The spherical helix and the strip are respectively proved firstly by Scofield and Sabuncuoglu and Hacısalihoglu. In this paper helix strip on sphere is investigated by using characteristics of spherical helix and strip. Firstly using strip after helixand finally spherical helix. So spherical helix strips are obtained. Furhermore Joachimsthal Theorem and Terquem Theorem are investigated when the strip and helix strips which lie on the sphere and given a characterization about spherical helix strips.
| Published in |
Pure and Applied Mathematics Journal (Volume 4, Issue 1-2)
This article belongs to the Special Issue Applications of Geometry |
| DOI | 10.11648/j.pamj.s.2015040102.11 |
| Page(s) | 1-5 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2015. Published by Science Publishing Group |
Helix, Strip, Spherical Helix Strip, 2010 Mathematics Subject Classification. 53A04, 53A05
| [1] | Blaschke, W., Monatsheftefürmathematik und physik 19, pp:188-204, (1908). |
| [2] | Blaschke, W., Differential Geometria, p:41, (1908). |
| [3] | Ertem Kaya F (2010). Terquem and Joachimsthal Type Theorems in E^n [PhD] Ankara University, Pages 72-78. |
| [4] | Ertem Kaya F, Yaylı Y, Hacısalihoglu H., Harmonic Curvatures of a Strip inE^3, Commun. Fac. Sci. Univ. Ank. Series A1, Volume 59, Number 2, Pages 1-14 ISSN 1303-5991, (2010). |
| [5] | Ertem Kaya F, Yaylı Y, Hacısalihoglu H., The Conical Helix Strip in E^3., Int. Journal of Pure and App. Mathematics, Volume 66, No(2), Pages:145-156, (2011). |
| [6] | Hacısalihoglu H. H., Differential Geometry, Fasc. I, Science Faculty of Ankara University Publications, Besevler, Ankara (in Turkish). |
| [7] | Hacısalihoglu H. H., Differential Geometry, Fasc. II, Science Faculty of Ankara University Publications, Besevler, Ankara (in Turkish). |
| [8] | Hacısalihoglu H. H., On The Relations Between The Higher Curvatures Of A Curve and A Strip., Communications de la faculté des Sciences De Universitéd.AnkaraSerie A1, Tome 31, (1982). |
| [9] | Hacısalihoglu H H., Lineer Algebra, Science Faculty of Ankara University Publications, Besevler, Ankara (in Turkish), (2008). |
| [10] | Keles, S. Joachimsthal theorems for Manifolds [PHD], Fırat University, Turkey, (1982).Communications de la faculté des Sciences De Universitéd.AnkaraSerie A1, Tome 31, (1982). |
| [11] | Sabuncuoglu, A. and Hacısalihoglu H. H., Higher Curvatures of a Strip, Communications de la Faculté des Sciences De L.Universitéd.AnkaraSérie A1, Tome 24 , pp: 25-33, (1975). |
| [12] | Scofield, P. D. "Curves of Constant Precession." Amer. Math. Monthly102, 531-537, 1995. |
APA Style
Filiz Ertem Kaya. (2015). Terquem Theorem with the Spherical Helix Strip. Pure and Applied Mathematics Journal, 4(1-2), 1-5. https://doi.org/10.11648/j.pamj.s.2015040102.11
ACS Style
Filiz Ertem Kaya. Terquem Theorem with the Spherical Helix Strip. Pure Appl. Math. J. 2015, 4(1-2), 1-5. doi: 10.11648/j.pamj.s.2015040102.11
AMA Style
Filiz Ertem Kaya. Terquem Theorem with the Spherical Helix Strip. Pure Appl Math J. 2015;4(1-2):1-5. doi: 10.11648/j.pamj.s.2015040102.11
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.pamj.s.2015040102.11,
author = {Filiz Ertem Kaya},
title = {Terquem Theorem with the Spherical Helix Strip},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {1-2},
pages = {1-5},
doi = {10.11648/j.pamj.s.2015040102.11},
url = {https://doi.org/10.11648/j.pamj.s.2015040102.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040102.11},
abstract = {The spherical helix and the strip are respectively proved firstly by Scofield and Sabuncuoglu and Hacısalihoglu. In this paper helix strip on sphere is investigated by using characteristics of spherical helix and strip. Firstly using strip after helixand finally spherical helix. So spherical helix strips are obtained. Furhermore Joachimsthal Theorem and Terquem Theorem are investigated when the strip and helix strips which lie on the sphere and given a characterization about spherical helix strips.},
year = {2015}
}
TY - JOUR T1 - Terquem Theorem with the Spherical Helix Strip AU - Filiz Ertem Kaya Y1 - 2015/01/11 PY - 2015 N1 - https://doi.org/10.11648/j.pamj.s.2015040102.11 DO - 10.11648/j.pamj.s.2015040102.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 1 EP - 5 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2015040102.11 AB - The spherical helix and the strip are respectively proved firstly by Scofield and Sabuncuoglu and Hacısalihoglu. In this paper helix strip on sphere is investigated by using characteristics of spherical helix and strip. Firstly using strip after helixand finally spherical helix. So spherical helix strips are obtained. Furhermore Joachimsthal Theorem and Terquem Theorem are investigated when the strip and helix strips which lie on the sphere and given a characterization about spherical helix strips. VL - 4 IS - 1-2 ER -
Email: