On Involute and Evolute of the Curve and Curve-Surface Pair in Euclidean 3-Space
Pure and Applied Mathematics Journal
Volume 4, Issue 1-2, January 2015, Pages: 6-9
Received: Nov. 8, 2014; Accepted: Nov. 12, 2014; Published: Jan. 12, 2015
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Author
Filiz Ertem Kaya, Department of Mathematics, Faculty of Science and Arts, Nigde University, Nigde, Turkey
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Abstract
In this paper, the involute and evolute of the curve is studied in type of the curve-surface pair at first time. In additional whenβ is considered evolute and involute of the curveα, involute and evolute curve-surface pairs (called as strip) and strip of the curveαis shown as(α,M) are given with depending on the constant angleφthat is between in and in Euclidean 3-Space E^3.
Keywords
Curve-Surface Pair,Evolute, Involute.2010 Mathematics Subject Classification. 53A04, 53A05
To cite this article
Filiz Ertem Kaya, On Involute and Evolute of the Curve and Curve-Surface Pair in Euclidean 3-Space, Pure and Applied Mathematics Journal. Special Issue: Applications of Geometry. Vol. 4, No. 1-2, 2015, pp. 6-9. doi: 10.11648/j.pamj.s.2015040102.12
References
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Keles, S. Joachimsthal theorems for Manifolds [PHD], Fırat University, Turkey, (1982).
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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).
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Sabuncuoglu, A., Differential Geometry, Nobel Publications, pp: 137-144, Ankara, (2004).
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