from 01.10.2008 until now
Russian Federation
514
Geometry by its nature is the most visual science of all that takes place in the life of mankind, and therefore the most visual for those who study at school or university – any book, even the most non-technical, contains drawings, and drawings, in turn, are directly related to geometry in general and descriptive geometry in general in particular. After all, geometry studies points, lines and surfaces, but if you look closely, any drawing consists of points, lines and surfaces. It is not difficult to notice, so it is difficult to refute. The clarity of the drawings for beginners to learn something is the most important help for understanding the text. From the clarity of the school with its drawings in textbooks, the first step is taken to abstraction: the study of exclusively points and flat geometric shapes that are included in planimetry. After studying the names of geometric shapes, the student begins to study the laws of construction, to study various theorems, to prove them, to apply these proofs to other, more complex theorems. Here comes into play a phenomenon that can be called heuristic thinking based on logical constructions. The article also shows the use of Olympiads – urban and All-Russian – to further improve the development of heuristic thinking among students in order to replenish the departments of geometric profiles of universities as a result, as well as replenish our country with scientists in the direction 2.5.1 — "Descriptive geometry and computer graphics. Digital product lifecycle support." And in other areas, too.
pedagogy, teaching, descriptive geometry, computer graphics, quality of education, heuristic thinking
1. Beglov I.A. Nachertatel'naya geometriya i inzhenernaya grafika: neobhodimost' izucheniya v shkole i v vuze [Tekst] / I.A. Beglov // Sbornik trudov Vserossiyskoy nauchno-metodicheskoy konferencii po inzhenernoy geometrii i komp'yuternoy grafike. — Ch. 1. — M.: Izdvo MITHT, 2008. — S. 32–34.
2. Beglov I.A. Poverhnosti kvazivrascheniya i ih primenenie v parametricheskoy arhitekture [Tekst]: avtoref. dis. … kand. tehn. nauk: 05.01.01. / I.A. Beglov. — Omsk, 2022. — 200 s. EDN: https://elibrary.ru/EXDWCY
3. Brylkin Yu.V. Modelirovanie mikro- i nanostruktury poverhnosti dlya resheniya zadach gazovoy dinamiki i teplomassoobmena [Tekst] / Yu.V. Brylkin // Geometriya i grafika. — 2018. — T. 6. — № 2. — S. 95–100. — DOI: 10.12737/ article_5b559f018f85a7.77112269 DOI: https://doi.org/10.12737/article_5b55a695093294.45142608; EDN: https://elibrary.ru/XVRAMH
4. Bubennikov A.V. Nachertatel'naya geometriya [Tekst] / A.V. Bubennikov, M.Ya. Gromov. — M.: Vysshaya shkola, 1973. — 416 s.
5. Vinnickiy I.G. Nachertatel'naya geometriya [Tekst] / I.G. Vinnickiy. — M.: Vysshaya shkola, 1975. — 280 s.
6. Vinogradov V.N. Nachertatel'naya geometriya [Tekst] / V.N. Vinogradov. — Minsk: Vysh. shkola, 1977. — 268 s.
7. Volkova M.Yu. Graficheskaya gramotnost' inzhenera kak sposob polucheniya fundamental'nyh professional' nyh znaniy [Tekst] / M.Yu. Volkova, E.V. Egorycheva // Geometriya i grafika. — 2013. — T. 2. — № 1. — S. 53–57. DOI:https://doi.org/10.12737/3849 EDN: https://elibrary.ru/SEEIEV
8. Vol'berg O.A. Lekcii po nachertatel'noy geometrii [Tekst] / O.A. Vol'berg. — M.: Gos. uchebno-pedagogicheskoe izd-vo Ministerstva prosvescheniya RSFSR, 1947. 348 s.
