Our website uses cookies. By continuing to use this site, you agree to our use of cookies in accordance with this notice and the Terms of Use.
Journals Monographies Textbooks Collections Authors
Submit manuscript
Geometry & Graphics
UDC 51

SCIENTIFIC AND METHODICAL QUESTIONS OF STUDENTS TRAINING FOR ACADEMIC OLYMPICS ON DESCRIPTIVE GEOMETRY Scientific and Methodical Questions of Students Training For Academic Olympics on Descriptive Geometry

Published in Geometry & Graphics · Volume 5, Issue 1 · Pages 73–81 · Rubric: Technique of preparation and carrying out academic competition
DOI: https://doi.org/10.12737/25126
Received: 05.05.1905 Accepted: 05.05.1905 Published: 05.05.1905 Language of publication: RUS
Authors
V.
V. Seregin
G.
G. Ivanov
IV
Ivan F. Borovikov
ABSTRACT
Academic Olympics on descriptive geometry are an important form of educational process in conditions when the discipline study’s teaching hours are reduced. The Academic Olympics allow identify talented students and motivate them to find possibilities on solutions for non-standard situations, to promote the formation of such qualities as persistence, endurance, accuracy. The Academic Olympics carrying requires not only organizational measures. Due to a low level of the geometrical knowledge gained at school, students need an additional theoretical training. Without it realizing of young people’s creative potential is impossible. The experience on carrying of the Academic Olympics on descriptive geometry at Bauman Moscow State Technical University and in other higher education institutions of this country allowed develop a technique of students training for such activities. In this paper scientific and methodical questions related to solution for tasks of increased complexity are considered. Simplification of solution algorithm and increase of its visualization can be reached by reduction of metric conditions to affine ones, and them, in turn — to projective ones. The attention in training for the Academic Olympics should be paid to the method of loci. School leavers know only about limited quantity of loci on a plane and have practically no ideas on the elementary loci in space. Therefore studying of loci on a plane and in space is necessary. For the method of loci the essence of simplification, decomposition and increments rules is revealed. If a return problem is solved more simply than a straight one, it is reasonable to use reverse ability method. Often the problem solution becomes simpler when using transformations, in particular, homothety and stretching (compression) transformations. The considered methods are illustrated by specific examples. Assimilation of the methods described in this publication isn't a complete guarantee of students’ success at the Academic Olympics, but, undoubtedly, it will be useful for them as will allow expand knowledge of the subject matter.
KEYWORDS
descriptive geometry, student Academic Olympics, loci, transformations, reverse ability method, problems of increased complexity.
Text References
Text

Введение


Начертательная геометрия как учебная дисциплина имеет большое значение для инженерного образования [3–5; 10; 11; 13]. Однако существенное уменьшение объемов учебных курсов приводит к снижению качества инженерно-геометрической подготовки студентов.

1. Aleksandrov I.I. Sbornik geometricheskih zadach na postroenie s reshenijami [Collection of geometric construction problems with solutions]. Мoscow, URSS Publ., 2004.176 p. (in Russian).

2. Asekritova S.V., Konstantinov A.V. Osobennosti provedenija predmetnyh olimpiad po disciplinam graficheskogo cikla [Features of the subject Olympiads in the disciplines of graphic cycle]. Sbornik trudov 2-oy Vserossijskoy nauchnometodicheskoy konferencii po inzhenernoy geometrii i komp′juternoy grafike [Proceedings of the 2nd Scientific and Technical Conference on Engineering geometry and computer graphics]. Moscow, 2009, pp. 87-92. (in Russian).

3. Borovikov I.F., Potapova L.A. Nachertatel'naja geometrija i inzhenernoe obrazovanie [Descriptive Geometry and Engineering Education]. Mashinostroenie i inzhenernoe obrazovanie [Engineering and engineering education], 2009, i. 1, pp. 62-67. (in Russian).

4. Borovikov I.F. Stoit li otmenjat' nachertatel'nuju geometriju? [Should the descriptive geometry be canceled?]. Sovremennye problemy informatizacii geometricheskoy i graficheskoy podgotovki inzhenerov: trudy Vserossijskoj nauchno-metodicheskoy konferencii [Contemporary problems of informatization of geometric and graphic preparation of engineers: proceedings of Russian scientific-methodical conference], Saratov, 2007, pp. 164-168. (in Russian).

5. Voloshinov D.V. O perspektivah razvitiya geometrii i ee instrumentariya [About Prospects of Development of Geometry and Its Tools]. Geometriya i grafika [Geometry and Graphics]. 2014. v. 2, i. 1, pp. 15-21. (in Russian). DOI:https://doi.org/10.12737/3844.

