
TL;DR
This paper proves that for certain knots, one can inscribe a trefoil knot within a smooth analytic curve by connecting six specific points on the curve, linking polynomial invariants to geometric constructions.
Contribution
It establishes the existence of a six-point inscribed trefoil knot within analytic curves representing knots with nontrivial quadratic Conway polynomial terms.
Findings
Existence of six points forming a trefoil inscribed in analytic curves.
Connection between polynomial invariants and geometric inscribed knots.
Method applicable to knots with nontrivial quadratic Conway polynomial term.
Abstract
Let be a knot type for which the quadratic term of the Conway polynomial is nontrivial, and let be an analytic -periodic function with non-vanishing derivative which parameterizes a knot of type in space. We prove that there exists a sequence of numbers so that the polygonal path obtained by cyclically connecting the points by line segments is a trefoil knot.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSurgical Sutures and Adhesives · Dupuytren's Contracture and Treatments