9. Vyshnepol'skiy V.I. Vserossiyskie nauchno-metodicheskaya konferenciya «Problemy inzhenernoy geometrii» i seminar «“Geometriya i grafika”: itogi 2021 g.» [Tekst] / V.I. Vyshnepol'skiy, N.S. Kadykova, T.A. Vereschagina // Geometriya i grafika. — 2022. — T. 10. — № 2. —C. 35–52. — DOI:https://doi.org/10.12737/2308-4898-2022-10-2-35-52 EDN: https://elibrary.ru/AMHCAF
10. Vyshnepol'skiy V.I. Celi i metody obucheniya graficheskim disciplinam [Tekst] / V.I. Vyshnepol'skiy, N.A. Sal'kov // Geometriya i grafika. — 2013. — T. 1. № 2. — C. 8–9. — DOI:https://doi.org/10.12737/777. EDN: https://elibrary.ru/RCLFQD
11. Glagolev N.A. Nachertatel'naya geometriya [Tekst] / N.A. Glagolev. — M.-L.: ONTI NKTP SSSR, Glavnaya red. obschetehn. literatury i nomografii, 1936. 160 s.
12. Gordon V.O. Kurs nachertatel'noy geometrii [Tekst] / V.O. Gordon, M.A. Semencov-Ogievskiy. — M.: Nauka, 1977. — 268 s.
13. Grafskiy O.A. Geometriya elektrostaticheskih poley [Tekst] / O.A. Grafskiy, Yu.V. Ponomarchuk, A.A. Holodilov // Geometriya i grafika. — 2018. — T. 6. — № 1. — C. 10–19. — DOI:https://doi.org/10.12737/article_5ad085a6d75bb5.99078854 EDN: https://elibrary.ru/YWMSCG
14. Grohot-pitatel': avtorskoe svidetel'stvo 1025461 SSSR, MKI3 V 07 V 1/16 / N.A. Sal'kov (SSSR). № 3333233/29-03; zayavleno 25.06.814
15. Gumen N.S. Geometricheskie osnovy teorii mnogoobraziy evklidovogo n-prostranstva primenitel'no k geometricheskomu modelirovaniyu mnogoparametricheskih sistem [Tekst]: avtoref. dis. … d-ra tehn. nauk: 05.01.01. / N.S. Gumen — Kiev, 1992. — 24 s. EDN: https://elibrary.ru/ZJBGEJ
16. Dvuhchervyachnyy smesitel' dlya pastoobraznyh materialov: avtorskoe svidetel'stvo 1199625 SSSR, MKI4 V 29 V 7/42 / Sal'kov N.A. (SSSR). — № 3773765/23-05; zayavleno 23.07.84; opublikovano 23.12.85, Byulleten' № 47. — 3 s.
17. Dobryakov A.I. Kurs nachertatel'noy geometrii [Tekst] / A.I. Dobryakov. — M.-L.: Gos. izd-vo literatury po stroitel'stvu i arhitekture, 1952. — 496 s.
18. Egiazaryan K.T. Kvantovo-himicheskoe modelirovanie mehanizmov allilirovaniya norbornadiena v prisutstvii kompleksov palladiya [Tekst]: avtoref. dis. … kand. him. nauk: 1.4.4. / K.T. Egiazaryan. — M.: Izd-vo MIREA, 2023. — 22 s. EDN: https://elibrary.ru/GVBISZ
19. Zhiharev L.A. Geometricheskie metody optimizacii topologii konstruktivnyh elementov na osnove teorii fraktalov [Tekst]: avtoref. dis. … kand. tehn. nauk:2.5.1. / L.A. Zhiharev. –Nizhniy Novgorod: Izd-vo NNGASU, 2023. — 22 s.
20. Ivanov G.S. Nachertatel'naya geometriya [Tekst] / G.S. Ivanov. — M.: Izd-vo MGUL, 2012. — 340 s.
21. Ischenko A.A. K voprosu o neobhodimosti prepodavaniya nachertatel'noy geometrii i grafiki dlya himikov i himikov-tehnologov [Tekst] / A.A. Ischenko // Geometriya i grafika. — 2013. — T. 1. — № 2. — S. 6–7. — DOIhttps://doi.org/10.12737/776 EDN: https://elibrary.ru/RCLFPT
22. Klimuhin A.G. Nachertatel'naya geometriya [Tekst] / A.G. Klimuhin. — M.: Stroyizdat, 1978. — 334 s.
23. Kolotov S.M. Kurs nachertatel'noy geometrii [Tekst] / S.M. Kolotov [i dr.]. — Kiev: Gos. izd-vo literatury po stroitel'stvu i arhitekture USSR, 1961. — 316 s.
