from 01.10.2008 until now
Russian Federation
Russian Federation
Among specialists prevails the primitive view, according to Prof. G.S. Ivanov, on descriptive geometry only as on a "grammar of a technical language", as it characterized V.I. Kurdyumov in the XIX Century. If in the century before last his definition was actual, although many contemporaries had a different opinion, then a century and a half later this definition became outdated, especially since have been revealed the close relationships of descriptive geometry with related sections: analytical, parametric, differential geometry, etc., and descriptive geometry became an applied mathematical science. In this paper it has been shown that an image is obtained as a result of display (projection). In this connection, according to prof. N.A. Sobolev, "All visual images – documentary, geometrographic, and creative ones – are formed on the projection principle". In other words, they belong, in essence, to descriptive geometry. Thus, all made by hand creative images – drawings, paintings, sculptures – can be attributed with great confidence to descriptive geometry as a theory of images. These creative images, of course, have a non-obvious projection origin, nevertheless, according to Prof. N.A. Sobolev, "They, including the most abstract fantasies, are essentially the projection ones". Further in the paper it has been shown which disciplines apply some or other of graphic models, and has been considered a number of drawings belonging to different textbooks, in which graphic models are present. Thus, clearly, and also referring to the authorities in the area of images and descriptive geometry, it has been proved that each of the mentioned textbooks has a direct or indirect connection with descriptive geometry, and descriptive geometry itself is present in all textbooks, at least, in the technical and medical ones.
geometry, pedagogy, higher education, descriptive geometry
1. Babanov V.V. Teoreticheskaya mexanika dlya arxitektorov [Theoretical mechanics for architects]. Moscow, «Akademiya» Publ., 2008. 256 p. (in Russian)
2. Babkov V.F., Andreev O.V. Proektirovanie avtomobil`ny`x dorog [Design of highways]. Moscow, Transport Publ., 1987, 368 p. (in Russian)
3. Bubennikov A.V. Nachertatel'naya geometriya [Descriptive geometry]. Moscow, Vysshaya shkola Publ., 1965. 338 p. (in Russian)
4. Vladimirskiy G.A. Naglyadnye izobrazheniya v parallel'nykh proektsiyakh [Visual images in parallel projections]. Moscow, Gos. uchebno-pedagogicheskoe izd-vo Ministerstva prosveshcheniya RSFSR Publ., 1960. 132 p. (in Russian)
5. Vol`vak S.F. Gidravlika [Hydraulics]. Moscow, INFRA-M Publ., 2021. 438 p. (in Russian)
6. Glazunov E.A. Aksonometriya [Axonometry]. Moscow, Gos. izd-vo tekhniko-teoreticheskoy literatury Publ., 1953. 292 p. (in Russian)
7. Gordon V.O. Kurs nachertatel'noy geometrii [Course descriptive geometry]. Moscow, Nauka Publ., 1977. 368 p. (in Russian)
8. Dobryakov A.I. Kurs nachertatel'noy geometrii [Course descriptive geometry]. Moscow, Gos. izd-vo literatury po stroitel'stvu i arkhitekture Publ., 1952. 496 p. (in Russian)
9. Ivanov G.S. Teoreticheskie osnovy` nachertatel`noj geometrii [Theoretical foundations of descriptive geometry]. Moscow, Mashinostroenie Publ., 1998. 157 p. (in Russian)
10. Ivanova T.P., Puxova G.V. Programmirovanie i vy`chislitel`naya matematika [Programming and computational mathematics]. Moscow, Prosveshhenie Publ., 1978. 320 p. (in Russian)
11. Kamenev V.I. Aksonometricheskie proektsii [Axonometric projection]. Moscow, Mashgiz Publ., 1946. 184 p. (in Russian)
12. Karbachevkij V.V. Ispol`zovanie instrumentov trexmernogo modelirovaniya i metodov nachertatel`noj geometrii dlya opredeleniya rasstoyaniya mezhdu skreshhivayushhimisya pryamy`mi [Using tools of three-dimensional modeling and methods of descriptive geometry to determine the distance between intersecting straight lines]. Mezhdunarodnaya internet-konferenciya «Kachestvo graficheskoj podgotovki: Problemy`, tradicii, innovacii» [International Internet conference "quality of graphic preparation: problems, traditions, innovations"]. Perm`, 2019. http://dgng.pstu.ru/conf2019/papers/68/ (in Russian)
13. Kolotov S.M. Voprosy` teorii izobrazhenij [Questions of image theory]. Kiev, Izdatel`stvo kievskogo universiteta Publ., 1972. 163 p. (in Russian)
14. Kolotov S.M. Kurs nachertatel'noy geometrii [Course descriptive geometry]. Kiev, Gos. izd-vo literatury po stroitel'stvu i arkhitekture USSR Publ., 1961. 316 p. (in Russian)
15. Korotkij V.A. Kubicheskiye krivyye v inzhenernoy geometrii [Cubic curves in engineering geometry]. Geometrija i grafika [Geometry and graphics]. 2020, V. 8, I. 3, pp. 3-24. DOI:https://doi.org/10.12737/2308-4898-2020-3-24. (in Russian)
