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The recurrence theorem of Frenet formulae

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Abstract

In this paper we generalize Frenet trihedron and we provide some other classes of trihedrons, called Frenet trihedrons of order n, n ≥ 1. Moreover we prove that those trihedrons can be defined recurrently and we emphasize their role in the study of the generalized helices of order n. As practical applications we present the influence of the recurrence theorem in some interdisciplinary domains like physics, chemistry and biology.
CREATIVE MATH. & INF.
23 (2014), No. 2, 175 - 182
Online version available at http://creative-mathematics.ubm.ro/
Print Edition: ISSN 1584 - 286X Online Edition: ISSN 1843 - 441X
The recurrence theorem of Frenet formulae
ABEL CAVAS¸I
ABSTRACT.
In this paper we generalize Frenet trihedron and we provide some other classes of trihedrons, called Frenet trihedrons of order n,n1.Moreover
we prove that those trihedrons can be defined recurrently and we emphasize their role in the study of the generalized helices of order n. As
practical applications we present the influence of the recurrence theorem in some interdisciplinary domains like physics, chemistry and biology.
Acknowledgements. Many thanks to Mrs. Teacher of Mathematics Alina-Ramona Baias, who made considerable
effort to translate and adapt this work from Romanian.
REFERENCES
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[9] Serret, J. A. Sur quelques formules relatives `a la th´eorie des courbes `a double courbure, J. de Math., 16 (1851)
[10] Uzunoglu, B., Gok, I. and Yayli, Y., A New Approach on Curves of Constant Precession, arXiv:1311.4730 [math.DG], (2013)
[11] Yayli, Y. and Saracoglu, S., Characterizations of Special Curves, arXiv:1202.0133 [math.DG], (2012)
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WEST UNIV ERSIT Y OF TI MIS¸OA RA
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE
ROMANI A
E-mail address:abel.cavasi@gmail.com
Received: 20.05.2014; In revised form: 20.10.2010; Accepted: 25.10.2014
2010 Mathematics Subject Classification. 53A04.
Key words and phrases. Frenet’s formulas, Darboux vector, recurrence theorem, helix.
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  • F Frenet
Frenet, F. (1847), Sur les courbesà double courbure, Thèse, Toulouse. Abstract in J. de Math., 17 (1852)
  • C Ramis
  • B Uzunoglu
  • Y Yayli
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