General Principles for Formation of Ruled Surfaces. Part 2

N. Sal&#039;kov

doi:10.12737/article_5c9201eb1c5f06.47425839

UDC 51

GENERAL PRINCIPLES FOR FORMATION OF RULED SURFACES. PART 2 General Principles for Formation of Ruled Surfaces. Part 2

АА Аа

Published in Geometry & Graphics · Pages 14–27 · Rubric: Scientific problems of geometry

DOI: https://doi.org/10.12737/article_5c9201eb1c5f06.47425839

Received: 20.03.2019 Accepted: 08.04.2019 Published: 08.04.2019 Language of publication: RUS

Authors

N. Sal'kov

Academic degree: candidate of technical sciences

Science rang: professor

MIREA – Russian technological university Russian Federation

ABSTRACT

In this paper the consideration related to formation of ruled surfaces with a single method for their set up that was proposed in the first part of the work, is continued. In the first part of the work were considered more than twenty variants for set up of ruled surfaces, including four set ups by guide lines, overall known in the literature, for example, in the books of S.A. Frolov, A.V. Bubennikov, M.Ya. Gromov. However, the set up of ruled surfaces with the help of guide lines was proposed in a new aspect – as a constituent of a single method for setting absolutely all ruled surfaces, taking place in science and industry, and with additional variants. Besides, have been proposed equation systems, which solution leads to generation of equation for the given ruled surface. New set ups of ruled surfaces have included eighteen examples, which is the main material of the work’s first part. Also was proposed a table in which have been put all possible variants for set up of geometric figures’ guiding lines to obtain ruled surfaces. Of course, the proposed variants of guiding lines’ combination were presented in the enlarged form. In the proposed paper have been considered new, not presented before, variants for set up of ruled surfaces. Have been presented 19 examples, including the ones with one or two guiding planes, as well as when the guiding line belongs to one of guiding surfaces. Such surfaces can be considered as ruled surfaces of smooth transition. As in the first part of the work, the equation systems leading to the equation of the set ruled surface are proposed.

KEYWORDS

surfaces, ruled surfaces, geometry, descriptive geometry, surface formation.

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GOST

Sal'kov N. A. General Principles for Formation of Ruled Surfaces. Part 2 // Geometry & Graphics. 2019. no. 1. pp. 14-27. DOI: https://doi.org/10.12737/article_5c9201eb1c5f06.47425839. (Date of access 17.09.2026).

MLA

N. Sal'kov. "General Principles for Formation of Ruled Surfaces. Part 2." Geometry & Graphics 7.1 (2019): 14-27. DOI: https://doi.org/10.12737/article_5c9201eb1c5f06.47425839.

APA

Sal'kov N. A. (2019). General Principles for Formation of Ruled Surfaces. Part 2. Geometry & Graphics, 7(1), 14-27. https://doi.org/10.12737/article_5c9201eb1c5f06.47425839

Chicago

N. Sal'kov. "General Principles for Formation of Ruled Surfaces. Part 2." Geometry & Graphics 7, no. 1 (2019): 14-27. https://doi.org/10.12737/article_5c9201eb1c5f06.47425839.

WIKI

{{cite journal | author = Sal'kov N. A. | title = General Principles for Formation of Ruled Surfaces. Part 2 | journal = Geometry & Graphics | year = 2019 | volume = 7 | issue = 1 | pages = 14-27 | doi = 10.12737/article_5c9201eb1c5f06.47425839 }}

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GENERAL PRINCIPLES FOR FORMATION OF RULED SURFACES. PART 2 General Principles for Formation of Ruled Surfaces. Part 2

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