### On Involute and Evolute of the Curve and Curve-Surface Pair in Euclidean 3-Space

Received: 8 November 2014     Accepted: 12 November 2014     Published: 12 January 2015
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

References
 [1] 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). [2] Keles, S. Joachimsthal theorems for Manifolds [PHD], Fırat University, Turkey, (1982). [3] 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). [4] Sabuncuoglu, A., Differential Geometry, Nobel Publications, pp: 137-144, Ankara, (2004).
• APA Style

Filiz Ertem Kaya. (2015). On Involute and Evolute of the Curve and Curve-Surface Pair in Euclidean 3-Space. Pure and Applied Mathematics Journal, 4(1-2), 6-9. https://doi.org/10.11648/j.pamj.s.2015040102.12

ACS Style

Filiz Ertem Kaya. On Involute and Evolute of the Curve and Curve-Surface Pair in Euclidean 3-Space. Pure Appl. Math. J. 2015, 4(1-2), 6-9. doi: 10.11648/j.pamj.s.2015040102.12

AMA Style

Filiz Ertem Kaya. On Involute and Evolute of the Curve and Curve-Surface Pair in Euclidean 3-Space. Pure Appl Math J. 2015;4(1-2):6-9. doi: 10.11648/j.pamj.s.2015040102.12

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title = {On Involute and Evolute of the Curve and Curve-Surface Pair in Euclidean 3-Space},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {1-2},
pages = {6-9},
doi = {10.11648/j.pamj.s.2015040102.12},
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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.},
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Author Information
• Department of Mathematics, Faculty of Science and Arts, Nigde University, Nigde, Turkey

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