Efficient Detection of Borromean Linking in Ellipses
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866909796075044864 |
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| author | Strange, Jonathan Blair, Ryan Klotz, Alexander R. |
| author_facet | Strange, Jonathan Blair, Ryan Klotz, Alexander R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15104 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient Detection of Borromean Linking in Ellipses Strange, Jonathan Blair, Ryan Klotz, Alexander R. Geometric Topology 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. |
| title | Efficient Detection of Borromean Linking in Ellipses |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2509.15104 |