from 01.01.2009 until now
Ul'yanovsk, Ulyanovsk, Russian Federation
The problem of teaching and formulating the tasks for the “Applied Geometry” discipline is considered in this paper. Currently, in aviation high educational institutions there is a tendency to reduce the number of hours allocated to graphic disciplines; in addition, “Descriptive Geometry” – the habitual name of the discipline – has been replaced by name “Applied Geometry”. This is certainly connected with the transition to learning on undergraduate programs, that implies a competency-based approach, i.e., training in accordance with the necessary knowledge and methods of activity in a particular area [4; 9; 23; 29; 30; 34]. The planned results of learning in “Applied Geometry” include knowledge of methods for solving applied engineering-geometric problems, as well as the ability to use the basic elements of applied geometry and engineering graphics in professional activities, and to solve specific applied problems of geometric modeling [4; 14; 20; 22; 32]. For these reasons arises the question of the need to adapt “Descriptive Geometry” to the requirements and programs for the training of bachelors, bringing it to conformity with the name “Applied Geometry” of the discipline. According to the results of “Applied Geometry” studying, students ought to gain experience and have the ability to independently solve cognitive, organizational and other problems related to their future professional activities [28–30]. In this paper is proposed a general approach to the formulation of “Applied Geometry” problems for cadets pursuing a bachelor's degree in “Air Navigation” (25.03.03) and “Operation of Airports and Flight Support of Aircraft” (25.03.04). Using rather simple examples, has been considered the possibility to formulate the problem in such a way that instead of the traditional formulation it could be applied for a specific bachelor's degree. As well has been considered a complex applied problem, which is suitable as a task for performing a computational and graphic work, since it integrates several topics of the discipline.
applied geometry, orthogonal projections, descriptive geometry, applied problems, undergraduate, aviation high educational institutions
1. Borovikov I.F., Ivanov G.S., Surkova N.G. O primenenii preobrazovanij pri reshenii zadach nachertatel'noj geometrii [On applicatoin of transformations at diecriptive geometry’s problems solution.] Geometriya i grafika [Geometry and graphics]. 2018, V. 6, I. 2, pp. 3-22. DOI:https://doi.org/10.12737/article_5b55a35d683a33.30813949. (in Russian)
2. Vasilevsky A.B. Metody resheniya geometricheskih zadach. [Methods for solving geometric problems]. Minsk, "Vysshaya shkola" Publ., 1969. 232 p. (in Russian)
3. Vinogradov V.N., Roitman I.A. Elementy nachertatel'noj geometrii (dlya fakul'tativnyh zanyatij). Posobie dlya uchashchihsya [Elements of descriptive geometry (for optional classes). Manual for students]. Moscow: Prosveshchenie Publ., 1978. 175 p. (in Russian)
4. Volkova M.Yu., Egorycheva E.V. Graficheskaya gramotnost' inzhenera kak sposob polucheniya fundamental'nyh professional'nyh znanij [Graphic literacy of an engineer as a way to obtain fundamental professional knowledge.] Geometriya i grafika [Geometry and Graphics]. 2013, V. 2, I. 1, pp. 53-57. DOI:https://doi.org/10.12737/3849. (in Russian)
5. Voloshinov D.V., Solomonov K.N. Konstruktivnoe geometricheskoe modelirovanie kak perspektiva prepodavaniya graficheskih disciplin [Constructive geometric modeling as a perspective of teaching graphic disciplines.] Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 2, pp. 10-13. DOI:https://doi.org/10.12737/778. (in Russian)
6. Vyshnepolsky V.I., Salkov N.A. Celi i metody obucheniya graficheskim disciplinam [Goals and methods of teaching graphic disciplines.] Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 2, pp. 8-9. DOI:https://doi.org/10.12737/777. (in Russian)
7. Gordon V.O., Sementsov-Ogievsky M.A. Kurs nachertatel'noj geometrii [A course in descriptive geometry]. Moscow, Science Publ., 1969. 368 p. (in Russian)