24. Koroev Yu.I. Nachertatel'naya geometriya [Tekst] / Yu.I. Koroev. — M.: KNORUS, 2011. — 432 s. EDN: https://elibrary.ru/QJXAAL
25. Korotkiy V.A. Nachertatel'naya geometriya: konspekt lekciy [Tekst] / V.A. Korotkiy, L.I. Hmarova, I.V. Butorina. — Chelyabinsk: Izd-vo YuUrGU, 2014. 191 s.
26. Krylov N.N. Nachertatel'naya geometriya [Tekst] / N.N. Krylov [i dr.]. — M.: Vysshaya shkola, 1977. — 231 s.
27. Krylov N.N. Nachertatel'naya geometriya [Tekst] / N.N. Krylov [i dr.]. — M.: Vysshaya shkola, 1990. — 240 s.
28. Kuznecov N.S. Nachertatel'naya geometriya [Tekst] / N.S. Kuznecov. — M.: Vysshaya shkola, 1981. — 262 s.
29. Markin L.V. Diskretnye geometricheskie modeli ocenki stepeni zatenennosti gelioenergetike [Tekst] / L.V. Markin // Geometriya i grafika. — 2019. — T. 7. — № 1. — S. 28–45. — DOI:https://doi.org/10.12737/article_5c9202d8d8 21b0. 81468033 DOI: https://doi.org/10.12737/article_5c9202d8d821b0.81468033; EDN: https://elibrary.ru/HKNWIZ
30. Mokin N.A. Chislennyy analiz deformirovaniya vozduhoopornyh obolochek pri staticheskih i dinamicheskih vozdeystviyah [Tekst]: avtoref. dis. … kand. tehn. nauk: 05.23.17 / N.A. Mokin. — M.: Izd-vo MIIT, 2019. — 22 s. EDN: https://elibrary.ru/NYVZUJ
31. Panchuk K.L. Geometricheskaya model' generacii semeystva konturno-parallel'nyh liniy dlya avtomatizirovannogo rascheta traektorii rezhuschego instrumenta [Tekst] / K.L. Panchuk, T.M. Myasoedova, I.V. Krysova // Geometriya i grafika. — 2019. — T. 7. — № 1. — S. 3–13. DOI:https://doi.org/10.12737/article_5c92012c51bba1.17153893 EDN: https://elibrary.ru/ZBHCLR
32. Peklich V.A. Nachertatel'naya geometriya [Tekst] / V.A. Peklich. — M.: Izd-vo Associacii stroitel'nyh vuzov, 2007. — 272 s. EDN: https://elibrary.ru/QJSJUH
33. P'yankova Zh.A. Formirovanie gotovnosti studentov operirovat' prostranstvennymi ob'ektami v processe izucheniya geometro-graficheskih disciplin [Tekst]: avtoref. dis. … kand. ped. nauk / Zh.A. P'yankova. — Ekaterinburg, 2015. — 31 s. EDN: https://elibrary.ru/ZPVUSP
34. Russkevich N.L. Nachertatel'naya geometriya [Tekst] / N.L. Russkevich. — Kiev: Vischa shkola, 1978. — 312 s.
35. Rynin N.A. Znachenie nachertatel'noy geometrii i sravnitel'naya ocenka glavneyshih ee metodov [Tekst] / N.A. Rynin. — Petrograd: Izd-vo Yu.N. Erlih, 1907. 96 s.
