Forming the Borromean Rings out of arbitrary polygonal unknots

  title={Forming the Borromean Rings out of arbitrary polygonal unknots},
  author={H. Howards},
  journal={arXiv: Geometric Topology},
  • H. Howards
  • Published 1 December 2013
  • Mathematics
  • arXiv: Geometric Topology
We prove the perhaps surprising result that given any three polygonal unknots in $\R^3$, then we may form the Borromean rings out of them through rigid motions of $\R^3$ applied to the individual components together with possible scaling of the components. We also prove that if at least two of the unknots are planar, then we do not need scaling. This is true even for a set of three polygonal unknots that are arbitrarily close to three circles, which themselves cannot be usedfigure to form the… Expand
1 Citations
Engaging with Elusive Connectivity and Coherence
  • 2020
Introduction Imagining the Flag of Europe otherwise? Borromean challenge to comprehension of any trinity? Requisite curvature: reconciling the Triple Helix, the Triskelion and the Borromean conditionExpand


In this paper, we show how to realize all knot (and link) types as smooth curves of constant curvature. Our proof is constructive: we build the knots with copies of a fixed finite number of "buildingExpand
Strange actions of groups on spheres
In [FS] we investigated certain topological analogs of Schottky groups, called admissible actions, and their compatibility with various structures on spheres. We constructed an action ϕ : F 2 × S 3→Expand
We prove that the Borromean Rings are the only Brunnian link of 3 or 4 components that can be built out of convex curves.
Brunnian Spheres
Brunnian Links of Five Components
  • Master’s thesis Wake Forest University
  • 2005
Links of Brunnian type
Über Verkettung
  • Sitzungsber. Bayerische Akad. Wiss., Math. Phys. Klasse 22
  • 1892