Journal
MATHEMATICS
Volume 10, Issue 18, Pages -Publisher
MDPI
DOI: 10.3390/math10183357
Keywords
Kiepert trefoil; plane curves; curvature; explicit parameterizations; intrinsic equation
Categories
Funding
- Simons Foundation [632274]
- Bulgarian Science Fund [KP-06-H22/2]
- Bulgarian Academy of Sciences
- Polish Academy of Sciences
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This article presents a comparative study of Kiepert's trefoil and its related curves, and solves some previously unsolved problems. The main goal of the paper is to characterize the general solution of the equation governing this curve's family of curves by involving elliptic functions and elastica theory.
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.
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