The Geometry of the Kiepert Trefoil

Vladimir I. Pulov (), Magdalena D. Toda, Vassil M. Vassilev and Ivaïlo M. Mladenov
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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

Mathematics, 2022, vol. 10, issue 18, 1-8

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.

Keywords: Kiepert trefoil; plane curves; curvature; explicit parameterizations; intrinsic equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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