16. Kuzneczov V.S. Zhelezobetonny`e i kamenny`e konstrukcii [Reinforced concrete and stone structures]. Moscow, ASV Publ., 2019, 360 p. (in Russian)
17. Lebedev V.M. Texnologiya i mexanizaciya processov gorodskogo stroitel`stva i xozyajstva [Technology and mechanization of urban construction and economy processes]. Moscow, INFRA-M Publ., 2019, 330 p. (in Russian)
18. Lixachev L.N. Kineperspektiva [Kineperspektiv]. Moscow, Vy`sshaya shkola Publ., 1975, 248 p. (in Russian)
19. 114. Mangushev R.A., Saxarov I.I. Mexanika gruntov [Soil mechanic]. Moscow, ASV Publ., 2020, 294 p. (in Russian)
20. Monzh G. Nachertatel'naya geometriya [Descriptive Geometry]. Moscow, Akademia Nauk SSSR Publ., 1947. 292 p. (in Russian)
21. Peklich V.A. Nachertatel`naya geometriya [Descriptive geometry]. Moscow, Associacii stroitel`ny`x vuzov Publ., 2007, 272 p. (in Russian)
22. Romanova Yu.D., Lesnichaya I.G. Informatika i informacionny`e texnologii. Konspekt lekcij [Informatics and information technologies. Lecture notes]. Moscow, E`ksmo Publ., 2009, 320 p. (in Russian)
23. Ry`zhov N.N. Nachertatel`naya geometriya (ponyatiya, ix opredeleniya i poyasneniya) [Descriptive geometry (concepts, their definitions and explanations)]. Moscow, MADI Publ., 1993, 60 p. (in Russian)
24. 106. Ry`zhov N.N. Parametricheskaya geometriya [Parametric geometry]. Moscow, MADI Publ., 1988, 56 p. (in Russian)
25. Sal'kov N.A. Geometricheskaja sostavljajushhaja tehnicheskih innovacij [Geometric component of technical innovations]. Geometrija i grafika [Geometry and graphics]. 2018, V. 18, I. 2, pp. 85-94. DOI: 10.12737/ article_5b55a-5163fa053.0722109. (in Russian)
26. Sal`kov N.A. Geometricheskoe modelirovanie i nachertatel`naya geometriya [Geometric modeling and descriptive geometry]. Geometriya i grafika [Geometry and graphics]. 2016, V. 4, I. 4, pp. 31-40. DOI:https://doi.org/10.12737/22841. (in Russian)
27. Sal`kov N.A., Goly`shev A.A., Garas`ko A.M. Geometriya dlya xudozhnikov [Geometry for artists]. Materialy` VIII Mezhdunar. internet-konferencii «Kachestvo gra-ficheskoj podgotovki: problemy`, tradicii, innovacii [Materials of the VIII Intern. Internet conference "The quality of graphic training: problems, traditions, innovations"]. Perm, 2019. Available at: http://dgng.pstu.ru/conf2019/papers/2/ (in Russian)
28. Sal`kov N.A., Goly`shev A.A., Garas`ko A.M. Geometriya dlya xudozhnikov [Geometry for artists]. Zhurnal estestvennonauchny`x issledovanij [Journal of Natural Science Research]. 2018, V. 3, I. 4, pp. 2-9. Available at: https://naukaru.ru/ru/nauka/article/24841/view (in Russian)
29. Sal`kov N.A. Grafo-analiticheskoe reshenie nekotory`x chastny`x zadach kvadratichnogo programmirovaniya [Graph-analytical solution of some particular problems of quadratic programming]. Geometriya i grafika [Geometry and graphics]. 2014, V. 2, I 1, pp. 3-8. DOI:https://doi.org/10.12737/3842. (in Russian)
30. Sal`kov N.A. Vvedenie v kineticheskuyu geometriyu [Introduction to kinetic geometry]. Moscow, INFRA-M Publ., 2019, 160 p. (in Russian)
31. Sobolev N.A. Obshhaya teoriya izobrazhenij [General theory of images]. Moscow, Arxitektura-S Publ., 2004, 672 p. (in Russian)
32. 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)
33. 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)
34. Sal`kov N.A. Nachertatel`naya geometriya: bazovy`j kurs [Descriptive geometry: basic course]. Moscow, INFRA-M Publ., 2013, 184 p. (in Russian)
35. Sal`kov N.A., Goly`shev A.A., Garas`ko A.M. Nachertatel`naya geometriya v tvorcheskix professiyax [Descriptive geometry in creative professions]. Zhurnal estestvennonauchny`x issledo-vanij [Journal of Natural Science Research]. 2018, V. 3, I. 4, pp. 2-9. Available at: https://naukaru.ru/ru/nauka/article/24841/view (in Russian)
36. Sal'kov N.A. Nachertatel'naya geometriya. Osnovnoy kurs [Descriptive geometry. Basic course]. Moscow, INFRA-M Publ., 2014. 235 p. (in Russian)
37. 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)
38. Samarskij A.A., Gulyaev A.V. Chislenny`e metody` [Numerical methods]. Moscow, Nauka. Gl. red. Fiz-mat. lit Publ., 1989, 432 p. (in Russian)
39. Sy`soeva E.V. Arxitekturny`e konstrukcii i teoriya konstruirovaniya: maloe`tazhny`e zhily`e zdaniya [architectural structures and design theory: low-rise residential buildings]. Moscow, INFRA-M Publ., 2016, 280 p. (in Russian)
40. S.I. Trushin Stroitel`naya mexanika: metod konechny`x e`lementov [Construction mechanics: finite element method: textbook. manual]. Moscow, INFRA-M Publ., 2016, 305 p. (in Russian)
41. E`nciklopediya e`lementarnoj matematiki. Geometriya [Encyclopedia of elementary mathematics. Geometry]. Moscow, Gosudarstvennoe izdatel`stvo fiziko-matematicheskoj literatury` Publ., 1963, V. 4, 568 p. (in Russian)
