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The Geometry of the Kiepert Trefoil

Author

Listed:
  • Vladimir I. Pulov

    (Department of Mathematics and Physics, Technical University of Varna, Studentska Str. 1, 9010 Varna, Bulgaria)

  • Magdalena D. Toda

    (Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79401, USA)

  • Vassil M. Vassilev

    (Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria)

  • Ivaïlo M. Mladenov

    (Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria)

Abstract

This article presents a comparative study of Kiepert’s trefoil and its related curves, combining a variety of tools from differential and algebraic geometry, integrable systems, elastica theory, and special functions. While this curve was classically known and well studied in the literature, some related open problems were recently solved, and the goal of this paper is to present and characterize the general solution of the equation that governs this trefoil’s family of curves by involving elliptic functions and elastica theory in the mechanics.

Suggested Citation

  • Vladimir I. Pulov & Magdalena D. Toda & Vassil M. Vassilev & Ivaïlo M. Mladenov, 2022. "The Geometry of the Kiepert Trefoil," Mathematics, MDPI, vol. 10(18), pages 1-8, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3357-:d:916112
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