TY  - JOUR
T1  - The Geometry of Ribbons
AU  - Öztürk, Günay
AU  - Arslan, Kadri
AU  - Bulca, Betül
PY  - 2021
DA  - April
JF  - Turkish Journal of Science
JO  - TJOS
PB  - Ahmet Ocak AKDEMİR
WT  - DergiPark
SN  - 2587-0971
SP  - 36
EP  - 44
VL  - 6
IS  - 1
LA  - en
AB  - In this study, the representations of the ribbonsin the 3-dimensional Euclidean space as the developable ruledsurface are given. However, by calculating the average curvature ofthe ribbon surface, the results regarding the mean curvatureaccording to the character of the centerline were obtained. Inaddition, examples supporting these results are given.
KW  - Ruled surface
KW  - Surface reconstruction
KW  - Helical Ribbons
KW  - Serret-Frenet frame
CR  - 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.
CR  - 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.
CR  - Referans3 Bohr J and Markvorsen S. Ribbon Crystals. Plos One. 8(10), 2013, 1-7.
CR  - 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.
CR  - 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.
CR  - Referans6 Gray A. Modern Differential Geometry of Curves and Surfaces.  Boca Raton. FL, CRC Press, 1993.
CR  - Referans7 Izumiya S and Takeuchi N. New special curves and developable surfaces. Turkish Journal of Mathematics. 28(2), 2004, 153-164.
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CR  - Referans10 Kong XY and Wang ZL. Spontaneous Polarization-Induced Nanohelixes, Nanosprings, and Nanorings of Piezoelectric Nanobelts. Nano Letters. 3(12), 2003, 1625-1631.
CR  - Referans11 Özyılmaz E and Yayl\i Y. On the closed space-like developable ruled surface. Hadronic Journal. 23(4), 2000,
439-456.
CR  - Referans12 Peternell M, Pottmann H and Ravani B. On the computational geometry of ruled surfaces. Computer Aided Design.  31(1), 1999, 17-32.
CR  - 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.
CR  - 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.
UR  - https://dergipark.org.tr/en/pub/tjos/article/891720
L1  - https://dergipark.org.tr/en/download/article-file/1619971
ER  -