Salkowski Curves and Their Modified Orthogonal Frames in $\mathbb{E}^{3}$
In this study, we examine some properties of Salkowski curves in $\mathbb{E}^{3}$. We then make sense of the angle $(nt)$ in the parametric equation of the Salkowski curves. We provide the relationship between this angle and the angle between the binormal vector and the Darboux vector of the Salkows...
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| Format: | Article |
| Language: | English |
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Naim Çağman
2022-09-01
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| Series: | Journal of New Theory |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/2525301 |
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| _version_ | 1850079855382626304 |
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| author | Mehmet Bektaş Süleyman Şenyurt Sümeyye Gür Mazlum |
| author_facet | Mehmet Bektaş Süleyman Şenyurt Sümeyye Gür Mazlum |
| author_sort | Mehmet Bektaş |
| collection | DOAJ |
| description | In this study, we examine some properties of Salkowski curves in $\mathbb{E}^{3}$. We then make sense of the angle $(nt)$ in the parametric equation of the Salkowski curves. We provide the relationship between this angle and the angle between the binormal vector and the Darboux vector of the Salkowski curves. Through this angle, we obtain the unit vector in the direction of the Darboux vector of the curve. Finally, we calculate the modified orthogonal frames with both the curvature and the torsion and give the relationships between the Frenet frame and the modified orthogonal frames of the curve. |
| format | Article |
| id | doaj-art-e4c453526ad64f68b2cd092d080e0882 |
| institution | DOAJ |
| issn | 2149-1402 |
| language | English |
| publishDate | 2022-09-01 |
| publisher | Naim Çağman |
| record_format | Article |
| series | Journal of New Theory |
| spelling | doaj-art-e4c453526ad64f68b2cd092d080e08822025-08-20T02:45:06ZengNaim ÇağmanJournal of New Theory2149-14022022-09-0140122610.53570/jnt.11405462425Salkowski Curves and Their Modified Orthogonal Frames in $\mathbb{E}^{3}$Mehmet Bektaş0https://orcid.org/0000-0002-5797-4944Süleyman Şenyurt1https://orcid.org/0000-0003-1097-5541Sümeyye Gür Mazlum2https://orcid.org/0000-0003-2471-1627FIRAT UNIVERSITYORDU UNIVERSITYGümüşhane ÜniversitesiIn this study, we examine some properties of Salkowski curves in $\mathbb{E}^{3}$. We then make sense of the angle $(nt)$ in the parametric equation of the Salkowski curves. We provide the relationship between this angle and the angle between the binormal vector and the Darboux vector of the Salkowski curves. Through this angle, we obtain the unit vector in the direction of the Darboux vector of the curve. Finally, we calculate the modified orthogonal frames with both the curvature and the torsion and give the relationships between the Frenet frame and the modified orthogonal frames of the curve.https://dergipark.org.tr/en/download/article-file/2525301salkowski curvemodified orthogonal framefrenet frame |
| spellingShingle | Mehmet Bektaş Süleyman Şenyurt Sümeyye Gür Mazlum Salkowski Curves and Their Modified Orthogonal Frames in $\mathbb{E}^{3}$ Journal of New Theory salkowski curve modified orthogonal frame frenet frame |
| title | Salkowski Curves and Their Modified Orthogonal Frames in $\mathbb{E}^{3}$ |
| title_full | Salkowski Curves and Their Modified Orthogonal Frames in $\mathbb{E}^{3}$ |
| title_fullStr | Salkowski Curves and Their Modified Orthogonal Frames in $\mathbb{E}^{3}$ |
| title_full_unstemmed | Salkowski Curves and Their Modified Orthogonal Frames in $\mathbb{E}^{3}$ |
| title_short | Salkowski Curves and Their Modified Orthogonal Frames in $\mathbb{E}^{3}$ |
| title_sort | salkowski curves and their modified orthogonal frames in mathbb e 3 |
| topic | salkowski curve modified orthogonal frame frenet frame |
| url | https://dergipark.org.tr/en/download/article-file/2525301 |
| work_keys_str_mv | AT mehmetbektas salkowskicurvesandtheirmodifiedorthogonalframesinmathbbe3 AT suleymansenyurt salkowskicurvesandtheirmodifiedorthogonalframesinmathbbe3 AT sumeyyegurmazlum salkowskicurvesandtheirmodifiedorthogonalframesinmathbbe3 |