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Dergiler / Konuralp Journal of Mathematics / 2016 / Volume: 4 Issue: 2

ON RECTIFYING SLANT HELICES IN EUCLIDEAN 3-SPACE

Bülent Altunkaya(Department of Mathematics, Faculty of Education, University of Ahi Evran)
Ferdağ K. Aksoyak(Department of Mathematics, Faculty of Education, University of Ahi Evran)
Levent Kula(Department of Mathematics, Faculty of Education, University of Ahi Evran)
Cahit Aytekin(Department of Mathematics, Faculty of Education, University of Ahi Evran)
Sayfa
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Yayın Tarihi
2016-10-15
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

After that, we have constructed a second order linear differential equation and by solving the equation, we have obtained a family of rectifying slant helices which lie on cones.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we study the position vector of rectifying slant helices in $E^3$.
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Temel Bulgular & Veri:First, we have found the general equations of the curvature and the torsion of rectifying slant helices.
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Sonuç & Katkı:After that, we have constructed a second order linear differential equation and by solving the equation, we have obtained a family of rectifying slant helices which lie on cones.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Rectifying Curve · Curvature · Torsion

Abstract

In this paper, we study the position vector of rectifying slant helices in $E^3$. First, we have found the general equations of the curvature and the torsion of rectifying slant helices. After that, we have constructed a second order linear differential equation and by solving the equation, we have obtained a family of rectifying slant helices which lie on cones.

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Bu Makaleye Atıf Yap

Altunkaya, B., Aksoyak, F. K., Kula, L., Aytekin, C. (2016). ON RECTIFYING SLANT HELICES IN EUCLIDEAN 3-SPACE. Konuralp Journal of Mathematics, Volume: 4 Issue: 2. https://ajindex.com/articles/1521865

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Kaynakça (10)

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  2. Chen, B. Y., When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly 110, 147-152, 2003.
  3. Chen, B. Y., Dillen, F. Rectifying curves as centrodes and extremal curves, Bull. Inst. Math. Academia Sinica 33, No. 2, 77-90, 2005.
  4. Izumiya S., Takeuchi N., New special curves and developable surfaces, Turk. J. Math. 28, 153-163, 2004.
  5. S. Izumiya, N. Takeuchi, Generic properties of helices and Bertrand curves, J. Geom. 74, 97-109, 2002.
  6. Kula, L. and Yayli, Y., On slant helix and its spherical indicatrix, Applied Mathematics and Computation, 169, 600-607, 2005.
  7. Kula, L.; Ekmekci, N. Yayl, Y. and Ilarslan, K., Characterizations of slant helices in Euclidean 3-space, Turkish J. Math. 34, no. 2, 261273, 2010.
  8. O'Neill B., Elementary Di erential Geometry, Academic Press, 2006.
  9. Struik D. J., Lectures on Classical Di erential Geometry, Dover, 1961.
  10. S. Izumiya, N. Takeuchi, Generic properties of helices and Bertrand curves, J. Geom. 74, 97-109, 2002.