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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Mosul University
2006-12-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
| Subjects: | |
| Online Access: | https://csmj.mosuljournals.com/article_164054_46d6bf9bd2c8d4597b059d5c795cc6d0.pdf |
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| Summary: | 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> |
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| ISSN: | 1815-4816 2311-7990 |