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The recurrence theorem of Frenet formulae

January 2014

DOI:10.37193/CMI.2014.02.15

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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.

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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,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.

Acknowledgements. Many thanks to Mrs. Teacher of Mathematics Alina-Ramona Baias, who made considerable

effort to translate and adapt this work from Romanian.

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[10] Uzunoglu, B., Gok, I. and Yayli, Y., A New Approach on Curves of Constant Precession, arXiv:1311.4730 [math.DG], (2013)

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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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