Some aspects of the geometry of the surfaces with the system of plane coordinate lines
In the article, the geometry of the surfaces with the system of the plane coordinate lines is investigated. The common vector formula of these surfaces is received. The formulas of the coefficients of the quadratic forms are presented too. The conditions, when of the plane coordinate lines are lin...
| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Peoples’ Friendship University of Russia (RUDN University)
2010-09-01
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| Series: | Structural Mechanics of Engineering Constructions and Buildings |
| Subjects: | |
| Online Access: | http://journals.rudn.ru/structural-mechanics/article/view/11015 |
| _version_ | 1828388763728871424 |
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| author | V N Ivanov |
| author_facet | V N Ivanov |
| author_sort | V N Ivanov |
| collection | DOAJ |
| description | In the article, the geometry of the surfaces with the system of the plane coordinate lines is investigated. The common vector formula of these surfaces is received.
The formulas of the coefficients of the quadratic forms are presented too. The conditions, when of the plane coordinate lines are lines of the principle curvatures of the surface, are received.
The subclass of the surfaces with the system of the plane coordinate lines in the normal plane of the directrix curve is investigated. The formula of the Monge's ruled surfaces is received on the base of the common formula.
The drawings of the Monge's ruled surfaces made in MathСad system are shown. |
| first_indexed | 2024-12-10T06:18:10Z |
| format | Article |
| id | doaj.art-71a3da5bf2dc457e989dbb2f07e10a0b |
| institution | Directory Open Access Journal |
| issn | 1815-5235 2587-8700 |
| language | English |
| last_indexed | 2024-12-10T06:18:10Z |
| publishDate | 2010-09-01 |
| publisher | Peoples’ Friendship University of Russia (RUDN University) |
| record_format | Article |
| series | Structural Mechanics of Engineering Constructions and Buildings |
| spelling | doaj.art-71a3da5bf2dc457e989dbb2f07e10a0b2022-12-22T01:59:24ZengPeoples’ Friendship University of Russia (RUDN University)Structural Mechanics of Engineering Constructions and Buildings1815-52352587-87002010-09-010361511014Some aspects of the geometry of the surfaces with the system of plane coordinate linesV N Ivanov0Российский университет дружбы народовIn the article, the geometry of the surfaces with the system of the plane coordinate lines is investigated. The common vector formula of these surfaces is received. The formulas of the coefficients of the quadratic forms are presented too. The conditions, when of the plane coordinate lines are lines of the principle curvatures of the surface, are received. The subclass of the surfaces with the system of the plane coordinate lines in the normal plane of the directrix curve is investigated. The formula of the Monge's ruled surfaces is received on the base of the common formula. The drawings of the Monge's ruled surfaces made in MathСad system are shown.http://journals.rudn.ru/structural-mechanics/article/view/11015поверхности с системой плоских координатных линийвекторное уравнениекоэффициенты квадратичных формлинии главных кривизннормальные поверхностирезные поверхности Монжа |
| spellingShingle | V N Ivanov Some aspects of the geometry of the surfaces with the system of plane coordinate lines Structural Mechanics of Engineering Constructions and Buildings поверхности с системой плоских координатных линий векторное уравнение коэффициенты квадратичных форм линии главных кривизн нормальные поверхности резные поверхности Монжа |
| title | Some aspects of the geometry of the surfaces with the system of plane coordinate lines |
| title_full | Some aspects of the geometry of the surfaces with the system of plane coordinate lines |
| title_fullStr | Some aspects of the geometry of the surfaces with the system of plane coordinate lines |
| title_full_unstemmed | Some aspects of the geometry of the surfaces with the system of plane coordinate lines |
| title_short | Some aspects of the geometry of the surfaces with the system of plane coordinate lines |
| title_sort | some aspects of the geometry of the surfaces with the system of plane coordinate lines |
| topic | поверхности с системой плоских координатных линий векторное уравнение коэффициенты квадратичных форм линии главных кривизн нормальные поверхности резные поверхности Монжа |
| url | http://journals.rudn.ru/structural-mechanics/article/view/11015 |
| work_keys_str_mv | AT vnivanov someaspectsofthegeometryofthesurfaceswiththesystemofplanecoordinatelines |