Volume 4, Issue 1-2, January 2015, Page: 1-5
Terquem Theorem with the Spherical Helix Strip
Filiz Ertem Kaya, Department of Mathematics, Faculty of Science and Arts, Nigde University, Nigde, Turkey
Received: Oct. 23, 2014;       Accepted: Oct. 25, 2014;       Published: Jan. 11, 2015
DOI: 10.11648/j.pamj.s.2015040102.11      View  3112      Downloads  188
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.
Keywords
Helix, Strip, Spherical Helix Strip, 2010 Mathematics Subject Classification. 53A04, 53A05
To cite this article
Filiz Ertem Kaya, Terquem Theorem with the Spherical Helix Strip, Pure and Applied Mathematics Journal. Special Issue: Applications of Geometry. Vol. 4, No. 1-2, 2015, pp. 1-5. doi: 10.11648/j.pamj.s.2015040102.11
Reference
[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.
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