Efficient Detection of Borromean Linking in Ellipses

Jonathan Strange; Ryan Blair; Alexander R. Klotz

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arXiv · 2509.15104

Efficient Detection of Borromean Linking in Ellipses

Jonathan Strange·Ryan Blair·Alexander R. Klotz

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Abstract

We describe a method by which the number of intersections one ellipse makes inside the plane of another can be determined. The method is based on applying a transformation that reverts one ellipse to the unit circle, and examining the intersection points of the transformed second ellipse with the unit circle. This may be used to efficiently determine Hopf linking between two ellipses, or Borromean linking between three ellipses.

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BibTeX RIS

Jonathan Strange, Ryan Blair, Alexander R. Klotz. 2025-09-18. Efficient Detection of Borromean Linking in Ellipses. https://arxiv.org/abs/2509.15104

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