Ruled surfaces generated by some special curves in Euclidean 3-Space
In this paper, a family of ruled surfaces generated by some special curves using a Frenet frame of that curves in Euclidean 3-space is investigated. Some important results are obtained in the case of general helices as well as slant helices. Moreover, as an application, circular general helices, sph...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2013-10-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X13000138 |
| _version_ | 1818196126115823616 |
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| author | Ahmad T. Ali Hossam S. Abdel Aziz Adel H. Sorour |
| author_facet | Ahmad T. Ali Hossam S. Abdel Aziz Adel H. Sorour |
| author_sort | Ahmad T. Ali |
| collection | DOAJ |
| description | In this paper, a family of ruled surfaces generated by some special curves using a Frenet frame of that curves in Euclidean 3-space is investigated. Some important results are obtained in the case of general helices as well as slant helices. Moreover, as an application, circular general helices, spherical general helices, Salkowski curves and circular slant helices, which illustrate the results, are provided and graphed. |
| first_indexed | 2024-12-12T01:29:07Z |
| format | Article |
| id | doaj.art-23b3f0cdedca46ffb2409bd17c991c18 |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-12-12T01:29:07Z |
| publishDate | 2013-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-23b3f0cdedca46ffb2409bd17c991c182022-12-22T00:43:01ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2013-10-0121328529410.1016/j.joems.2013.02.004Ruled surfaces generated by some special curves in Euclidean 3-SpaceAhmad T. Ali0Hossam S. Abdel Aziz1Adel H. Sorour2King Abdul Aziz University, Faculty of Science, Department of Mathematics, PO Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Sohag University, Sohag, EgyptDepartment of Mathematics, Faculty of Science, Sohag University, Sohag, EgyptIn this paper, a family of ruled surfaces generated by some special curves using a Frenet frame of that curves in Euclidean 3-space is investigated. Some important results are obtained in the case of general helices as well as slant helices. Moreover, as an application, circular general helices, spherical general helices, Salkowski curves and circular slant helices, which illustrate the results, are provided and graphed.http://www.sciencedirect.com/science/article/pii/S1110256X13000138Ruled surfacesFrenet frameGeneral helicesSlant helicesEuclidean 3-space |
| spellingShingle | Ahmad T. Ali Hossam S. Abdel Aziz Adel H. Sorour Ruled surfaces generated by some special curves in Euclidean 3-Space Journal of the Egyptian Mathematical Society Ruled surfaces Frenet frame General helices Slant helices Euclidean 3-space |
| title | Ruled surfaces generated by some special curves in Euclidean 3-Space |
| title_full | Ruled surfaces generated by some special curves in Euclidean 3-Space |
| title_fullStr | Ruled surfaces generated by some special curves in Euclidean 3-Space |
| title_full_unstemmed | Ruled surfaces generated by some special curves in Euclidean 3-Space |
| title_short | Ruled surfaces generated by some special curves in Euclidean 3-Space |
| title_sort | ruled surfaces generated by some special curves in euclidean 3 space |
| topic | Ruled surfaces Frenet frame General helices Slant helices Euclidean 3-space |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X13000138 |
| work_keys_str_mv | AT ahmadtali ruledsurfacesgeneratedbysomespecialcurvesineuclidean3space AT hossamsabdelaziz ruledsurfacesgeneratedbysomespecialcurvesineuclidean3space AT adelhsorour ruledsurfacesgeneratedbysomespecialcurvesineuclidean3space |