Quadrisecant approximation of hexagonal trefoil knot

Gyo Taek Jin; Seojung Park

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arXiv · 1010.2926

Quadrisecant approximation of hexagonal trefoil knot

Gyo Taek Jin·Seojung Park

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Abstract

It is known that every nontrivial knot has at least two quadrisecants. Given a knot, we mark each intersection point of each of its quadrisecants. Replacing each subarc between two nearby marked points with a straight line segment joining them, we obtain a polygonal closed curve which we will call the quadrisecant approximation of the given knot. We show that for any hexagonal trefoil knot, there are only three quadrisecants, and the resulting quadrisecant approximation has the same knot type.

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Gyo Taek Jin, Seojung Park. 2010-10-14. Quadrisecant approximation of hexagonal trefoil knot. https://arxiv.org/abs/1010.2926

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