8. Ivanov G.S. Perspektivy nachertatel'noj geometrii kak uchebnoj discipliny [Perspectives of descriptive geometry as an educational discipline.] Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 1, pp. 26-27. DOI:https://doi.org/10.12737/775. (in Russian)
9. Ishenko A.A. K voprosu o neobhodimosti prepodavaniya nachertatel'noj geometrii i grafiki dlya himikov i himikov-tekhnologov [To the question of the need for teaching descriptive geometry and graphics for chemists and chemical technologists]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 2, pp. 6-7. DOI:https://doi.org/10.12737/776. (in Russian)
10. Kozhevnikov Yu. G. Opticheskie prizmy. Proektirovanie, issledovanie, raschet. [Optical prisms. Design, research, calculation]. Moscow: Mashinostroenie Publ., 1984, 152 p. (in Russian)
11. Kochurova L.V., Grosheva T.V., Turitsyna I.A. K voprosu ob organizacii samostoyatel'noj raboty studentov v processe graficheskoj podgotovki [On the organization of students' independent work in the process of graphic preparation.] Geometriya i grafika [Geometry and Graphics]. 2014, V. 2, I. 2, pp. 43-48. DOI:https://doi.org/10.12737/5592. (in Russian)
12. Lyzlov A. N., Rakitskaya M. V., Tikhonov-Bugrov D. E. Nachertatel'naya geometriya. Zadachi i resheniya. [Descriptive geometry. Challenges and solutions:a training manual]. Saint-Petersberg: Lan Publ., 2011. 96 p. (in Russian)
13. Nazarova O.N., Zimina N.G., Shishkarev V.V. Obosnovanie graficheskogo resheniya nekotoryh zadach mekhaniki [Justification of graphic solution of some mechanics tasks.] Colloquium-journal. 2019, I. 12 (36), pp. 57-60. DOI:https://doi.org/10.24411/2520-6990-2019-10335. (in Russian)
14. Nazarova O. N., Shagarova A. A., Zimina N. G. Primenenie metodov nachertatel'noj geometrii v reshenii prikladnyh tekhnicheskih zadach [Application of descriptive geometry methods in solving applied technical problems.] Colloquium-journal. 2019, I. 21 (45), pp. 68-72. (in Russian)
15. Nazarova O.N. Analiz nekotoryh zadach kursa teoreticheskoj mekhaniki, reshaemyh metodami nachertatel'noj geometrii. [Analysis of some problems from a course on theoretical mechanics solved by descriptive geometry’s methods]. Geometriya i grafika [Geometry and Graphics]. 2019, V. 7, I. 4, pp. 76-83. DOI:https://doi.org/10.12737/2308-4898-2020-76-83. (in Russian)
16. Nartova L.G. Nachertatel'naya geometriya [Descriptive geometry]. Moscow: Academia Publ., 2018. 512 p. (in Russian)
17. Pavlova A.A., Glazkova I.V. Nachertatel'naya geometriya. Praktikum dlya studentov VUZov. V 2 chastyah. Chast' 1. [Descriptive geometry. Workshop for University students. In 2 parts. Part 1]. Moscow: Gumanitarno-izdatel'skij centr «Vlados» Publ., 2005. 95 p. (in Russian)
18. Pavlova A. A., Glazkova I. V. Nachertatel'naya geometriya. Praktikum dlya studentov VUZov. V 2 chastyah. Chast' 2. [Descriptive geometry. Workshop for University students. In 2 parts. Part 2]. Moscow: Gumanitarno-izdatel'skij centr «Vlados» Publ., 2005. 95 p. (in Russian)
19. Peklich V. A. Mnimaya nachertatel'naya geometriya [Imaginary descriptive geometry]. Moscow: ASV Publ., 2007. 104 p. (in Russian)
20. Polikarpov Y.V. Soderzhanie vuzovskogo kursa nachertatel'noj geometrii v epohu tret'ej promyshlennoj revolyucii [The content of desriptive geometry course for high educational institution’s in the third industrial revolution’s era]. Geometriya i grafika [Geometry and graphics]. 2018, V. 6, I. 3, pp. 49-55. DOI:https://doi.org/10.12737/article_5bc453447db654.91666264. (in Russian)
21. Rudaev A.K. Sbornik zadach po nachertatel'noj geometrii [Collection of problems in descriptive geometry]. Moscow, 1953. 343 p. (in Russian)
22. Sal’kov N.A. Geometricheskaya sostavlyayushchaya tekhnicheskih innovacij [The geometric component of technical innovations]. Geometriya i grafika [Geometry and graphics]. 2018, V. 6, I. 2, pp. 85-93. DOI:https://doi.org/10.12737/article_5b55a5163fa053.07622109. (in Russian)
23. Salkov N.A. Analiz FGOSov novogo pokoleniya. [Analysis of FSS of a new generation]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 1, I. 1, pp. 28-31. DOI:https://doi.org/10.12737/2082. (in Russian)
24. Salkov N.A. Nachertatel'naya geometriya - baza dlya geometrii analiticheskoj [Descriptive geometry - the basis for analytic geometry]. Geometriya i grafika [Geometry and Graphics]. 2016, V. 4, I. 1, pp. 44-54. DOI:https://doi.org/10.12737/18057. (in Russian)
