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Journal ArticleDOI: 10.12737/2308-4898-2021-8-4-47-60

Quality of Geometric Education in Various Approaches to Teaching Methods

04 Mar 2021-Geometry & Graphics (Infra-M Academic Publishing House)-Vol. 8, Iss: 4, pp 47-60
Abstract: In the 2017-18 and 2018-19 academic years, in Moscow State Academic Art Institute named after V.I. Surikov a two-year experiment for architecture students on determination variances in different approaches to teaching methods for geometric education was conducted. The experiment was caused by the fact that many teachers believe that if there are computers in the Institute, it is necessary to use graphic programs as soon as possible – immediately introduce students to work on the computer even without allocating hours for this. No one wants to prevent implementation of computers, but we must not forget some nuances related to high technology. As in any case connected with complex hardware unknown for future users, here at the University, at the beginning it is also necessary to teach students how to work with the graphics program itself, and only then allow them perform geometric problems. You can give such an example: put an untrained person at the control panel of interceptor missiles and force him to shoot down a border trespasser in combat conditions. They will notify us that we are engaged in voluntarism. However to put an untrained student at a computer and forcing him to solve a purely geometric problem immediately is not voluntarism. Is it? The experiment had showed that a student, even if he knows how to solve a particular problem, is not ready at all to perform it immediately on a computer in a graphic software. He begin to lose a lot of time getting familiar with the program and only after obtaining at least a minimum of knowledge about working with this program becomes ready to start the task.

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Topics: Quality (business) (56%)
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Journal ArticleDOI: 10.12737/2308-4898-2021-9-1-3-18
Viktor Korotkiy1, Igor' VitovtovInstitutions (1)
Abstract: Physical spline is a resilient element whose cross-sectional dimensions are very small compared to its axis’s length and radius of curvature. Such a resilient element, passing through given points, acquires a "nature-like" form, having a minimum energy of internal stresses, and, as a consequence, a minimum of average curvature. For example, a flexible metal ruler, previously used to construct smooth curves passing through given coplanar points, can be considered as a physical spline. The theoretical search for the equation of physical spline’s axis is a complex mathematical problem with no elementary solution. However, the form of a physical spline passing through given points can be obtained experimentally without much difficulty. In this paper polynomial and parametric methods for approximation of experimentally produced physical spline with large deflections are considered. As known, in the case of small deflections it is possible to obtain a good approximation to a real elastic line by a set of cubic polynomials ("cubic spline"). But as deflections increase, the polynomial model begins to differ markedly from the experimental physical spline, that limits the application of polynomial approximation. High precision approximation of an elastic line with large deflections is achieved by using a parameterized description based on Ferguson or Bezier curves. At the same time, not only the basic points, but also the tangents to the elastic line of the real physical spline should be given as boundary conditions. In such a case it has been shown that standard cubic Bezier curves have a significant computational advantage over Ferguson ones. Examples for modelling of physical splines with free and clamped ends have been considered. For a free spline an error of parametric approximation is equal to 0.4 %. For a spline with clamped ends an error of less than 1.5 % has been obtained. The calculations have been performed with SMath Studio computer graphics system.

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Topics: Spline (mathematics) (65%), Tangent (52%), Curvature (52%) ... read more


Open accessJournal ArticleDOI: 10.12737/2308-4898-2021-9-3-39-45
H. Damchaasuren1Institutions (1)

Open accessJournal ArticleDOI: 10.12737/2308-4898-2021-9-3-3-11
Nikolay Sal'kov1Institutions (1)
Topics: Descriptive geometry (68%)

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MonographDOI: 10.12737/18057
08 Jul 2019-
Abstract: The textbook contains theoretical information on morphemics and word formation of the modern Russian language; Glossary of terms, plans of practical classes, tasks and exercises for them; tasks for self-control, options for tests and tests; schemes and samples of analysis of language units, a list of scientific and educational literature; questions for the exam. Prepared in accordance with the Federal state educational standard of higher education in directions of preparation "Pedagogical education", "Philology", in accordance with the approximate program of the course "Modern Russian language" and is intended for students enrolled in the profile "Russian language and literature, Russian language and foreign language", "national Philology", for students of the specialist degree, students majoring in "Russian language and literature", master of Philology, as well as for foreign students studying Russian language.

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Topics: Word formation (70%)

17 Citations