MathsAdapted from Wikipedia
Mathematicians have proved that every nontrivial "tame" knot in three-dimensional space has a straight line passing through it at four points.
Such a line is called a quadrisecant. Nontrivial rules out the unknot, a loop that can be deformed into a round circle. Tame means the knot can be represented as a finite closed polygonal chain; knots that are not tame are called wild. Erika Pannwitz first proved it for knotted polygons and smooth knots, and it was later extended to all nontrivial tame knots and links.
Sources
- Quadrisecant Wikipedia
- Alternating Quadrisecants of Knots (E. Denne) arXiv
- Wild knot Wikipedia
- Unknot Wikipedia
Adapted from Wikipedia's article Quadrisecant, first featured in its "Did you know" section, text available under CC BY-SA 4.0. Browse reworded it after checking the sources above; this fact's text is offered under the same licence.
What the wording keeps
- nontrivial knots or links only
- tame (not wild) knots only
- three-dimensional Euclidean space
Checked against its sources by an AI research agent on 4 November 2026; not yet reviewed by a person.
Changed on 4 November 2026: rewritten to keep the theorem's exact conditions, nontrivial and tame, each defined, in place of the plainer "ordinary".
Something wrong? Tell us and we will correct it. How Browse picks and checks facts: Facts.