6. Vyshnepolsky V.I., Voloshin-Chelpan Je.K., Pavlova A.A. Istorija moskovskih gorodskih olimpiad po nachertatel′noy geometrii i inzhenernoy grafike [The history of the city Olympiads on descriptive geometry and engineering graphics]. Nachertatel′naya geometriya, inzhenernaya i komp′juternaya grafika. Mezhdunarodnyy mezhvuzovskiy nauchno-metodicheskiy sbornik trudov kafedr graficheskih disciplin, vypusk 5 [Descriptive geometry, engineering and computer graphics. International interuniversity scientific and methodical collection of works of graphic disciplines, Issue 5]. Nizhnij Novgorod, Poligrafcentr NNGASU Publ., 2000, pp. 29-32. (in Russian).

7. Vyshnepolsky V.I. Metodicheskie osnovy podgotovki i provedeniya olimpiad po graficheskim disciplinam v vysshey shkole [Methodical bases of training and the competition for graphic disciplines in higher education]. Moscow, 2000. 18 p. (in Russian).

8. Vyshnyepolskiy V.I. Otkrytaja Vserossijskaya studencheskaya olimpiada po nachertatel′noy geometrii, inzhenernoy i komp'juternoy grafike 2015 goda [Open All-Russian Olympiad on Descriptive Geometry, Engineering and Computer Graphics 2015]. Geometriya i grafika [Geometry and Graphics]. 2016, v. 4, i. 1, pp. 73-89. (in Russian). DOI:https://doi.org/10.12737/18060.

9. Vyshnepolsky V.I. Funkcii olimpiad [Competitions options]. Geometriya i grafika [Geometry and graphics]. 2013, v. 1, i. 3-4, pp. 44-47. (in Russian). DOI:https://doi.org/10.12737/21331.

10. Vyshnepolsky V.I., Sal′kov N.A. Celi i metody obuchenija graficheskim disciplinam [Objectives and methods of training to graphic disciplines]. Geometrija i grafika [Geometry and graphics]. 2013, v. 1, i. 2, pp. 8-9. (in Russian). DOI:https://doi.org/10.12737/777.

11. Ivanov G.S. Kompetentnostniy podhod k soderjaniyu kursa nachertatelnoy geometrii [Competence approach to the course content of descriptive geometry]. Geometriya i grafika [Geometry and Graphics]. 2013, v. 1, i. 2, pp. 3-5. (in Russian). DOI:https://doi.org/10.12737/775.

12. Ivanov G.S. Nachertatel′naya geometriya [Descriptive geometry]. Moscow, MSUL Publ., 2012. 340 p. (in Russian).

13. Ivanov G.S. Perspektivy nachertatelnoy geometrii kak uchebnoy discpliny [Perspectives of descriptive geometry as a discipline]. Geometriya i grafika [Geometry and Graphics]. 2013, v. 1, i. 1, pp. 26-27. (in Russian). DOI:https://doi.org/10.12737/467.

14. Ivanov G.S. Teoreticheskie osnovy nachertatel′noj geometrii [Theoretical Foundations of descriptive geometry]. Moscow, Mashinostroenie Publ., 1998. 158 p. (in Russian).

15. Losev N.V. 200 olimpiadnyh zadach po nachertatel′noy geometrii [200 programming problems of descriptive geometry]. Moscow, Vysshaja shkola Publ., 1992. 126 p. (in Russian).

16. Mel′nichenko N.P. Olimpiada kak sposob aktivacii uchebnogo processa [The Olympics as a way of activating the educational process]. Sbornik trudov Mezhdunarodnoy nauchno-metodicheskoy konferencii po inzhenernoy geometrii i komp′juternoy grafike [Proceedings of the International Scientific Conference on Engineering geometry and computer graphics]. Moscow, 2010, pp. 144-148. (in Russian).

17. Metodicheskie ukazaniya po organizacii i provedeniyu studencheskih olimpiad i konkursov v VUZah Moskvy [Methodical instructions on the organization and conduct of student contests and competitions in Universities of Moscow]. Moscow, Moskovskiy aviacionnyj institut Publ., 1981. 52 p. (in Russian).

18. Modenov P.S., Parhomenko A.S. Geometricheskie preobrazovanija [Geometric transformations]. Moscow, MSU Publ., 1961. 232 p. (in Russian).

19. Naumovich N.V. Geometricheskie mesta v prostranstve i zadachi na postroenie [The gejmetric places in space and construction tasks]. Moscow, Gosudarstvennoe nauchno-pedagogicheskoe Publ., 1962. 152 p. (in Russian).

20. Naumovich N.V. Prostejshie geometricheskie preobrazovanija v prostranstve i zadachi na postroenie [The simplest geometric transformation in space and construction tasks]. Moscow, Gosudarstvennoe nauchno-pedagogicheskoe Publ., 1959. 132 p. (in Russian).

