from 01.10.2008 until now
Russian Federation
In the first part of work was addressed mainly the issue of properties under Dupin cyclide, and given some examples of their applications: three ways of solving the problem of Apollonius using only compass and ruler, using the identified properties of Dupin cyclid. The second part of work continued with consideration of the use of property under a lie of Dupin. It is determined that the focal surface of cyclid of Dupin is degenerated in the lines and represent curves of the second order. Here under a lie can be defined conic curve and a sphere whose center lies on the focal curve. Polyconic conformity these focal curves is revealed. The article show the formation of the surface of the fourth order on the basis of defocusing curves of the second order. In this issue of the journal the reader is invited to consider the practical application of properties under a lie of Dupin for example of well known problems with on-voltage. If the first part of the work was cited only three ways of solving the problem of Apollonius, in the third part the author considers other possible mates: as at zero the size of the radius of the circle and the demon is of course great. All decisions – both known and not really based on properties of Dupin cyclide. In the course of engineering graphics, introductory tests, as they say now, drawing on architectural faculties there are tasks, dedicated to the mating arcs of circles with straight lines, and circles passing through the points in various combinations. Therefore, the proposed practical application cannot be considered far-fetched – it is based on the practical utility of method.
pairing, descriptive geometry, cyclic surfaces, canal surface, Dupin cyclide, the problem of Apollonius.
1. Anisimov N.N., Kuznecov N.S., Kirillov A.F. Cherchenie i risovanie [The drawing and painting]. Moscow, Strojizdat Publ., 1983. 368 p.
2. Argunov B.I., Balk M.B. Geometricheskie postroenija na ploskosti [The geometric construction on the plane]. Moscow, Uchpedgiz Publ., 1957. 267 p.
3. Bakel´man I.Ja. Inversija [Inversion]. Moscow, Nauka Publ., 1966.
4. Berzhe M. Geometrija [Geometry]. V. 1, V. 2. Moscow, Mir Publ., 1984.
5. Botvinnikov A.D., Vinogradov V.N., Vyshnepol´skij I.S. Cherchenie. 9 klass [Drawing. Grade 9]. Moscow, AST Publ., Astrel´ Publ., 2015.
6. Budasov B.V., Kaminskij V.P. Stroitel´noe cherchenie [Construction drawing]. Moscow, Strojizdat Publ., 1990. 464 p.
7. Vyshnepol´skij I.S., Vyshnepol´skij V.I. Cherchenie [Drawing]. Moscow, INFRA-M Publ., 2016.
8. Gil´bert D., Kon-Fossen S. Nagljadnaja geometrija [Visual geometry]. Moscow, Leningrad, Ob´edinennoe nauchnotehnicheskoe izdatel´stvo NKTP SSSR Publ., Glavnaja redakcija obshhetehnicheskoj literatury i nomografii Publ., 1936. 302 p.
9. Godik E.I., Lysjanskij V.M., Mihajlenko V.E., Ponomarev A.M. Tehnicheskoe cherchenie [Technical drawing]. Kiev, Vishha shkola Publ., 1983.
10. Gordon V.O. Cherchenie dlja ploskih i prostranstvennyh figur [For drawing of plane and solid figures]. Moscow, Gosudarstvennoe uchebno-pedagogicheskoe izdatel´stvo ministerstva prosveshhenija RSFSR Publ., 1951.
11. Zelenin E.V. Nachertatel´naja geometrija i cherchenie [Descriptive geometry and drawing]. Moscow, Gosudarstvennoe izdatel´stvo tehniko-teoreticheskoj literatury Publ., 1953. 524 p.
12. Klejn F. Vysshaja geometrija [Higher geometry]. Moscow, Leningrad, GONTI Publ., 1939. 400 p.
13. Koroev Ju.I. Cherchenie dlja stroitelej [Drawing for builders]. Moscow, KNORUS Publ., 1915. 256 p.
14. Kostovskij A.N. Geometricheskie postroenija odnim cirkulem [The geometric construction of one compass]. Moscow, Nauka Publ., 1984.
15. Krivoshapko S.N., Ivanov V.N. Jenciklopedija analiticheskih poverhnostej [Encyclopedia of analytical surfaces]. Moscow, LIBROKOM Publ., 2010. 560 p.
16. Levickij V.S. Mashinostroitel´noe cherchenie [Machine drawing]. Moscow, Vyssh. shk. Publ., 1988. 351 p.
17. Levickij V.S. O teme «Soprjazhenija» v kurse «Inzhenernaja grafika» [About "Mates" in the course "Engineering graphics"]. Sbornik nauchno-metodicheskih statej po nachertatel´noj geometrii i inzhenernoj grafike. Moscow, Vysshaja shkola Publ., 1980, pp. 44-51.
18. Lomonosov G.G. Inzhenernaja grafika [Engineering graphics]. Moscow, Nedra Publ., 1984. 287 p.
19. Mihajlenko V.E., Ponomarev A.M. Inzhenernaja grafika [Engineering graphics]. Kiev, Vishha shkola Publ., 1980. 280 p.
20. Russkevich N.L., Tkach D.I., Tkach M.N. Spravochnik po inzhenerno-tehnicheskomu chercheniju [Handbook of the engineering drawing]. Kiev, Budivel´nik Publ., 1980. 512 p.
21. Salkov N.A. Linejchatye poverhnosti [Ruled surfaces]. UkrNINTI 12.04.84, №6584 Uk-84. 106 p.
22. Salkov N.A. O racional´nom graficheskom reshenii zadach po teme "Soprjazhenija" [About rational graphical solution of problems on the subject of "Pairing"]. Sb. nauchno-metodicheskih statej po nachertatel´noj geometrii i inzh. grafike. Moscow, Vysshaja shkola Publ., 1985, I. 12, pp. 42-47
23. Salkov N.A. Svojstva ciklidy Djupena i ih primenenie. Chast´ 1 [Properties Dupin Dupin and their application. Part 1]. Geometrija i grafika [Geometry and Graphics]. 2015, V. 3, I. 1, pp. 16-25. DOI:https://doi.org/10.12737/10454.
24. Salkov N.A. Svojstva ciklidy Djupena i ih primenenie. Chast´ 2 [Properties Dupin Dupin and their application. Part 2]. Geometrija i grafika [Geometry and Graphics]. 2015, V. 3, I. 2, pp. 9-23. DOI:https://doi.org/10.12737/12164.
25. Sberegaev N.P., Gerb M.A. Kratkij spravochnik po nachertatel´noj geometrii i mashinostroitel´nomu chercheniju [A brief guide on descriptive geometry and engineering drawing]. Moscow, Leningrad, Mashinostroenie Publ., 1965. 264 p.
26. Simonin S.I. Inzhenerno-topograficheskoe cherchenie i nagljadnye izobrazhenija [Engineering and topographical drawing and descriptive image]. Moscow, Nedra Publ., 1979. 192 p.
27. Chetveruhin N.F. Proektivnaja geometrija [Projective geometry]. Moscow, Uchpedgiz Publ., 1961
28. Chumachenko G.V. Tehnicheskoe cherchenie [Technical drawing]. Moscow, KNORUS Publ., 2013. 296 p.
29. Jenciklopedija jelementarnoj matematiki. Kniga chetvertaja - Geometrija [Encyclopedia of elementary mathematics. Book four - Geometry]. Moscow, Nauka Publ., 1966. 568 p.
30. Dupin Ch. Développements de géometrié, P., 1813.
