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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
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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.

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.2015040102.12
Page(s) 6-9
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

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).
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  • 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

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    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

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    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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  • @article{10.11648/j.pamj.s.2015040102.12,
      author = {Filiz Ertem Kaya},
      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},
      url = {https://doi.org/10.11648/j.pamj.s.2015040102.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040102.12},
      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.},
     year = {2015}
    }
    

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    AU  - Filiz Ertem Kaya
    Y1  - 2015/01/12
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    AB  - 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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