21. Peklich V.A. Zadachi Moskovskih i vserossijskih olimpiad po nachertatel′noj geometrii [Objectives Moscow and all-Russian Olympiads on descriptive geometry]. Moscow, Izdatel′stvo Associacii stroitel′nyh vuzov Publ., 2003. 156 p. (in Russian).

22. Peklich V.A. Nachertatel′naja geometrija [Descriptive geometry]. Moscow, Associacii stroitel′nyh vuzov Publ., 2007. 248 p. (in Russian).

23. Posvjanskij A.D., Leont′ev A.I., Ognivenko V.M. 50 zadach povyshennoj trudnosti po nachertatel′noj geometrii [50 challenges with increased difficulty in descriptive geometry]. Kalinin, 1970. 52 p. (in Russian).

24. Savel′ev Ju.P., Zhernosekov G.I., Tihonov-Bugrov D.E. Olimpiada shkola tvorchestva [Olympics school of art]. Vestnik vysshej shkoly [Journal of Higher School]. Moscow, 1987, i. 6, pp. 61-63. (in Russian).

25. Sal′kov N.A., Kadykova N.S. Organizacija studencheskih predmetnyh olimpiad vysshego urovnja [Organization of student′s competitions of the highest level]. Geometriya i grafika [Geometry and graphics]. 2013, v. 1, i. 1, pp. 44-47. (in Russian). DOI:https://doi.org/10.12737/2099.

26. Sal′kov N. Predmetnye olimpiady kak pokazatel' kachestva obuchenija [Subject Olympiads as an indicator of the quality of education]. Geometriya i grafika [Geometry and Graphics]. 2016, v. 3, i. 4, pp. 45-54. (in Russian). DOI:https://doi.org/10.12737/17350.

27. Borovikov I., Ivanov G., Senchenkova L., Seregin V. Geometricheskie preobrazovanija v nachertatel'noj geometrii i inzhenernoj grafike [Geometric Transformations in Descriptive Geometry and Engineering Graphics]. Geometriya i grafika [Geometry and Graphics]. 2015, v. 3, i. 2, pp. 23-28. (in Russian). DOI:https://doi.org/10.12737/12165.

28. Seregin V.I., Ivanov G.S., Dmitrieva I.M., Murav′ev K.A. Mezhdisciplinarnye svjazi nachertatel′noy geometrii i smezhnyh razdelov vysshey matematiki [Interdisciplinary connections of descriptive geometry and related sections of higher mathematics]. Geometriya i grafika [Geometry and Graphics]. 2014, v. 2, i. 3-4, pp. 8-12. (in Russian). DOI:https://doi.org/10.12737/2124.

29. Suprun L.I. Olimpiady - odin iz sposobov povyshenija akademicheskoy aktivnosti studentov [The Olympics is one way of increasing the academic activity of students]. Aktual′nye voprosy graficheskogo obrazovanija molodezhi: Tezisy dokladov Vserossijskoj nauchno-metodicheskoj konferencii [Topical issues of graphic education of youth: Theses of reports of the All-Russia scientific-methodical conference]. Rybinsk, RGAGA Publ., 1998, pp. 11-12. (in Russian).

30. Shebashev V.E. Predmetnye olimpiady kak sredstvo priobshheniya studentov k nauchnoy deyatel′nosti [Olympiad as a means of familiarizing students to scientific activity]. Sbornik trudov Vserossijskoj nauchno-metodicheskoj konferencii po inzhenernoj geometrii i komp′juternoj grafike [Proceedings of the All-Russian Scientific Conference on Engineering geometry and computer graphics]. Moscow, 2008, pp. 15-17. (in Russian).

31. Jemanov S.L. Trebovaniya i process sozdaniya olimpiadnyh zadach po nachertatel′noy geometrii [The requirements and the process of creating programming problems of descriptive geometry]. Sbornik trudov Mezhdunarodnoy nauchno-metodicheskoy konferencii po inzhenernoy geometrii i komp′juternoy grafike [Proceedings of the International Scientific Conference on Engineering geometry and computer graphics]. Moscow, 2010, pp. 152-156. (in Russian).

JATS XML
The contact persons
Zamestitel' glavnogo redaktora, chlen redsoveta
Vladimir Vyshnyepolskiy
Glavnyy redaktor
A. A. Ishchenko
Vypuskayuschiy redaktor
Dar'ya Sklyankina
501@infra-m.ru
Deputy editor-in-chief, member of the editorial Board
N. Sal'kov
nikolaysalkov@mail.ru
RINC
© INFRA-M
Agreement Personal data protection and processing policy Support Powered by Editorum, 2026 Instructions
Login or Create
* Forgot your password?