IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i23p3077-d691253.html
   My bibliography  Save this article

Characterization of Rectifying Curves by Their Involutes and Evolutes

Author

Listed:
  • Marilena Jianu

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania)

  • Sever Achimescu

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania)

  • Leonard Dăuş

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania)

  • Adela Mihai

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania
    Interdisciplinary Doctoral School, Transilvania University of Braşov, 500036 Braşov, Romania)

  • Olimpia-Alice Roman

    (Faculty of Hydrotechnics, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania)

  • Daniel Tudor

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania)

Abstract

A rectifying curve is a twisted curve with the property that all of its rectifying planes pass through a fixed point. If this point is the origin of the Cartesian coordinate system, then the position vector of the rectifying curve always lies in the rectifying plane. A remarkable property of these curves is that the ratio between torsion and curvature is a nonconstant linear function of the arc-length parameter. In this paper, we give a new characterization of rectifying curves, namely, we prove that a curve is a rectifying curve if and only if it has a spherical involute. Consequently, rectifying curves can be constructed as evolutes of spherical twisted curves; we present an illustrative example of a rectifying curve obtained as the evolute of a spherical helix. We also express the curvature and the torsion of a rectifying spherical curve and give necessary and sufficient conditions for a curve and its involute to be both rectifying curves.

Suggested Citation

  • Marilena Jianu & Sever Achimescu & Leonard Dăuş & Adela Mihai & Olimpia-Alice Roman & Daniel Tudor, 2021. "Characterization of Rectifying Curves by Their Involutes and Evolutes," Mathematics, MDPI, vol. 9(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3077-:d:691253
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/23/3077/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/23/3077/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3077-:d:691253. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.