employee from 01.10.2008 until now
Russian Federation
Dupin cyclide belongs to channel surfaces. These surfaces are the single known ones whose focal surfaces, i.e. surfaces consisting of point sets of centers of curvatures, have been degenerated into two confocal second order curves. In the works devoted to Dupin cyclide and published in the "Geometry and Graphics" journal, are presented various cyclides’ properties and demonstrated application of these surfaces in various industries, mostly in construction. Based on Dupin cyclides’ properties have been developed several inventions relating to drawing devices and having the opportunity to apply in various geometric constructions with the use of computer technologies. It is possible because the Dupin cyclides’ geometric properties suppose not only to create devices recognized as inventions, but also provide an opportunity to apply these properties to write programs for drawing v arious kinds of curves on a display screen: the second order curves, their equidistant in the direction of normals or tangents, as well as to perform other constructions. It should be said that in inventions belonging to technical areas, which include the drawing devices, the geometric component is always decisive. This position with the express aim of technical inventions can justify any copyright certificate of the USSR, any patent of Russia and foreign countries. Unfortunately, currently in schools geometry is not studied as a component of pupil’s intellectual horizons, that broadens his area of interests and teaches to analytical understanding the world, but as an inevitable, almost unnecessary appendage in preparation for the Unified State Examination.
Dupin cyclide, second order curves, geometry, invention, higher education.
Плавные очертания изделий привносят эстетический комфорт и прочность при их использовании. Этому способствуют плавные сопряжения при переходах от одной поверхности к другой [17]. Поэтому в различных учебниках по черчению [1; 12; 14; 15; 18–20; 32–34] рассматриваются кривые второго порядка, применяемые в настоящее время в качестве образующих для таких переходных поверхностей.
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3. Sal'kov N.A. A.s. 1299833 SSSR, MKI3 V 43 L 11/00. Kulisno-rychazhnyj parabolograf [Rocker-lever instrument for drawing parabolas]. I. 12, 2 p. (in Russian).
4. Sal'kov N.A., Sal'kov A.V. A.s. 1361024 SSSR, MKI4 V 43 L 11/00. Pribor Sal'kova dlja vosproizvedenija krivyh vtorogo porjadka [Device of Salkov for playback of the second order curves]. I. 47, 4 p. (in Russian).
5. Sal'kov N.A., Sal'kov A.V. A.s. 1375483 SSSR, MKI4 V 43 L 13/00. Chertezhnyj pribor Sal'kovyh [The drawing device of Salkov's]. I. 7, 3 p. (in Russian).
6. Sal'kov N.A. A.s. 1447706 SSSR, MKI4 V 43 L 11/00. Pribor Sal'kova dlja graficheskih postroenij [Device of Salkov for graphic creations]. I. 48, 3 p. (in Russian).
7. Sal'kov N.A. A.s. 1447709 SSSR, MKI4 V 43 L 13/00. Kulisno-rychazhnyj parabolograf N.A. Sal'kova [Rocker-lever instrument of N.A. Salkov]. I. 48, 3 p. (in Russian).
8. Sal'kov N.A. A.s. 1447710 SSSR, MKI4 V 43 L 11/00. Pribor Sal'kova dlja postroenija krivyh vtorogo porjadka [Device of Salkov to build the curves of the second order]. I. 48, 3 p. (in Russian).
9. Sal'kov N.A., Sal'kov A.V. A.s. 1458249 SSSR, MKI4 V 43 L 11/00. Chertezhnyj pribor Sal'kovyh dlja postroenija prjamyh, fiksirujushhih v prostranstve polozhenie ploskosti, kasatel'noj k trem napered zadannym okruzhnostjam [Salkov's drawing tool to draw straight, fixing in space the position of the plane tangent to three given circles in advance]. I. 6, 3 p. (in Russian).
10. Sal'kov N.A. A.s. 1519925 SSSR, MKI4 V 43 L 11/00. Chertezhnyj pribor N.A. Sal'kova [The drawing device N.A. Salkova]. I. 41, 2 p. (in Russian).
11. Sal'kov N.A. A.s. 1567413 SSSR, MKI4 V 43 L 13/00. Pribor Sal'kovyh dlja vosproizvedenija krivyh [Device of Salkov's for playback curves]. I. 20, 3 p. (in Russian).
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25. Sal'kov N.A. Svoystva tsiklid Dyupena i ikh primenenie. Chast' 1 [Properties Dupin Cyclide and their application. Part 1]. Geometriya i grafika [Geometry and Graphics]. 2015, V. 3, I. 1, pp. 16-25. (in Russian).
26. Sal'kov N.A. Svoystva tsiklid Dyupena i ikh primenenie. Chast' 2 [Properties Dupin Cyclide and their application. Part 2]. Geometriya i grafika [Geometry and Graphics]. 2015, V. 3, I. 2, pp. 9-23. (in Russian).
27. Sal'kov N.A. Svoystva tsiklid Dyupena i ikh primenenie. Chast' 3: sopryazheniya [Properties Dupin Cyclide and their application. Part 3]. Geometriya i grafika [Geometry and Graphics]. 2015, V. 3, I. 4, pp. 3-14. (in Russian).
28. Sal'kov N.A. Svoystva tsiklid Dyupena i ikh primenenie. Chast' 4: prilozheniya [Properties Dupin Cyclide and their application. Part 4]. Geometriya i grafika [Geometry and Graphics]. 2016, V. 4, I. 1, pp. 21-32. DOI:https://doi.org/10.12737/17347. (in Russian).
29. Sal'kov N.A. Tsiklida Dyupena i ee prilozhenie [Dupin Cyclide and its application]. Moscow, INFRA-M Publ., 2016. 142 p. (in Russian).
30. Sal'kov N.A. Tsiklida Dyupena i krivye vtorogo poryadka. Chast' 1 [Dupin Cyclide and second-order curves. Part 1]. Geometriya i grafika [Geometry and Graphics]. 2016, V. 4, I. 2, pp. 19-28. DOI:https://doi.org/10.12737/19829. (in Russian).
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35. Jakubovskij A.M. Issledovanija analiticheskogo metoda zadanija ciklid Djupena pri vyjavlenii ih iz kongrujencij okruzhnostej [Investigations of the analytical method for specifying Dupin cyclides when they are detected from congruences of circles]. Trudy UDN [Proceedings of UDN]. Moscow, V. 53, I. 4, 1971, pp. 26-40. (in Russian).
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