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Dergiler / Turkish Journal of Science / 2026 / Cilt: 6 Sayı: 1

The Geometry of Ribbons

Kadri Arslan(ULUDAĞ ÜNİVERSİTESİ)0000-0002-1440-7050
Günay Öztürk(İZMİR DEMOKRASİ ÜNİVERSİTESİ)0000-0002-1608-0354
Betül Bulca(ULUDAĞ ÜNİVERSİTESİ)0000-0001-5861-0184
Sayfa
36–44
Yayın Tarihi
2021-04-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In addition, examples supporting these results are given.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this study, the representations of the ribbons in the 3-dimensional Euclidean space as the developable ruled surface are given.
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Temel Bulgular & Veri:However, by calculating the average curvature of the ribbon surface, the results regarding the mean curvature according to the character of the centerline were obtained.
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Sonuç & Katkı:In addition, examples supporting these results are given.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Ruled surface · Surface reconstruction · Helical Ribbons

Abstract

In this study, the representations of the ribbons in the 3-dimensional Euclidean space as the developable ruled surface are given. However, by calculating the average curvature of the ribbon surface, the results regarding the mean curvature according to the character of the centerline were obtained. In addition, examples supporting these results are given.

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Bu Makaleye Atıf Yap

Arslan, K., Öztürk, G., Bulca, B. (2021). The Geometry of Ribbons. Turkish Journal of Science, Cilt: 6 Sayı: 1, 36–44. https://ajindex.com/articles/1557542

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Kaynakça (14)

  1. Referans1 Alegre P, Arslan K, Carriazo A, Murathan C and Öztürk G. Some Special Types of Developable Ruled Surface. Hacettepe Journal of Mathematics and Statics. 39(3), 2010, 319-325.
  2. Referans2 Armon S, Aharoni H, Moshe M and Sharon E. Shape selection in chiral ribbons: from seed pods to supramolecular assemblie. Soft Matter. 10, 2014, 2733-2740.
  3. Referans3 Bohr J and Markvorsen S. Ribbon Crystals. Plos One. 8(10), 2013, 1-7.
  4. Referans4 Chen BY. When does the position vector of a space curve always lie in its rectifying plane?. The American Mathematical Monthly. 110(2), 2003, 147-152.
  5. Referans5 Charrondi\`{e}re R, Descoubes F-B, Neukirch S, Romero V. Numerical modeling of inextensible elastic ribbons with curvature-based elements. Computer Methods in Applied Mechanics and Engineering. 364, 2020, 1-24.
  6. Referans6 Gray A. Modern Differential Geometry of Curves and Surfaces. Boca Raton. FL, CRC Press, 1993.
  7. Referans7 Izumiya S and Takeuchi N. New special curves and developable surfaces. Turkish Journal of Mathematics. 28(2), 2004, 153-164.
  8. Referans8 Izumiya S and Takeuchi N. Special curves and ruled surfaces. Contributions to Algebra and Geometry. 44(1), 2003, 200-212.
  9. Referans Izumiya S, Katsumi H and Yamashi T. The rectifying developable and spherical Darboux image of a space curve. Geometry and Topology of Caustics'98. 50, 1999, 137-149.
  10. Referans10 Kong XY and Wang ZL. Spontaneous Polarization-Induced Nanohelixes, Nanosprings, and Nanorings of Piezoelectric Nanobelts. Nano Letters. 3(12), 2003, 1625-1631.
  11. Referans11 Özyılmaz E and Yayl\i Y. On the closed space-like developable ruled surface. Hadronic Journal. 23(4), 2000, 439-456.
  12. Referans12 Peternell M, Pottmann H and Ravani B. On the computational geometry of ruled surfaces. Computer Aided Design. 31(1), 1999, 17-32.
  13. Referans13 S\'{a}nchez MIG, Uriel AG and Rios IG. Ruled Surfaces and Parametric Design. Congreso Internacional de Expresi\'{o}n Gr% \'{a}fica Arquitect\'{o}nica EGA 2018, Spain, 2018, 231-241.
  14. Referans14 Srivastava S, Santos A, Critchley K, Kim K-S, Podsiadlo P, Sun K, Lee J, Xu C, Lilly GD, Glotzer SC, Kotov NA. Light-Controlled Self-Assembly of Semiconductor Nanoparticles into Twisted Ribbons. Science. 327(5971), 2010, 1355-1359.