On the Generalized Curvature
By using methods of nonstandard analysis given by <strong>Robinson, A.</strong>, and axiomatized by <strong>Nelson, E.</strong>, we try in this paper to establish the generalized curvature of a plane curve at regular points and at points infinitely close to a singular point....
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| Format: | Article |
| Language: | English |
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Mosul University
2006-12-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
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| Online Access: | https://csmj.mosuljournals.com/article_164054_46d6bf9bd2c8d4597b059d5c795cc6d0.pdf |
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| author | Tahir Ismail Ibrahim Hamad |
| author_facet | Tahir Ismail Ibrahim Hamad |
| author_sort | Tahir Ismail |
| collection | DOAJ |
| description | By using methods of nonstandard analysis given by <strong>Robinson, A.</strong>, and axiomatized by <strong>Nelson, E.</strong>, we try in this paper to establish the generalized curvature of a plane curve at regular points and at points infinitely close to a singular point. It is known that the radius of <strong>curvature</strong> of a plane curve is the limit of the radius of a circle circumscribed to a triangle <strong><em>ABC</em></strong>, where <strong><em>B</em></strong> and <strong><em>C</em></strong> are points ofinfinitely close to <strong><em>A</em></strong>. Our goal is to give a nonstandard proof of this fact. More precisely, if <strong><em>A</em></strong> is a standard point of a standard curve and <strong><em>B</em></strong>, <strong><em>C</em></strong> are points of defined by and where and are infinitesimals, we intend to calculate the quantity in the cases where <strong><em>A</em></strong> is <strong>biregular</strong>, <strong>regular</strong>, <strong>singular</strong> or <strong>singular </strong>oforder <strong><em>p.</em></strong> |
| format | Article |
| id | doaj-art-6ee93e8d7eaf44ae83323e3f21d3bc5a |
| institution | OA Journals |
| issn | 1815-4816 2311-7990 |
| language | English |
| publishDate | 2006-12-01 |
| publisher | Mosul University |
| record_format | Article |
| series | Al-Rafidain Journal of Computer Sciences and Mathematics |
| spelling | doaj-art-6ee93e8d7eaf44ae83323e3f21d3bc5a2025-08-20T02:13:19ZengMosul UniversityAl-Rafidain Journal of Computer Sciences and Mathematics1815-48162311-79902006-12-0132839810.33899/csmj.2006.164054164054On the Generalized CurvatureTahir Ismail0Ibrahim Hamad1College of Computer Sciences and Mathematics University of MosulCollege of Science University of SalahaddinBy using methods of nonstandard analysis given by <strong>Robinson, A.</strong>, and axiomatized by <strong>Nelson, E.</strong>, we try in this paper to establish the generalized curvature of a plane curve at regular points and at points infinitely close to a singular point. It is known that the radius of <strong>curvature</strong> of a plane curve is the limit of the radius of a circle circumscribed to a triangle <strong><em>ABC</em></strong>, where <strong><em>B</em></strong> and <strong><em>C</em></strong> are points ofinfinitely close to <strong><em>A</em></strong>. Our goal is to give a nonstandard proof of this fact. More precisely, if <strong><em>A</em></strong> is a standard point of a standard curve and <strong><em>B</em></strong>, <strong><em>C</em></strong> are points of defined by and where and are infinitesimals, we intend to calculate the quantity in the cases where <strong><em>A</em></strong> is <strong>biregular</strong>, <strong>regular</strong>, <strong>singular</strong> or <strong>singular </strong>oforder <strong><em>p.</em></strong>https://csmj.mosuljournals.com/article_164054_46d6bf9bd2c8d4597b059d5c795cc6d0.pdfinfinitesimalscurvaturetorsionsingularity |
| spellingShingle | Tahir Ismail Ibrahim Hamad On the Generalized Curvature Al-Rafidain Journal of Computer Sciences and Mathematics infinitesimals curvature torsion singularity |
| title | On the Generalized Curvature |
| title_full | On the Generalized Curvature |
| title_fullStr | On the Generalized Curvature |
| title_full_unstemmed | On the Generalized Curvature |
| title_short | On the Generalized Curvature |
| title_sort | on the generalized curvature |
| topic | infinitesimals curvature torsion singularity |
| url | https://csmj.mosuljournals.com/article_164054_46d6bf9bd2c8d4597b059d5c795cc6d0.pdf |
| work_keys_str_mv | AT tahirismail onthegeneralizedcurvature AT ibrahimhamad onthegeneralizedcurvature |