25. Salkov N.A. Nachertatel'naya geometriya - baza dlya komp'yuternoj grafiki [Descriptive geometry - the basis for computer graphics]. Geometriya i grafika [Geometry and Graphics]. 2016, V. 4, I. 2, pp. 37-47. DOI:https://doi.org/10.12737/19832. (in Russian)
26. Salkov N.A. Nachertatel'naya geometriya: Osnovnoj kurs [Descriptive Geometry: Basic Course]. Moscow: INFRA-M Publ., 2014. 235 p. (in Russian)
27. Salkov N.A. Nachertatel'naya geometriya - teoriya izobrazhenij [Descriptive Geometry - Image Theory]. Geometriya i grafika [Geometry and Graphics]. 2016, V. 4, I. 4, pp. 41-47. DOI:https://doi.org/10.12737/22842. (in Russian)
28. Salkov N.A. Problemy sovremennogo geometricheskogo obrazovaniya [Problems of modern geometric education]. Problemy kachestva graficheskoj podgotovki studentov v tekhnicheskom vuze: tradicii i innovacii [Quality problems of graphic preparation of students at a technical university: traditions and innovations]. 2014, V. 1, pp. 38-46. (in Russian)
29. Stolbova I.D. Aktual'nye problemy graficheskoj podgotovki studentov v tekhnicheskih vuzah [Actual problems of graphic preparation of students in technical universities.] Geometriya i grafika [Geometry and Graphics]. 2014, V. 2, I. 1, pp. 30-41. DOI:https://doi.org/10.12737/3846. (in Russian)
30. Tikhonov-Bugrov D.E. O nekotoryh problemah graficheskoj podgotovki v tekhnicheskih vuzah (vzglyad iz Sankt-Peterburga) [About some problems of graphic preparation in technical universities (view from St. Petersburg)]. Geometriya i grafika [Geometry and Graphics]. 2013, V. 2, I. 1, pp. 46-53. DOI:https://doi.org/10.12373/3848. (in Russian)
31. Trautman N.F. Sbornik zadach po nachertatel'noj geometrii v primenenii k razlichnym oblastyam nauki i tekhniki [Collection of problems in descriptive geometry as applied to various fields of science and technology]. Moscow: Mashgiz Publ., 1953. 280 p. (in Russian)
32. Fedoseeva M.A. Metodika podgotovki studentov tekhnicheskih vuzov graficheskim disciplinam [Training procedure in graphic disciplines for students of technical high educational institutions.] Geometriya i grafika [Geometry and graphics]. 2019, V. 7, I. 1, pp. 68-73. DOI:https://doi.org/10.12737/article_5c91fed8650bb7.79232969. (in Russian)
33. Fedotova E.L., Fedotov A.A. Informacionnye tekhnologii v nauke i obrazovanii [Information technologies in science and education]. Moscow: ID FORUM Publ., SIC INFRA-M Publ., 2013. 336 p. (in Russian)
34. Filimonova O.S. Disciplina «Inzhenernaya i komp'yuternaya grafika» v sisteme vysshego voennogo obrazovaniya [«Engineering and computer graphics» discipline in the system of higher military education.] Geometriya i grafika [Geometry and graphics]. 2018, V. 6, I. 4, pp. 88-99. DOI:https://doi.org/10.12737/article_5c21fba3f26c35.85693389. (in Russian)
35. Frolov S.A. Nachertatel'naya geometriya Sbornik zadach [Descriptive geometry Collection of problems]. Moscow: INFRA-M Publ., 2011. 172 p. (in Russian)
36. Frolov S.A. Nachertatel'naya geometriya [Descriptive geometry]. Moscow: NIC INFRA-M Publ., 2013. 285 p. (in Russian)
37. Shishkarev V.V., Nazarova O.N., Zimina N.G. Osobennosti primeneniya nachertatel'noj geometrii v zadachah tekhnicheskoj optiki [Features of the use of descriptive geometry in the problems of technical optics]. Advanced solutions and experience in the NTI “Circle Movement”: Materials of the All-Russian Scientific and Practical Conference (Ulyanovsk, May 24, 2019) [Advanced solutions and experience in the "Circle movement" of NTI: Materials of the all-Russian scientific and practical conference (Ulyanovsk, may 24, 2019)]. Ulyanovsk, 2019, pp. 66-73. (in Russian)
38. Yumatova E.G. Sistema mezhintegrativnyh konstruktivno-analiticheskih zadach kak metod formirovaniya professional'no orientirovannyh sposobnostej budushchih inzhenerov [System of interintegraptive constructive-analytical problems as a method for forming of future engineers’ professionally-oriented abilities]. Geometriya i grafika [Geometry and graphics]. 2017, V. 5, I. 2, pp. 75-83. DOI:https://doi.org/10.12737/article_5953f350da7151.85721309. (in Russian)