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On the Generalized Curvature | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 8, Volume 3, Issue 2, 2006, Pages 83-98 PDF (506.27 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2006.164054 | ||
| Authors | ||
| Tahir H. Ismail1; Ibrahim O. Hamad2 | ||
| 1College of Computer Sciences and Mathematics University of Mosul | ||
| 2College of Science University of Salahaddin | ||
| Abstract | ||
| By using methods of nonstandard analysis given by Robinson, A., and axiomatized by Nelson, E., 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 curvature of a plane curve is the limit of the radius of a circle circumscribed to a triangle ABC, where B and C are points ofinfinitely close to A. Our goal is to give a nonstandard proof of this fact. More precisely, if A is a standard point of a standard curve and B, C are points of defined by and where and are infinitesimals, we intend to calculate the quantity in the cases where A is biregular, regular, singular or singular oforder p. | ||
| Keywords | ||
| infinitesimals; curvature; torsion; singularity | ||
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