Research Article
Year 2021,
Volume: 6 Issue: 1, 36 - 44, 30.04.2021
Abstract
References
- 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.
- 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.
- Referans3 Bohr J and Markvorsen S. Ribbon Crystals. Plos One. 8(10), 2013, 1-7.
- 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.
- 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.
- Referans6 Gray A. Modern Differential Geometry of Curves and Surfaces. Boca Raton. FL, CRC Press, 1993.
- Referans7 Izumiya S and Takeuchi N. New special curves and developable surfaces. Turkish Journal of Mathematics. 28(2), 2004, 153-164.
- Referans8 Izumiya S and Takeuchi N. Special curves and ruled surfaces. Contributions to Algebra and Geometry. 44(1), 2003, 200-212.
- 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.
- Referans10 Kong XY and Wang ZL. Spontaneous Polarization-Induced Nanohelixes, Nanosprings, and Nanorings of Piezoelectric Nanobelts. Nano Letters. 3(12), 2003, 1625-1631.
- Referans11 Özyılmaz E and Yayl\i Y. On the closed space-like developable ruled surface. Hadronic Journal. 23(4), 2000, 439-456.
- Referans12 Peternell M, Pottmann H and Ravani B. On the computational geometry of ruled surfaces. Computer Aided Design. 31(1), 1999, 17-32.
- 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.
- 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.
Year 2021,
Volume: 6 Issue: 1, 36 - 44, 30.04.2021
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.
References
- 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.
- 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.
- Referans3 Bohr J and Markvorsen S. Ribbon Crystals. Plos One. 8(10), 2013, 1-7.
- 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.
- 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.
- Referans6 Gray A. Modern Differential Geometry of Curves and Surfaces. Boca Raton. FL, CRC Press, 1993.
- Referans7 Izumiya S and Takeuchi N. New special curves and developable surfaces. Turkish Journal of Mathematics. 28(2), 2004, 153-164.
- Referans8 Izumiya S and Takeuchi N. Special curves and ruled surfaces. Contributions to Algebra and Geometry. 44(1), 2003, 200-212.
- 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.
- Referans10 Kong XY and Wang ZL. Spontaneous Polarization-Induced Nanohelixes, Nanosprings, and Nanorings of Piezoelectric Nanobelts. Nano Letters. 3(12), 2003, 1625-1631.
- Referans11 Özyılmaz E and Yayl\i Y. On the closed space-like developable ruled surface. Hadronic Journal. 23(4), 2000, 439-456.
- Referans12 Peternell M, Pottmann H and Ravani B. On the computational geometry of ruled surfaces. Computer Aided Design. 31(1), 1999, 17-32.
- 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.
- 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.
There are 14 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Volume VI Issue I 2021 |
| Authors | |
| Publication Date | April 30, 2021 |
| Published in Issue | Year 2021 Volume: 6 Issue: 1 |