36. Sal'kov N.A. Vvedenie v kineticheskuyu geometriyu [Tekst] / N.A. Sal'kov. — M.: INFRA-M, 2016. — 142 s.
37. Sal'kov N.A. Geometricheskoe modelirovanie poverhnostey zemlyanyh sooruzheniy [Elektronnyy resurs] // Zhurnal tehnicheskih issledovaniy. — 2020. — T. 6. № 1. — S. 3–10. — URL: https://naukaru.ru/ru/nauka/ article/36439/viehttps://doi.org/10.12737/776 EDN: https://elibrary.ru/KWREZP
38. Sal'kov N.A. Geometricheskaya sostavlyayuschaya tehnicheskih innovaciy [Tekst] / N.A. Sal'kov // Geometriya i grafika. — 2018. — T. 6. — № 2. — C. 85–93. DOI: https://doi.org/10.12737/article_5b55a5163fa053.07622109; EDN: https://elibrary.ru/XVRALZ
39. Sal'kov N.A. Grafoanaliticheskoe reshenie nekotoryh chastnyh zadach kvadratichnogo programmirovaniya [Tekst] / N.A. Sal'kov // Geometriya i grafika. — 2014. T. 2. — № 1. — S. 3–8. — DOI:https://doi.org/10.12737/3842 EDN: https://elibrary.ru/SEEICD
40. Sal'kov N.A. Zachem nuzhna nachertatel'naya geometriya [Elektronnyy resurs] / N.A. Sal'kov // Zhurnal estestvenno-nauchnyh issledovaniy. — 2021. — T. 6. № 1. — S. 39–44. — URL: https://naukaru.ru/ru/nauka/ article/43279/view EDN: https://elibrary.ru/PDWNSZ
41. Sal'kov N.A. Modelirovanie avtomobil'nyh dorog [Tekst]: monografiya / N.A. Sal'kov. — M.: INFRA-M, 2012. — 120 s. EDN: https://elibrary.ru/VERUPR
42. Sal'kov N.A. Nachertatel'naya geometriya — baza dlya geometrii analiticheskoy [Tekst] / N.A. Sal'kov // Geometriya i grafika. — 2016. — T. 4. — № 1. — S. 44–54. DOI:https://doi.org/10.12737/18057 EDN: https://elibrary.ru/VSFWWV
43. Sal'kov N.A. Nachertatel'naya geometriya — baza dlya komp'yuternoy grafiki [Tekst] / N.A. Sal'kov // Geometriya i grafika. — 2016. — T. 4. — № 2. — S. 37–47. — DOIhttps://doi.org/10.12737/19832 EDN: https://elibrary.ru/WJEJOL
44. Sal'kov N.A. Nachertatel'naya geometriya: Konstruirovanie poverhnostey [Tekst] / N.A. Sal'kov. — M.: INFRA-M, 2022. — 220 s. DOI: https://doi.org/10.12737/1196545; EDN: https://elibrary.ru/TYWIIK
45. Sal'kov N.A. Nachertatel'naya geometriya — teoriya izobrazheniy [Tekst] / N.A. Sal'kov // Geometriya i grafika. 2016. — T. 4. — № 4. — S. 41–47. — DOI:https://doi.org/10.12737/22842 EDN: https://elibrary.ru/XKYHRX
46. Sal'kov N.A. Ob izobrazheniyah [Tekst] / N.A. Sal'kov // Geometriya i grafika. — 2022. — T. 10. — № 2. — S. 3–10. DOI:https://doi.org/10.12737/2308-4898-2022-10-2-3-10 EDN: https://elibrary.ru/LANGNE
47. Sal'kov N.A. O vozrastayuschey roli geometrii [Elektronnyy resurs] / N.A. Sal'kov // Zhurnal estestvenno-nauchnyh issledovaniy. — 2017. — T. 2. — № 2. S. 53–61. — URL: https://naukaru.editorum.ru/ru/nauka/ article/16413/view EDN: https://elibrary.ru/YKKGLD
48. Sal'kov N.A. Olimpiady po nachertatel'noy geometrii kak katalizator evristicheskogo myshleniya [Tekst] / N.A. Sal'kov, V.I. Vyshnepol'skiy, V.M. Aristov, V.P. Kulikov // Geometriya i grafika. 2017. — T. 5. — № 2. — S. 93–101. — DOI:https://doi.org/10.12737/article_5953f3767b1e80.12067677 EDN: https://elibrary.ru/YTYAPH
