papers for publication in the journal, as well as introduction the apparatus for independent peer review sorting out papers not falling outside the level of the State Commission for Academic Degrees and Titles’ journal. In 2018 the specialty 13.08.00 was removed, only Engineering Geometry and Computer Graphics remained – the third period in the journal's life began, which was characterized by a sharp fall in the number of pedagogical papers, and little wonder. This trend has been demonstrated in the present paper. As a result, if in the first period pedagogical papers in the journal were equal to 3/4 of papers’ total number, in the third period pedagogical papers number had become only 1/4, that is, had decreased by 3 times. From 2019 (No. 4) Pedagogy has returned to the journal – the fourth period has started. Now in the journal there were two specialties again. When the pedagogical direction was again included in the list, the situation related to publication of pedagogical papers in the journal improved, and on the example of three recently published journal numbers, we can say that they began to publish in the journal technical and pedagogical papers in equal measure. This paper aims to show to the reader the scope of pedagogical issues in papers published in the journal and related to geometric education.

Geometric Education’s Problems Displaying in the “Geometry and Graphics” Journal

Sal'kov¹

2020

Modern Means of Graphic Disciplines Teaching for Extramural Students

Панченко¹

2019

When studying ''Engineering and Computer Graphics'' discipline, extramural students are faced with a number of difficulties. Age groups of these students differ from full-time students from behind a greater number of students related to more age categories. Also, unlike full-time students, the level of extramural students’ primary education is higher, but it has been acquired for a long time, and knowledge, in the vast majority of cases, leaves much to be desired. In addition to the described differences it is possible to report a lesser amount of free time, which an extramural student can use for his independent work because of his primary employment’s strained activity timetable. An important moment that plays a key role in discipline understanding is the complexity of "Engineering and Computer Graphics" subject itself, which requires drawing skills (in the school some students did not even have such a discipline) and the ability for spatial thinking. In the presented paper have been considered features on age groups, primary education and drawing skill level for two streams of extramural students learning on the "Railway Operations" specialty in the Russian University of Transport (MIIT). In view of students’ contingent peculiarities the use of modern teaching tools in the process of studying "Engineering and Computer Graphics" discipline has been suggested as a method for enhancement of effectiveness for understanding of educational material. As an illustration of obtained theoretical concepts has been presented a plan for carrying out a laboratory work on "Engineering and Computer Graphics" discipline using modern teaching techniques. In the process of performing the laboratory work, modern teaching tools are used, and after its completion the trainees receive a useful solid piece (a stand for a smartphone) made on a 3D printer, obtained with the help of a three-dimensional model prepared by students, that increases the efficiency of received material’s understanding.

Golden Section and Golden Rectangles When Building Icosahedron, Dodecahedron and Archimedean Solids Based On Them

Vasil'eva¹

2019

A brief history of the development of the regular polyhedrons theory is given. The work introduces the reader to modelling of the two most complex regular polyhedrons – Platonic solids: icosahedron and dodecahedron, in AutoCAD package. It is suggested to apply the method of the icosahedron and dodecahedron building using rectangles with their sides’ ratio like in the golden section, having taken the icosahedron’s golden rectangles as a basis. This method is well-known-of and is used for icosahedron, but is extremely rarely applied to dodecahedron, as in the available literature it is suggested to build the latter one as a figure dual to icosahedron. The work provides information on the first mentioning of this building method by an Italian mathematician L. Pacioli in his Divine Proportion book. In 1937, a Soviet mathematician D.I. Perepelkin published a paper On One Building Case of the Regular Icosahedron and Regular Dodecahedron, where he noted that this “method is not very well known of” and provided a building based “solely on dividing an intercept in the golden section ratio”. Taking into account the simplicity and good visualization of the building based on golden rectangles, a computer modeling of icosahedron and dodecahedron inscribed in a regular hexahedron is performed in the article. Given that, if we think in terms of the golden section concepts, the bigger side of the rectangle equals a whole intercept – side of the regular hexahedron, and the smaller sides of the icosahedron and dodecahedron rectangles are calculated as parts of the golden section ratio (of the bigger part and the smaller one, respectively). It is demonstrated how, using the scheme of a wireframe image of the dual connection of these polyhedrons as a basis, to calculate the sides of the rectangles in the golden section ratio in order to build an “infinite” cascade of these dual figures, as well as to build the icosahedron and dodecahedron circumscribed about the regular hexahedron. The method based on using the golden-section rectangles is also applied to building semiregular polyhedrons – Archimedean solids: a truncated icosahedron, truncated dodecahedron, icosidodecahedron, rhombicosidodecahedron, and rhombitruncated icosidodecahedron, which are based on icosahedron and dodecahedron.