Application of Dupin Cyclide’s Properties to Inventions

N. Sal&#039;kov

doi:10.12737/article_5a17fd233418b2.84489740

UDC 51

APPLICATION OF DUPIN CYCLIDE’S PROPERTIES TO INVENTIONS Application of Dupin Cyclide’s Properties to Inventions

АА Аа

Published in Geometry & Graphics · Volume 5, Issue 4 · Pages 37–43 · Rubric: Scientific problems of geometry

DOI: https://doi.org/10.12737/article_5a17fd233418b2.84489740

Received: 24.11.2017 Accepted: 24.03.2024 Language of publication: RUS

Authors

N. Sal'kov

Academic degree: candidate of technical sciences

Science rang: professor

MIREA – Russian technological university Russian Federation

ABSTRACT

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.

KEYWORDS

Dupin cyclide, second order curves, geometry, invention, higher education.

Text

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JATS XML

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

GOST

Sal'kov N. A. Application of Dupin Cyclide’s Properties to Inventions // Geometry & Graphics. 2017. no. 4. pp. 37-43. DOI: https://doi.org/10.12737/article_5a17fd233418b2.84489740. (Date of access 24.09.2026).

MLA

N. Sal'kov. "Application of Dupin Cyclide’s Properties to Inventions." Geometry & Graphics 5.4 (2017): 37-43. DOI: https://doi.org/10.12737/article_5a17fd233418b2.84489740.

APA

Sal'kov N. A. (2017). Application of Dupin Cyclide’s Properties to Inventions. Geometry & Graphics, 5(4), 37-43. https://doi.org/10.12737/article_5a17fd233418b2.84489740

Chicago

N. Sal'kov. "Application of Dupin Cyclide’s Properties to Inventions." Geometry & Graphics 5, no. 4 (2017): 37-43. https://doi.org/10.12737/article_5a17fd233418b2.84489740.

WIKI

{{cite journal | author = Sal'kov N. A. | title = Application of Dupin Cyclide’s Properties to Inventions | journal = Geometry & Graphics | year = 2017 | volume = 5 | issue = 4 | pages = 37-43 | doi = 10.12737/article_5a17fd233418b2.84489740 }}

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APPLICATION OF DUPIN CYCLIDE’S PROPERTIES TO INVENTIONS Application of Dupin Cyclide’s Properties to Inventions

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