49. Sal'kov N.A. Organizaciya studencheskih predmetnyh olimpiad vysshego urovnya [Tekst] / N.A. Sal'kov, N.S. Kadykova // Geometriya i grafika. — 2013. — T. 1. № 1. — S. 80–82. — DOI:https://doi.org/10.12737/485 EDN: https://elibrary.ru/RDFXVP
50. Sal'kov N.A. Predmetnye olimpiady kak pokazatel' kachestva obucheniya [Tekst] / N.A. Sal'kov // Geometriya i grafika. — 2015. — T. 4. — № 4. — S. 45–54. DOI: https://doi.org/10.12737/17350; EDN: https://elibrary.ru/VQDUQX
51. Sal'kov N.A. Fenomen prisutstviya nachertatel'noy geometrii v drugih uchebnyh disciplinah [Tekst] / N.A. Sal'kov, N.S. Kadykova // Geometriya i grafika. 2020. — T. 8. — № 4. — S. 61–73. — DOI:https://doi.org/10.12737/23084898-2021-8-4-61-73 DOI: https://doi.org/10.12737/2308-4898-2021-8-4-61-73; EDN: https://elibrary.ru/XNZZGT
52. Sal'kov N.A. Ciklida Dyupena i ee prilozhenie [Tekst] / N.A. Sal'kov. — M.: INFRA-M, 2016. — 142 s. DOI: https://doi.org/10.12737/18824; EDN: https://elibrary.ru/WBVAGJ
53. Sal'kov N.A., Voloshinov D.V. Parabola. Svidetel'stvo o registracii programmy dlya EVM RU 2020614640. Zayavka № 2020612401 ot 04 marta 2020.
54. Sal'kov N.A., Voloshinov D.V. Giperbola. Svidetel'stvo o registracii programmy dlya EVM RU 2020616015. Zayavka № 2020612357 ot 04 marta 2020.
55. Sal'kov N.A., Voloshinov D.V. Ellips. Svidetel'stvo o registracii programmy dlya EVM RU 2020616140. Zayavka № 2020612388 ot 04 marta 2020.
56. Sposob profilirovaniya avtomobil'nyh dorog: avtorskoe svidetel'stvo 1714046 SSSR. MKI4 E 02 F 1/00 / Sal'kov N.A. (SSSR) — № 1714046 A1; zayavleno 27.04.89, opublikovano 23.02.92, Byulleten' № 7, 1992. — 6 s.
57. Stanok Sal'kovyh dlya obrabotki mnogogrannyh poverhnostey: avtorskoe svidetel'stvo 1505669 SSSR, MKI4 V 23 V 5/44 / Sal'kov N.A., Sal'kov A.V., Sal'kova V.A. (SSSR). — № 4293668/31-08; zayavleno 01.06.87; opublikovano 07.09.89, Byulleten' № 33. — 4 s.
58. Timrot E.S. Nachertatel'naya geometriya [Tekst] / E.S. Timrot. — M.: Gos. izd-vo literatury po stroitel'stvu, arhitekture i stroitel'nym materialam, 1962. — 280 s.
59. Filippov P.V. Nachertatel'naya geometriya mnogomernogo prostranstva i ee prilozheniya [Tekst] / P.V. Filippov. — L.: Izd-vo Leningradskogo un-ta, 1979. — 280 s.
60. Frolov S.A. Nachertatel'naya geometriya [Tekst] / S.A. Frolov. — M.: Mashinostroenie, 1983. — 240 s.
61. Chetveruhin N.F. Kurs nachertatel'noy geometrii [Tekst] / N.F. Chetveruhin [i dr.]. — M.: Gos. izd-vo tehniko-teoreticheskoy literatury, 1956. — 436 s.
62. Chetveruhin N.F. Nachertatel'naya geometriya [Tekst] / N.F. Chetveruhin [i dr.]. — M.: Vysshaya shkola, 1963. 420 s.
63. Scheglov G.A. O geometricheskoy interpretacii kvaternionov konusami [Tekst] / G.A. Scheglov // Geometriya i grafika. — 2022. — T. 10. — № 3. — S. 23–34. — DOI:https://doi.org/10.12737/2308-4898-2022-10-3-23-34 EDN: https://elibrary.ru/UCZODI
64. Sal’kov N.A., Ivanov G.S., Slavin R.B. Areas of existence of ruled surfaces. IOP Conf. Series: Journal of Physics: Conf. Series 1260 (2019) 072018. DOI:https://doi.org/10.1088/17426596/1260/7/072018
