Dergiler / Gazi University Journal of Science / 2018 / Cilt: 31 - Sayı: 1

Directional Bertrand Curves

Sayfa
202–211
Yayın Tarihi
2018-03-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Our main result is that every space curve isa directional Bertrand curve with innite directional Bertrand mates.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:It is well known that a characteristic property of the Bertrand curve isthe existence of a linear relation between its curvature and torsion.
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Temel Bulgular & Veri:In thispaper, we propose a new method for generating Bertrand curves, whichavoids the basic restrictions.
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Sonuç & Katkı:Our main result is that every space curve isa directional Bertrand curve with innite directional Bertrand mates.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Bertrand Curves · offset · Frenet frame

Abstract

It is well known that a characteristic property of the Bertrand curve isthe existence of a linear relation between its curvature and torsion. In thispaper, we propose a new method for generating Bertrand curves, whichavoids the basic restrictions. Our main result is that every space curve isa directional Bertrand curve with innite directional Bertrand mates.

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Bu Makaleye Atıf Yap

Dede, M., Ekici, C. (2018). Directional Bertrand Curves. Gazi University Journal of Science, Cilt: 31 - Sayı: 1, 202–211. https://ajindex.com/articles/254683

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Kaynakça (2)

  1. Bloomenthal, J. 1990. Calculation of reference frames along a space curve. Graphics Gems, 1: 567-571.
  2. Choi, J.H., Kang, T.H. & Kim, Y.H. 2012. Bertrand curves in 3- dimensional space forms. Applied Mathematics and Computation, 219: 1040-1046. Ekmekci, N. & Ilarslan, K. 2001. On Bertrand curves and their characterization. Di fferential Geometry Dynamical System, 3: 17-24.